Colonization of a smooth surface by Pseudomanas aeruginosa : image analysis methods by Andreas R Escher A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering Montana State University © Copyright by Andreas R Escher (1986) Abstract: Primary adsorption of bacteria to a clean substratum has generally been described by measuring net accumulation. Thus, the independent processes that contribute to the overall accumulation of biofilm, such as adsorption, desorption, cell multiplication, and erosion, cannot be considered separately to help to elucidate mechanisms of early colonization. With the use of image analysis techniques and additional software, these individual processes at the substratum in a continuous flow system have been measured directly. Additional parameters, such as cell movement and direction, orientation of the colony forming units (CFU), spatial distribution at the surface, and shape are also quantified with this technique. With the continuous flow system, the influences of operational parameters such as fluid shear stress, the bulk properties of the fluid, and the characteristic of the substratum can also be delineated in a fundamental manner. Two experimental variables, bulk CFU concentration and shear stress have been used to investigate early colonization under different conditions and to determine the rate controlling factor in biomass accumulation. In addition, a novel method for quantitative analysis of spatial distribution has been developed. It was found that adsorption and desorption rates are independent of the surface concentration whereas growth and surface related processes are independent of bulk concentrations. At low surface concentration, P. aeruginosa tend to adsorb randomly. With increase in surface concentration the spatial distribution of adsorbing CFU becomes uniform indicating a formation of a repulsing area around adsorbed cells.  COLONIZATION OF A SMOOTH SURFACE BY PSEUDOMONAS AERUGINOSA: IMAGE ANALYSIS METHODS by Andreas R. Escher A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering Montana State University Bozeman, Montana December 1986 i D37% i - v s / f p ii APPROVAL of thesis submitted by Andreas R- Escher This thesis has been read by each member of the thesis committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and is ready for submission to the College of Graduate Studies. z Date Chairperson, Graduate Committee Approved for the Major Department Date r Approved for the College of Graduate Studies Date Graduate Dean ill STATEMENT OF PERMISSION TO USE In presenting this thesis in partial fulfillment of the requirements for a doctoral degree at Montana State University, I agree that the Library shall make it available to borrowers under the rule of the Library. I further agree that copying of the thesis is allowable only for scholarly purposes, consistent with "fair use" as prescribed in the U.S. Copyright Law. Requests for extensive copying or reproduction of this thesis should be referred to University Microfilms International, 300 North Zeeb Road, Ann Arbor, Michigan 48106, to whom I have granted "the right to reproduce and distribute copies of the dissertation in and from microfilm and the right to reproduce and distribute by abstract in any format." Date: / 2 / Z 2 / Signature: TABLE OF CONTENTS Page LIST OF TABLES ........................................ . vii LIST OF FIGURES ..................... viii ABSTRACT.................... I ................. . . . . xii INTRODUCTION .......................................... I Relevance o£ Blofilma........... . I Previous Research . -.............. 3 Goal of Research.................... 5 Objectives of Research . . . . G BACKGROUND ...................................... 7 Process Analysis . . . . . . . . ........ . . . . 7 Transport ...................... 10 Transport and Adsorption to the Substratum . . 11 Diffusivity .................. . . . . . 11 Transport Rate to the Substratum . . . . 13 Assay for Substratum Properties.......... 14 Growth-Related Processes . ................... 16 Spatial Distribution . 18 Fluid Dynamics...................... 19 Turbulent F l o w ................................ 19 Laminar F l o w .................................. 21 CONCEPTUAL MODEL OF SURFACE COLONIZATION .............. 23 Population Balance in Terms of C F U ................ 23 Transport . . . . . 23 Adsorption........................ 25 • Reversible versus Irreversible Adsorption . . 25 Desorption .................... 27 CFU-Separation ...................... 28 Other Processes at the Substratum............ 28 Population Balance in Terms of Cells ............ 29 Multiplication and Erosion .................. 29 Kinetic Expressions in Terms of CFU '. . . ............ 30 Transport from Bulk Flow to Substratum . . . . 31 Population Balance at Substratum . . 34 Kinetic Expressions in Terms of Cells ............ 37 Transport from Bulk to Substratum . . . . . . 38 Population Balance at Substratum ............ 39 Sticking Efficiency .............................. 42 Summary of the Conceptual Model ........ . . . . . 43 Table o£ Contents (continued) EXPERIMENTAL SYSTEM AND METHODS . . . . . . . 44 Experimental System .............................. 44 Image Analyzer............ 46 Modification of the Programs...................... 47 Data Collection and Analysis...................... 48 Image Collection . . 48 Fixpoint Calculation ........................ 50 Image Analysis................................ 50 Data Assembly................................ 51 Method of Analysis and Chemostat Operation . . . . 54 Direct Cell C o u n t .................... 54 Cell Size Distribution ............ 55 Mounting of Capillary Tube ..................... 56 Chemostat Operation .............................. 56 RESULTS .................... 58 Progression of Experiments . . . . . . . . . . . . 58 Kinetic Results ................ . . . . . . . . . 63 Directly Measured Results ............. . . . 63 Derived R e s u l t s ............. 74 Behavioral Distribution ^ ...........78 Residence Time . . . . . . . . . . . 79 Orientation of CFU During Adsorption . . . . . 81 Motility at Substratum . . . . . . 82 Cell Number per CFU . .................. 85 Spatial Distribution of CFU during Adsorption . . . 85 DISCUSSION .................................... . . . . . 89 Sorption-Related Processes ...................... 89 Offset Time of Desorption............ 95 Growth Related Processes ........................ 96 CFU-Separation . . . . . . . . . . 96 Multiplication Rates ........................ 97 Erosion . ..................................... 98 Summary of Kinetic Results ...................... 100 Simulation with the Kinetic Results . . . . . 102 Spatial Distribution ............................ 105 CONCLUSION............................................. 108 NOMENCLATURE/SYMBOLS'. ............................ 109 Nomenclature..................................... H O Symbols .................................... Ill v ed) Page LITERATURE CITED 113 Vi Table o£ Contents (continued) APPENDICES........................................ 117 APPENDIX A ...................................... .. THEORY OF SPATIAL DISTRIBUTION . . .......... 118' SPATIAL DISTRIBUTION ......................... 119 No Influence.......................... 120 Positive Influence . .................... 120 Negative Influence . .................... 120 THEORY OF QUANTITATIVE SPATIAL DISTRIBUTION . 121 Spatial Interaction Indices ............. 122 Relative Nearest Neighbor Distance . 122 Relative Influence Number . . . . . 124 CALIBRATION OF SPATIAL DISTRIBUTION . . . . . 125 TEST OF THE SPATIAL DISTRIBUTION............. 131 Uniform Test Distribution ............... 132 Aggregated Test Distribution 1........ 133 Aggregated Test Distribution 2........ 135 Conclusion of the Test Distributions . . 137 APPENDIX B .................. •................ . 139 ORGANIZATION OF DATA FILES................... 139 Data Organization.................... 140 APPENDIX C . . . 144 TABLES OF DIRECTLY MEASURED RESULTS . .........144 APPENDIX D ........................................ 160 FIGURES OF KINETIC RESULTS . . . . 160 APPENDIX E . ...................................... 191 TABLES OF DERIVED RESULTS . . . . . . . . . . 191 APPENDIX F .......................... . . . . . . 200 DISTRIBUTIONS OF "BEHAVIORAL" CHARACTERISTICS 200 APPENDIX G ............................. 215 . RESULTS OF SPATIAL DISTRIBUTIONS ............ 215 Page n] on vii 1. Summary o£ directly measured rates at 0.5 N m""2 shear stress........................................ 67 2. Summary of directly measured rates at 0.75 and 1.0 N m™2................. 68 3. Summary of directly measured rates at 1.25 N m-2. . 69 4. Summary of derived rates calculated for 0.5 N m"2. 74 5. Summary of derived rates calculated for 0.75 N m-2.......................................... 75 Summary of derived rates calculated for 1.0 N m~2. 75 Summary of derived rates calculated for 1.25 N m "2................. 75 8. Residence time probability for reversibly adsorbed CFU under different shear stresses. . . . . . . . . 94 9. Directly measured results of series AAl. . ........ 145 10. Directly measured results of series AA2. . . . . . 146 11. Directly measured results of series AA3............. 147 12. Directly measured results of series AA4............. 148 13. Directly measured results of series ABl. . . . . . 149 14. Directly measured results of series AB2........... 150 15. Directly measured results of series AB3............. 151 16. Directly measured results of series AB4............. 152 17. Directly measured results of series AB5. ........ 153 18. Directly measured results of series AB6............. 154 19. Directly measured results of series ACl............. 155 20. Directly measured results of series AC2............. 156 21. Directly measured results of series AC3J ........ 157 22. Directly measured results of series AC4............. 158 23. Directly measured results of series AC5............. 159 24. Derived results of series AAl. ................. . 192 25. Derived results of series AA2............. 192 26. Derived results of series, AA3............. 193 27. Derived results of series AA4..................... 193 28. Derived results of series ABl....................... 194 29. Derived results of series AB2.- 194 30. Derived results of series AB3. . 195 31. Derived results of series AB4. . . . . . . 195 32. Derived results of series AB5........... 196 33. Derived results of series AB6. .................... 196 34. Derived results of series ACl. 197 35. Derived results of series AC2..................... 197 36. Derived results of series AC3....................... 198 37. Derived results of series AC4..................... 198 38. Derived results of series AC5....................... 199 LIST OF TABLES Table Page N) H viii Experimental data from Powell and Slater (1983) . . 4 Definition of processes during early colonization of a substratum. . ............................... 8 3. Schematic of the system. 45 4. Tracking Image. 1.0 N m™2 , IOe- cells/ml........ 49 5. Tracking Image: 0.5 N m~2 , !.I-IOs CFU ml-"1 . . . . 59 6. Tracking Image: 0.5 N m™2, IO-IOs CFU ml"1 . . . . 60 7. Tracking Image: 1.25 N m”2, 12.2-10® CFU ml"1 . . . 61 8. Typical progression of colonization .............. 64 9. Adsorption rates plotted against cell concentration in the bulk f l o w .................. 70 10. Desorption rates plotted against cell concentration.................................... 71 11. CFU-separation as a first order rate plotted against cell concentration . ....................... 72 12. First order rate coefficient for cell multiplication (12a) and cell erosion (12b) . . . . 73 13. Correlation between desorption and adsorption at 0.5 N/m2 .......................................... 76 14. Correlation between erosion and multiplication at 0.5 N/m2 . ......................................... 76 15. Correlation between offset time and bulk CFU concentration .................................... 77 16. Residence time distribution Series AA (0.5 N m”2) . 80 17. Orientation of adsorbing CFU . . . . . 82 18. Integrated movement at substratum ................ 83 19. Cells per CFU (Series AA) .......................... 84 20. Spatial distribution of adsorbing CFU ............ 88 21. Sticking efficiency $ .............................. 90 22. Surface-particle capture factor € for CFU . . . . . 92 23. Surface-particle capture factor € for cells . . . . 92 24. Probability of desorption of C F U ........ 93 25. Probability of desorption in terms of cell . . . . 93 26. Comparison of residence time of reversibly1 adsorbed CFU as a function of shear stress . . . . 94 27. CFU-separation rates ............................ 97 28. Multiplication rates of cells............ 99 29. Erosion rates of cells within colonies .......... 99 30. Probability of erosion of cells................. 100 31. Simulation of accumulation of cells under constant shear s t r e s s ................ 103 32. Simulation of accumulation of cells under constant CFU concentration.................... 104 LIST OF FIGURES Figure Page Figure Page 33. Example of a true random distribution for calibration . ...................................... 127 34. Example of a uniform distribution for calibration . 127 35. Example of aggregated distribution for calibration 128 35. Frequency contour plot of the calibration distributions . ................................ . . 129 36. Frequency contour plot (Figure 35) displayed in linear scaling ................................... 130 37. Example of a uniform test distribution........... 132 38. Frequency contour plot of the uniform test distribution .................................... 133 39. Example of aggregated test distribution I ......... 134 40. Frequency contour plot of aggregated test distribution I ................................... 135 41. Example of aggregated test distribution 2 . . . . . 136 42. Frequency contour plot of aggregated test distribution 2 ............. .................... 137 43. Progression of colonization (Series AM) in terms of CFU (a) and area coverage (b)..................161 44. Progression in terms of cells (Series AM) . . . . 162 45. Progression of colonization (Series AA2) in terms of CFU (a) and area coverage ( b ) ................. 163 46. Progression in terms of cells (Series AA2) . . . . 164 47. Progression of colonization (Series AA3) in terms of CFU (a) and area coverage (b) ................ 165 48. Progression in terms of cells (Series AA3) . . . . 166 49. Progression of colonization (Series AA4) in terms of CFU (a) and area coverage ( b ) .......... .. 167 50. Progression in terms of cells (Series AA4) . . . . 168 51. Progression of colonization (Series ABl) in terms of CFU (a) and area coverage (b) ................. 169 52. Progression in terms of cells (Series ABl) . . . . 170 53. Progression of colonization (Series AB2) in terms of CFU (a) and area coverage (b) .................171 54. Progression in terms of cells (Series AB2) . . . . 172 55. Progression of colonization (Series AB3) in terms of CFU (a) and area coverage ( b ) ................ 173 56. Progression in terms of cells (Series AB3) . . . . . 174 57. Progression of colonization (Series AB4) in terms of CFU (a) and area coverage ( b ) ................ 175 58. Progression in terms of cells (Series AB4) . . . ,. 176 59. Progression of colonization (Series AB5) in terms of CFU (a) and area coverage (b) . . . . . . . . . 177 60. Progression in terms of cells (Series AB5) . . . . 178 61. Progression of colonization (Series AB6) in terms of CFU (a) and area coverage ( b ) ................ 179 ix List of Figures (continued) XFigure Page 62. Progression in terms of cells (Series AB6) . . . . 180 S3. Progression of colonization (Series ACl) in terms of CFU (a) and area coverage (b) ............ 181 64. Progression in terms of cells (Series ACl) . . . . 182 65. Progression of colonization (Series AC2) in terms of CFU (a) and area coverage (b) . . . . . . . . . 183 66. Progression in terms of ceils (Series AC2) . . . . 184 67. Progression of colonization (Series AC3) in terms of CFU (a) and area coverage ( b ) ............ 185 68. Progression in terms of cells (Series AC3J . . . . 186 69. Progression of colonization (Series AC4) in terms of CFU (a) and area coverage ( b ) ............ 187 70. Progression in terms of cells (Series AC4) . . . . 188 71. Progression of colonization (Series AC5) in terms of CFU (a) and area coverage (b) 189 72. Progression in terms of cells (Series AC5) . . . . 190 73. Residence time distribution Series AA (0.5 N m™-8 ) . 201 74. Residence time distribution (0.75 N m-2 ) .... 202 75. Residence time distribution (1.0 N m"2 ) ...... 203 76. Residence time distribution (1.25 N m""2 ) . . . . . 204 77. Orientation of CFU after adsorption. Shear, stress: 0.5 N/m2 ................................. 205 78. Orientation of CFU after adsorption. Shear stress: 0.75 N/m2 ................................. 205 79. Orientation of CFU after adsorption. Shear stress: 1.0 N/m2 ................................. 206 80. Orientation of CFU after adsorption. Shear stress: 1.25 N/m2 ................................. 206 SI. Integrated movement at substratum (Series AA, 0.5 N m--2 > ...................... ,...............207 82. Integrated movement at substratum (0.75 N m-"2 ) . . 208 83. Integrated movement at substratum (1.0 N m"-2 ) . . . 209 84. Integrated movement at substratum (1.25 N m"2) . . 210 85. Cells per CFU (Series AAr 0.5 N m™2 ) 211 86. Cells per CFU ( 0.75 N, m"2 ) .............. 212 87. Cells per CFU ( I .0 N m"2 ) 213 88. Cells per CFU ( 1.25 N m~-2> .............. 214 89. Spatial distribution of adsorbing CFUr Series AAl . 216 90. Spatial distribution of adsorbing CFUr Series AB3 . 217 91. Spatial distribution of adsorbing CFU, Series AA4 . 218 92. Spatial distribution of adsorbing CFUr Series AB2 . 219 93. Spatial distribution of adsorbing CFUr Series AA3 . 220 94. Spatial distribution of adsorbing CFUr Series AC2 . 221' 95. Spatial distribution of adsorbing CFU, Series ACl . 222 96. Spatial distribution of adsorbing CFUr Series ABl . 223 97. Spatial distribution of adsorbing CFUr Series AA2 . 224 List of Figures (continued) xi List of Figures (continued) Figure 98. Spatial distribution of adsorbing CFU, Series AB4 Page 225 99. Spatial distribution of adsorbing CFU, Series AC3 226 100. Spatial distribution distribution of adsorbing CFU, Series AB5 227 101 . Spatial of adsorbing CFU, Series AC4 228 102. Spatial distribution of adsorbing CFU, Series ABG 229 103. Spatial distribution of adsorbing CFU, Series AC5 230 xii ABSTRACT Primary adsorption of bacteria to a clean substratum has generally been described by measuring net accumulation. Thus, the independent processes that contribute to the overall accumulation of biofilm, such as adsorption, desorption, cell multiplication, and erosion, cannot be considered separately to help to elucidate mechanisms of early colonization. ■ With the use of image analysis techniques and additional software, these individual processes at the substratum in a continuous flow system have been measured directly. Additional parameters, such as cell movement and direction, orientation of the colony forming units (CFU), spatial distribution at the surface, and shape are also quantified with this technique. With the continuous flow system, . the influences of operational parameters such as fluid shear stress, the bulk properties of the fluid, and the characteristic of the substratum can also be delineated in a fundamental manner. Two experimental variables, bulk CFU concentration . and shear stress have been used to investigate early colonization under different conditions and to determine the rate controlling factor in biomass accumulation. In addition, a novel method for quantitative analysis of spatial distribution has been developed. It was found that adsorption and desorption rates are independent of the surface concentration whereas growth and surface related processes are independent of bulk concentrations. At low surface concentration, P. aeruginosa tend to adsorb randomly. With increase in surface concentration the spatial distribution of adsorbing CFU becomes uniform indicating a formation of a repulsing area around adsorbed cells. IINTRODUCTION Microbial cells attach f irmly to almost any surface submerged in aquatic environments. The immobilized cells grow, reproduce, and produce extracellular polymers which extend from the cell forming a matrix of molecular fibers which provide structure to the assemblage termed a biofilm. Biofilms are sometimes distributed relatively evenly over the wetted surface . and other times are quite "patchy" in appearance. Biofilms can consist of a monolayer of cells covering only a fraction of the substratum or can be 300- 400 mm thick as observed in algal mats. Biofilms are generally heterogenous, frequently containing more than one distinct microbial environment. For example, biofilms with aerobic as well as anaerobic environments are frequently observed. Consequently, the term biofilm does not necessarily reflect a surface accumulation which is uniform in time and/or space. Relevance of Biofilms Biofilms serve beneficial purposes in the natural environment as well as in some modulated or engineered biological systems. Biofilms are responsible for removal of 2contaminants from natural streams and in wastewater treatment plants. Biofilms in natural waters frequently control water quality by influencing dissolved oxygen levels and serve as a sink for many toxic and/or hazardous materials. Blofilm reactors are used in some common fermentation processes (e.g. "guick" vinegar process) and are being considered more frequently for biotechnological applications. On the negative side biofilms result in fouling. Fouling is the accumulation of a deposit on equipment surfaces which result in decreased performance and/or reduced equipment lifetime. Biofilms have been observed to increase fluid, frictional resistance in water conduits and on ship hull surfaces. Microbial (as opposed to macrobial) films can significantly increase drag of a ship. Biofilm accumulation in pipes has been observed to reduce the flow rate by as much as 50% even when the film thickness was 0.1% of the pipe diameter (Characklis, 1973). Biofouling deposits decrease heat transfer in power plant condensers on shipboard as well as in land based power plants (Turakhia and Characklis, 1984). As a result, the power plant consumes more fuel to produce the same amount of power. The accumulation of biofilms has also been linked with accelerated corrosion of metallic surfaces, deterioration of 3wooden structures, and degradation of concrete structures. Reduced performance may be observed in many other ways. For a better understanding of biofilma it is essential not only to study fully developed biofilms but also the mechanisms of the buildup, i.e. the early colonization of surfaces.by bacteria, the separation between adsorption and desorption, and between other, growth related processes. Previous Research Much of the emphasis on adsorption of microbial cells has concentrated on biological and chemical aspects of mechanisms with little emphasis on physical factors in the environment or concern about the rate of adsorption. Nor has much consideration been given to the influence of the initial events on the extent of subsequent biofilm accumulation or the biofilm composition. In most, if not all reported research on microbial cell adsorption, net cell accumulation at the substratum is observed (Figure I). Most of the microbial adsorption research has been conducted in quiescent (i.e., fluid velocity equals zero), closed (i.e., no input or output flows) systems. Such systems create a significant number of 42500 2 000 Time (min) Figure I. Experimental data from Powell and Slater (1983) for adsorption of Bacillus cereus to the surface of clean glass at a shear stress of 0.075 N m--1 and temperature of 53* C. The straight line represents the theoretical adsorption rate for non-motile cells calculated from Bowen et aI. (1979). experimental artifacts leading to rate data which are irrelevant to environmental and/or technical applications. Thus, open, continuous flow experimental systems will be described. The initial events in the accumulation of cells at the substratum consist of the following steps, each occurring with a characteristic rate: I- Transport of the cell from the liquid phase to the substratum. 52. Cell adsorption to the substratum, a direct substratum-partide interaction. 3. Desorption of some of the adsorbed cells and ,their reentrainment in the liquid phase. 4. In some cases, microbial reproduction may contribute to the initial events. These processes occur either in parallel or in series and, thus, the overall rate of cell accumulation at the substratum will be determined by the combination of the different rates. Variables such as fluid shear stress. liquid phase cell density. and nutrient concentration influence each individual process rate to a different extent and, therefore, influence net cell accumulation. Consequently, the process for cell accumulation in a tube enclosing turbulent flow will be very different from the one for a glass slide immersed in quiescent water, even though the net rate of accumulation may appear to be equal in both cases. Therefore, a closer look at each process is essential to develop a useful, predictive model for cell adsorption. Goal of Research The goal of the research is to determine the influence of different independent parameters, such as fluid dynamics. 6biomass concentration in the bulk flow, surface characteristics (interface free energy), and cell physiology on early colonization of surfaces. Objectives of Research The specific objectives of the research related to early colonization of substrata are as follows: 1. Develop a method to directly measure the rate of different processes contributing to colonization. 2. Develop a method to observe individual “behavioral" •L characteristics of the organisms at the substratum for elucidating mechanisms contributing to early colonization of surfaces. 3. Derive a mathematical model describing the accumulation of biomass during the early stage of biofilms accumulation. ± "Behavioral" characteristics include all the characteristics which can be observed but are not part of the kinetic system, such as shape, orientation, gliding at, the substratum, and more. 7BACKGROUND Process Analysis During the early events of fouling, biomass can be expressed as colony forming units (CFU), or, cells. This distinction is essential since cells can adsorb in groups or as single cells. Moreover, not all the cells accumulate at the surface through transport alone. Cells can be produced at the substratum (growth), the number of cells per colony can change with time, or cells may glide away from their colony of origin to form a new colony. The following four processes must be distinguished (Figure 2) in terms of CFU: Transport: This process is responsible for carrying the CFU to a point adjacent to the substratum. This step does not include the adsorption process. Adsorption: This process is defined as the linking of the CFU with the substratum. The cell is adsorbed to the substratum only if it has a linkage to it and, hence, becomes immobilized for a finite time. Desorption: Desorption is the breaking of the linkage of the CFU and its complete removal from the substratum. Desorption is the reverse of adsorption. CFU - Separation: A CFU with more than one cell can split into two independent CFU. This process forms a new CFU at the substratum and, hence, contributes to the accumulation of CFU at the substratum. CFU-separation is a growth related process. 8T R A N S P O R T A D S O R P T I O N Xp MU L T I P L I C A T I O N E R O S I O N C P U - S E P A R A T I O N D E S O R P T I O N /m,S Figure 2. Definition of processes during early colonization of a substratum. 9These four processes can be expressed in terms of cells by using the number of cells in each individual CFU. However, CFU - separation does not contribute to the accumulation in terms of cells. Two additional processes can be defined (after transport, adsorption, and desorption) when cell accumulation is considered: Multiplication: Multiplication is related to cellular growth,, but only refers to those daughter cells which remain within the same CFU. Cells within a CFU multiply and increase the number of cells within this CFU. This does not change the accumulated number of CFU but does change the accumulated number of cells. CFU - Erosion: Cells within a CFU can "detach" and, hence, reduce the cell number of the CFU. This process is the reverse of multiplication. Therefore, processes of early colonization can be separated into sorption- and growth-related which then can be expressed as rates. With these rates, mass balances for accumulation both in terms of CFU and cells can be accomplished: d CFU dt + Kjads Kj +des K 2.1sep Accumulation CFU Adsorption CFU Desorption CFU Separation CFU 10 d cell Kj +desdt T tx .ads m^ul Kero Accumu­ lation cells Adsorption cells Desorption cells Multipli­ cation cells Erosion cells Equatiorts 2.1 and 2.2 demonstrate the importance of measuring the different process rates for a better understanding of surface colonization mechanisms, since they reveal whether growth- or sorption-related processes dominate the accumulation. Transport For a better understanding of adsorption processes and comparison between adsorbed and suspended biomass, the transport process must be understood very well, both in terms of transport of biomass to the substratum and the transport of nutrients to the adsorbed biomass. Currently, most of the information about kinetics of cellular adsorption and desorption has been derived from stagnant systems with no shear stress. The absence of flow or shear forces in natural and engineered systems is not common and, therefore, not of great practical interest. To define transport in quiescent systems is not an easy task. 11 since it depends on parameters , i.e. diffusiyity, which can not be measured directly. Additionally, adsorption kinetics in stagnant systems are subject to artifacts produced by the combination of sedimentation and active adsorption rates. Some studies in flow systems have been published, focusing on net accumulation rates at the substratum. From the literature, it appears that it is essential to measure both adsorption and desorption rates independently. Figure I (Powell and Slater, 1983) illustrates the difficulty in determining adsorption rates from the accumulation alone. The data fit the theoretical calculated rates poorly. Measuring accumulation rates instead of adsorption can lead to artifacts since accumulation can include other processes,. such as cellular multiplication at the substratum, which are not related to adsorption itself but which can be a major contribution to an increased accumulation. Transport and Adsorption to the Substratum Piffusivity: Under laminar flow conditions, particles are transported to the substratum by diffusion perpendicular to the flow. Microorganisms with a size of I to 4 pm3 have a very small Brownian motion and, hence, a small Brownian diffusiyity. Therefore, motility is of considerable importance during the processes of transport but has often 12 been neglected in adsorption studies. Jang and Yen C1985) calculated the non-Brownian diffusivity (motility) for different microorganisms to be in the range of 0.4"IO-3 to 5.6“ 10'”3 mm2 s”1, compared to the Brownian diffusivity of 50HlO"® mm * t—1. They used the following equation to calculate non-Brownian diffusion: v » d Dc = --- £--- — --- 2.3 3 • ( I - a ) Dc. : diffusivity [ L1 t-1] Vv- : velocity of motility CL t-1] dr : free length of random run [L3 a : main cosine of angle of turn [-] Under condition of no chemotaxis, a can be assumed to be zero. If motility is not considered as a contributing factor in the process of transport to the substratum, the transport rate might be underestimated 20 to 50 times. The non-Brownian diffusivity can be calculated from the velocity and the meah free path length. Vaituzi and Doetsch (1969) measured speeds up to 55.8 pm s~1 for Pseudomonas aeruginosa with "track photography". Their results suggest a mean free path length of random run in the range of 50 to 85 pm. These values yield a non-Brownian diffusivity (Equation 2.3) of 10 3 mm"'" s— for P aeruginosa. 13 Transport Rate to the Substratum: available for the transport and particles to different substrata. proposed an analysis with a approximation for the surface-particle Good information is adsorption of inert Bowen et al. (1976) first-order-reaction capture rate, which leads to an expanded Graetz solution. This solution converges well for relatively large Peclet numbers and proved to be accurate for inert particles adsorbing to charged surfaces. The resulting equation has the following form: C0-Dc CFU 2.4 Kcfu I Adsorption rate of CFU to the substratum [# L-2 t-1] C0 2 CFU concentration in bulk liquid [.# L“3] D0 : Diffusivity of CFU CL”2 t"1] h : Half-thickness of channel CL! Ki : Dimensionless distance from channel inlet [-] € : Surface-particle capture factor [-] F 2 Gamma function [ F (4Z3) = 0.89338 ] In the special case where the surface-particle capture rate € approaches infinity (€=m ),.Equation 2.4 becomes: 14 NCFU •Dc h 2 9Ki 1/3 r 43 \ 2.5 Ncr-Lj I Flux of CFU to Substratum [# L-1 t- ^ 3 The strength of this solution is that one can estimate the flux of particles to the substratum (€=«,, Eq. 2.5) and obtain a discrete value for the surface-particle capture factor, independent of concentration and motility, for different substrata. In addition, a "sticking efficiency" can be calculated with Equations 2.4 and 2.5 by dividing adsorption rate by the CFU flux to the substratum. Assay for Substratum Properties: The use of Equations 2.4 and 2.5 to describe transport and adsorption processes, especially the dimensionless factor €, is a good analysis for studying the effects of different degrees of hydrophobicity of substrata Cindependent of concentration and diffusivity). Fletcher and Marshall (1982) show an increase of accumulation with an increased hydrophobicity. They use the double-layer theory (DLVO) of the colloidal chemistry to explain these mechanisms, based on the calculated charge of the substratum measured with the bubble contact angle method 15 and the overall charge of the organisms. Van Pelt et al. (1985) showed that there is statistically seen a very poor correlation between the free surface energy and extent of accumulation. They propose as possible reasons for this poor correlation that accumulation as the measured value is not the most appropriate parameter to describe adsorption, that the free surface energy during the experiment is not the same as that previously measured, or that the mechanisms of adsorption are different depending on the free surface energy. Van Pelt's first proposition is that the change in accumulation or the net adsorption is the result of adsorption minus desorption and, therefore, measurements of accumulation does not reflect the primary occurring process. The second proposition is in accordance with the observation of the "conditioning film". This change of well defined surfaces due to exposure to water containing organic macro molecules has been described by Loeb and Neihof (1975), Baler and Weiss (1975), Abbott et al. (1983), and Little and Zsolnay (1986). They summarize the effect of a conditioning film that a solid surface in contact with liquids containing diverse organic macromolecules alter due to the formation of a monolayer of adsorbed macromolecules; This results in the following: hydrophobic surfaces become 16 hydrophilic, positively- and negatively-charged surfaces acquire a net negative charge and Zeta potentials, contact potentials, and critical surface tensions are increased. The third proposition is that depending on the free surface energy cells use a different mechanism for adsorption. Fletcher and Marshall (1982) indicated the importance of proteins in the processes of adsorption. By adding Pronase they reduced the increase of accumulation. Paul and Jeffrey (1985) showed that for hydrophobic substrata, such as polystyrene, the protein linking is essential, whereas for hydrophilic substrata other adsorptive mechanisms dominate. Their result indicates that, indeed, different mechanisms of adsorption dominate depending on the free energy of the substratum. Growth-Related Processes Very little work has been done in regard to growth-" related processes during early colonization of surfaces. Only two groups of studies are available: 1. The early phase of biofilm accumulation (Trulear, 1983; Turakhia, 1986). 2. Growth measurements with Image Analysis (Caldwell and Lawrence, 1986,). 17 Trulear and Turakhia determined growth rates in biofilms grown under constant shear stress and turbulent flow. During the first or second day after exposure of acrylic plastic surfaces to P. aeruginosa. the adsorbed biomass had a growth rate (jaiO.65 h"3-) exceeding the maximum . growth rate in suspension h”1). After this initial time, the measured overall growth rates were reduced to levels below the maximum rate in suspension. Their results do not indicate whether this increased initial activity is due to prior physiologic or genetic phenomena or due to analytical variations after adsorption. Data suggest that the process of adsorption is very selective for the "more active" organisms (cells with a high motility have a greater diffusivity). Caldwell and Lawrence (1986) measured "behavior" of adsorbed P. fluorescens under laminar flow conditions. They observed different patterns of adsorption and subsequent growth at the substratum. Unfortunately, they do not state the shear stress of the liquid on the wall but only an average velocity. From the publication, shear stress cannot be calculated since the geometry is unknown. The growth rates measured do not answer all questions since the substrate concentration used were unusually high (I g glucose I-1 and 100 mg glucose I-1). The cells were grown in batch cultures and washed twice before being used in the IS adsorption study. The measured specific growth rates are in the range of 0.42 h-1. Spatial Distribution The spatial distribution of the CFU during adsorption can be of great value since it can determine whether the process is controlled by the adsorbing cells alone or a cell - substratum interaction (including the existing colonization). If the process is due to cells only, without any influence by the substratum's present state of colonization, a random distribution would be expected. If conditioning and occupation of the surface positively influences adsorption, then an aggregated distribution can be anticipated. A uniform distribution, conversely, results when the area around an existing CFU is blocked for adsorption indicating a negative influence. Classic Nearest Neighborhood Analysis cannot be used for this analysis since only distance to the single nearest neighbor is used ignoring the other adsorbed cells. An analysis is needed which accounts for the overall population density. An extensive description of a unique solution for spatial distribution analysis is presented in Appendix A. 19 Fluid Dynamics Defined fluid dynamics is essential for adsorption studies under constant shear stress. Hydrodynamics control both transport and adsorption: Transport is a function of the loading rate and adsorption.depends on shear stress. Due to this relationship, it. is difficult to compare experimental results obtained under different hydrodynamic conditions without their precise definition. Two different flow patterns must be considered: 1. Turbulent flow 2. Laminar flow Turbulent Flow The nature of turbulent flow does not allow an easy determination of the velocity gradients near the wall. Depending on the Reynolds number of the flow and the roughness of the wall, a wide variety of velocity gradients and, thus, shear stresses are possible. Using the theory of the "viscous sublayer", within its limitations, i.e. smooth surface, it is possible to estimate the shear forces. 20 According to Prandtl, this viscous sublayer can be explained and estimated in the following way: Due to the viscosity of the liquid, the velocity at the wall is zero and the resulting shear forces in the liquid adjacent result in reduction of the velocity. This generates a layer with a viscous flow which extends into,the flow with an increasing velocity up to the point where the flow starts to become fully turbulent. The transition from the boundary layer to the turbulent bulk flow is asymptotical.. Therefore, the thickness of this layer cannot be determined unequivocally. Generally, the thickness of the layer is defined as the point where the theoretical flow velocity reaches 99% of the outer bulk velocity. In reality, this problem is complicated by the possible existence of three forms in the viscous sublayer: a laminar boundary layer, a transition region, and a turbulent boundary layer with a laminar sublayer. In addition, any disturbance of the substratum changes the development of the boundary layer. According to Dracos (1973), the shear stress at the wall can be estimated if the friction factor is known (flat plate): Laminar boundary layer: Cf = 0.66 - 1/2 2.6 C friction factor 1-3 V „ , X H 21 mean bulk velocity CL t™13 length of layer development CL] viscosity CL1 f"-1] Turbulent boundary layer: v • x -1/5 0.059 - COC'f 2.7 with the c-r values of Equations 2.6 or 2.7 the shear force at the wall can be calculated: According to Equations 2.6 - 2.8, a turbulent flow with mean bulk velocity of 0.5 m s”3- will produce a shear stress of 0.34 N m""1 along a flat plate after a length of 10 m. This calculation for flat plates can, with caution, be used for larger diameters of pipes, especially if one assumes frequent irregularities and, hence, uses Equation 2.6 for the calculation of the friction factor. Laminar Flow 2 CO • 2.8 To d shear stress at wall CF L~23 density of liquid CF t2 L"A3 Laminar flow is analytically much simpler than 22 turbulent flow. The velocity profile ia parabolic and shear stress can be calculated according Newton's law: 'T =xy dv X y « length axis of system ‘ height The boundary conditions for this system are fairly simple: both the wall velocity and the shear stress at the symmetry point are zero. There are no undefined boundary layers troublesome asymptotic approaches as in turbulent flow. or 23 CONCEPTUAL MODEL OF SURFACE COLONIZATION The analysis of adsorption, desorption and growth related processes during the early colonization of" a substratum cannot be considered in traditional terms of continuum mass balances. Rather, population balances, where the single observed particles are individual members of the total population must be used. For population balances, the probability of an event, in terms of the total population, is the key factor. Population Balance in Terms of CFU The population balance will be made in terms of Colony Forming Units (CFU), an individual observable particle which consists of one to many cells. Each CFU can be observed and treated individually with the image analyzing system. Transport Particles or cells are transported by momentum transport in the laminar flow parallel to the substratum. There is no momentum transport perpendicular to the 24 substratum. However, the particles or cells are transported to the surface by a diffusive random movement. Assuming that chemotaxis is absent, this diffusive transport is either a Brownian motion or the random motility of the cell itself. Hence, a Brownian and a "non-Brownian" diffusion is responsible for the transport to the substratum. The non- Brownian diffusion, which can be calculated with the average free path length and velocity of the random movement, can exceed the Brownian motion by orders of magnitude. "Transport" does not define the physicochemical interaction of the particles with the substratum, but only the transport to the substratum. Particles might "hit" the substratum due to transport and come to a brief stop. But as long as they do not interact with the substratum, even if they are visible to the observer, they are not considered adsorbed. Transport depends on the total concentration of particles through the system and the particle diffusivity Dc,. The rate of transport is the number of particles transported to the substratum per unit area and per time. ^ — — L 25 Adsorption Adsorption refers to a direct particle-substratum interaction. It does not include the transport to the substratum but only the direct interaction of a. particle, which has been transported to the substratum, with the substratum. The probability of adsorption for a CFU transported to the substratum can be defined as "sticking efficiency". This probability may depend on surface characteristics of the particles and the substratum as well as the fluid shear ,stress at the surface. Last, but not least, the physiological state of organisms can influence adsorption. The rate of adsorption, therefore, is a function of the rate of transport and the probability of adsorption and has units of particles per unit area per time. Reversible versus Irreversible Adsorption When CFU adsorb to a substratum, their linkage can be relatively weak, but strong enough to resist- shear stress of the liquid for some time. Due to the poor connection, they have a probability to desorb after a short time. By 26 improving their linkage to the substratum with time, their probability of desorption decreases. Hence, as soon as their probability to desorb reaches zero, they are irreversibly adsorbed. During the period where their probability to desorb is greater than zero, they are "reversibly adsorbed". The time interval between adsorption and the time at which CFUzS are either sheared off or irreversibly adsorbed, is the offset time of desorption for reversibly adsorbed CFU. This concept of reversibly adsorbed CFU and ■offset time is not the same as used in other experiments (Fletcher and Marshall, 1982), where the term "irreversibly adsorbed CFU" indicates the amount of CFU washed off after termination of an experiment. In this text, it is used to describe a mechanism during the process of adsorption; Therefore, the offset time is a specific time interval during the process of adsorption dependent on the physiology of the adsorbing CFU, shear stress, and substratum. This concept can be used to describe kinetically the findings by Brash and Samak, 1978. They found that there is a dynamic equilibrium (turnover) between proteins in the bulk flow and adsorbed to the substratum. As soon the bulk concentration was reduced to zero, the surface concentration remained constant in a static equilibrium (no turnover). 27 indicating that the molecules went through the state from reversibly to irreversibly adsorbed. Desorption Desorption refers to an entire CFU detaching from the substratum and reentering the bulk liquid. The probability of desorption is more related to probability of adsorption than to the total number of CFU at the substratum, indicating that the chances for a CFU remaining at the substratum increases as its residence time increases (see reversible adsorption versus irreversible adsorption). Thus, the probability of desorption is not equal for all adsorbed CFU since a CFU improves its bonding to the substratum with time. The rate of desorption can be defined as the product of the probability of desorption (3) with the rate of adsorption. This probability is a function of shear stress, physiological state of CFU, and characteristics of the substratum. Desorption offset time, t,..., defines the time interval between the start of adsorption Ct=O) and the first desorption event (t = t,.) in an experimental run. 28 CFU-Separation CFU-separation is the separation of a CFU into two independent CFU's and is a process related to growth at the substratum. CFU-separation increases the number of CFU at the substratum but not the number of cells so it is important to the CFU population balance. Since all irreversibly adsorbed CFU have the same probability per time to separate, this probability is defined as a first order kinetic rate coefficient. The total rate expression of CFU- separation has the units of number of CFU per area and per time. The probability (not the rate) of CFU-separation depends on shear stress, substratum characteristics, and physiology of the CFU, but . is independent of the CFU concentration at the substratum. Other Processes at the Substratum Adsorption, desorption, and CFU-separation are the only processes, relevant to the description of the colonization processes in terms of CFU. However, the experimental system only permits observation of a limited substratum area and CFU can enter or exit the field of observation. Therefore, for experimental purposes, two additional processes have to 29 be considered: I.) CFU entering and 2.) CFU exiting the field. Population Balance in Terms of Cells The number of cells per CFU can be calculated (area measurement and division by standard cell size) to obtain a population balance in terms of cells. All processes described in terms of CFU can be translated into terms of cells. As indicated before, CFU-separation does not contribute to ■ the cell accumulation. However, other growth related processes contribute to the population balance in terms of cells. Multiplication and Erosion Multiplication is a growth related process at the substratum. Whenever a cell within a discrete CFU is growing and the newly formed daughter cell remains within the same CFU, the process of multiplication is observed. If the newly formed cell is lost immediately due to shear forces, no multiplication will be observed since this process describes only the formation of new cells which remain within the same CFU. In case an established cell 30 ® CFU (with more than one cell) detaches and reenters the bulk flow, the CFU is eroding. If a CFU erodes, it loses cells to the bulk flow without being removed itself. The ;probabilities of multiplication and erosion are ; defined in the same way as CFU-separation. All the irreversibly adsorbed cells have the same probability for multiplication and subsequent erosion. The probability terms for both are defined as a probability per time (analog to first order kinetics). The rates for multiplication and erosion are expressed as number of cells per area per time. Kinetic Expressions in Terms of CFU The rate expressions of the model, conceptually described above, will be used in this section more explicitly to derive the kinetic equations of the population balance. According to the previously described processes the "stoichiometry" of the CFU population balance can be written in the following way: 31 ™("bulk < -- > ECFU3 -> ECFU3rev irrev suspended reversible irreversible biomass adsorbed biomass 3.1 a ECFU]tot [CPU] +rev [CPU]Irrev Total adsorbed CPU total reversibly t total irreversibly adsorbed CPU adsorbed CPU 3.1 b Using these stoichiometric equations (3.1 a and 3.1 b), the kinetics and surface concentrations can be determined with the equations that follow. Transport from Bulk Flow to Substratum Deposition rate of colloidal particles from a laminar flow to the walls of a parallel plate, as described by Bowen et al. (1976) will be used for CFU. The local transport rate to the substratum is given by: 3.2 K c f u : Adsorption rate of CPU to the substratum [# CPU L~J t-1] C0 : CPU concentration in bulk liquid [# CPU L“3] . D0 : Diffusivity of CPU EL2 t“l3 h : half-thickness of channel EU Ki : dimensionless distance from channel inlet E-] 6 : surface-particle capture factor E-3 F : Gamma function E F(4Z3) = 0.89338 3 32 Equation 3.2 accounts for the CFU transport to the region ultimately adjacent to the substratum and also for the particle-substratum interaction (adsorption). K x , the dimensionless length, is calculated with the following equation: ( " ( 8x3h ) h : Half-thickness o£ channel x : Length from inlet CL] Pe ' : Peclet number C-J 3.3 Peclet number describes the ratio of bulk velocity to convective velocity and is defined: 4 » v • h Pe . ----*---- C Vm : Average velocity in channel Dm : Diffusivity CL1 t”1] 3.4 CL t-i] The non-Brownian diffusivity of bacteria (motility) (Equation 2.3) can be calculated with the free path length and the rate of motion in the random movement of bacteria (Jang and Yen, 1985): Dc v » d r r 3 ( 1 - « ) 3.5 vv, dv. a "linear swimming speed" CL t-*] mean' traveling length of random run CL] mean cosine of angle in random turn 33 If a non chemotactic movement is assumedf CCFU] V-ToV = O and t SL t,- ---> Kfiae,.,, Ko1s m m = 0 Ct=O : first observation of adsorption). This boundary condition leads to a discontinuous function with respect to t: CCFU]rev : Offset time of reversible adsorption Ct"11 The rates Kocleam and Kotl^ mv., (for t i tva) can be expressed by the probability term Ci0 for desorption: CCFU]rev = kCFU " [ 11 " tBc + ( 1 " fcr 1 3 3.11 If O0 is independent of time, then the population balance of reversible adsorbed CFU in Equation 3.11 can (for t i t0> be reduced to: = K * t rev CFU r t i tv CFU ckCFU ' ^ ‘ (Kcdes+ Kctran 3 * Ct ™ 3.10 t I tv CCFU] 3.12 I36 Equation 3.12 states that the number of reversibly, adsorbed CFU per area is independent of time. The population balance for the irreversible CFU (Eq. 3.8 ) can be integrated with the boundary conditions: t = tv. > CCFUl !Ivivimv = O . This boundary condition stands for the assumption that, for any time smaller than tvl no transformation from CFUvimv to CFUivivimv will occur. This assumption leads to a discontinuous function for CCFUli^vlmv with the break point t=tv,: CCFU].irrev 0 K . ""I. ctran k ■ ^ ^too p - I L seP _ — —I t i t r 3.13 t i t r In Equation 3.13 the term for Ktrffcvi^ vi can be replaced with the probability term: K = Kctran CFU ( 1 - 6 ) c 3.14 which puts irreversible accumulation into a direct relationship to the adsorption rather than the transformation rate. According to Equation 3.1 b, Equations 3.12 and 3.13 can be combined for total CFU, using the assumption of Equation 3.14: I37 ECFUJ kCFU * t t i t t + r I-Bc . kgaoB C t 3.15 t 2 t This equation describes the kinetics in terms of total CFU. Kinetic Expressions in Terms of Cells Since the cell number for each individual CFU can be measured, all the events in term of CFU can be translated into terms of cells. Additionally, a change in cells per individual CFU can be observed. Hence, the processes of cell multiplication and erosion can also be defined. CFU- separation, a process which does not contribute to the change of total cells adsorbed, is omitted. 38 Transport from Bulk to Substratum Transport can be defined in the same way as for CFU (Eq. 3.2): 3.16 Adsorption rate of cells [# cell L-1 t-1] cell concentration in bulk liquid [# cell L-=] Diffusivity of CFU CL2 t"1] half-thickness of channel CL] dimensionless distance from channel inlet [-] surface-particle capture factor [-] The main difference between Equation 3.2 and Equation 3.16 is the difference of concentration. As is the case for Equation 3.2, Equation 3.16 represents the rate of adsorption. The dimensionless distance Ki is the same for both equations, since the initial measurement is made in terms of CFU and then translated into cells. Hence, Equation 3.3 - 3.5 are unchanged. The rate of transport (not adsorption) can be defined in analogy to Equation 3.6: Ck Dc h Ki € .2 S K 1 1/ 3 3.17Nx C X -D C h r 43 flux of cells to substratum E# cell .L"2 t"13 Population Balance at Substratum Cells at the substratum undergo a transformation from reversibly to irreversibly adsorbed cells. The population balances for cells are similar to those for CFU Cxlvirov=O and t * ty.---> Kxclefro=O, Kxt^mn=O. This boundary condition leads to a . discontinuous function in respect of t: [x]rev KX ' t t I tv (K ■ t) X xdes + Kxtran r t i tv 3.20 If the probability Bh of desorption is independent of time then Equation 3.20 can for the case of t Z tv, simplified (analogous to Eq.ll and 12) to: Cxl = K « t rev x r 3.21 With that simplification, Cxl^rov becomes independent of time. For the irreversible adsorbed cells Equation ‘ 3.13 can be adapted after combining and krov.oro in Equation 3.18: 41 k = kxnet mult keros Then Equation 3.13 becomes: — :0 Ex] . = —irrev “ K . ~xtran . x^net 3.22 kxnto-b Ct — ti t i t t i t 3.23 Using an analogous step to Equation 3.14 and combining Equations 3.20 - 3.23, the Equation for the total cell concentration at the substratum can be written as it has been done in Equation 3.15 for CFU: t i t tr + I-Gx , x^net kxnot * ^t 1 ) e -I 3.24 t i t Thus, with Equation 3.15 and 3.24 it is possible to estimate the accumulation of both CFU and cells at the substratum with time. 42 Sticking Efficiency Sticking efficiency is a parameter frequently used to describe the ratio of adsorption rates to the flux to the substratum. Thus, it is an overall probability of adsorption. The sticking efficiency is not identical to the Surface-Particle Capture Factor €, but rather a function of it. In terms of CFU, the sticking efficiency can be described by the ratio of Equations 3.2 to 3.7, and in terms of cells by the ratio of Equations 3.1(5 to 3.17: 3.25 B : Sticking efficiency [-] € : Surface-particle capture factor [-] • Dimensionless distance from channel inlet [-] r : Gamma function [ T(aZ3) = 0.89338 ] Thus, the sticking efficiency I has a range of zero to one. Sticking efficiency, 3, is the probability that a CFU being transported to the substratum will adsorb. The surface- particle capture factor € is part of the extended Graetz solution for a mass balance of the bulk liquid and the substratum in terms of adsorption. 43 Summary of the Conceptual Model The model describes the population balance for both CFU and cells at the substratum. The parameters used in this model can vary with cell concentration in the bulk liquid and shear stress at the substratum. All relevant parameters in this model, with the exception of the non-Brownian diffusivity, can be measured experimentally or calculated with the method described in "kinetic Results". Non- Brownian diffusivity can be estimated with literature values and direct observations. 44 EXPERIMENTAL SYSTEM AND METHODS Experimental System The experimental system consists of" a chemostat system, a rectangular capillary tube, and an image analyzer similar to the system described by Powell and Slater (1983): Microbial cells grown in continuous culture (chemostat) provide continuous inoculum for the experimental system with minimal variation in cell physiological state and cell concentration throughout an experiment. Prior to beginning the experiment, cell concentration in the chemostat is measured by direct count. The cell size distribution is also determined for calculating cell numbers per CFU. The desired cell concentration at the capillary entrance is obtained by dilution in the mixing chamber. The effluent from the mixing chamber is pumped through the rectangular capillary (Wale Apparatus) at a constant rate using a non-pulsing gear pump. The inside surface of the rectangular capillary is the substratum in these experiments and the processes occurring at this surface are monitored continuously by a video camera mounted on the microscope. 45 ImageGrowth AnalyzeMedium Dilution Medium Camera Meter PumpMixing h a m b e rCFSTR ___Capillary 0.2 m m f Figure 3. Schematic of the system. The video signal is transmitted to the image analyzer which then converts the grey image into a binary image. The image analyzer accumulates this image into a "tracking" image which is similar to a multiple exposure and displays all of the images simultaneously in different colors on the screen. 46 A single binary image of" the specimen is stored on disk at constant time intervals % : - Z fM m v ^ V - Z-T-.--V. -- .--ft'*': — " - - . z_"-r i . * >;2-r u?- -■ - ~ Jc :-;V-'. ■ : ~ r * - - - ----- ’ ------- -^s£: -ZZZi--IV-; -e$s • - .. -EL: _ - -\s. / Z « z , ► W - ---- ■ «3*. v; -I" - -■ ^ s.--“_Z -. r - I j i - g t e W - -V . - - - - - - - - - - : : V " W *. - ". - --T». „ -^= . -- = - - --VJ=:-V ... - --V. :,- ; »_V = : ,T - - - - -: V- -U-S--.-.:. -- - - -’-• # - - - _ — ^ Z- _- ^IiSiMiS :-; ‘ ■ - .v- -rtE-' Figure 4. Tracking Image. 1.0 N m-2, 10G cells/ml. Flow direction from left to right. The grayish areas are the tracks of the colonies and the dark areas within the tracks the colony forming units (CFU). The streaks are markings of "hits" by CFU transported to the substratum without adsorbing. Size of observed image: 150 ■ 150 pm 50 Fixpoint Calculation After completion of the real time experiment and prior to the analysis of the single timages, the movement of the fixpoint has to be calculated. This step requires that the fixpoint be isolated from all the other CFU within the image. The easiest way to achieve this task is by manually editing the image of the total tracks for the track of the -fixpoint alone. Then, with a logical exclusion, the feature 0-f the fixpoint for each image can be separated and measured individually. The measurements include the true midpoint coordinates which are stored in a data file. This routine can be done either before or within the analysis routine. Image Analysis Once the coordinates of the fixpoint have been calculated, it is then possible to analyze the images for the CFU. For each CFU detected, the following measurements are done: X- and Y- coordinates of each detected CFU (feature count point). 51 Minimum and maximum X- and Y- values of the CFU to calculate the true midpoint corrected for the drift of the specimen holder. Area, Length, Width, ' Orientation of the length axis. Shape (roundness). At the same time, the cell number per CFU is calculated to obtain a cell number per CFU distribution for the analyzed field. In this routine, the results will be corrected for the possible drift of the specimen holder during the experimental run using the fixpoint coordinates. All the data obtained are stored on disk in form of random access files for further analysis. Up to this point, the evaluation of the data is done in a two dimensional way with the coordinates as the two dimensions. Data Assembly In this routine, data will sorted and assembled for each CFU with time as the third dimension. This can either be done with the image analyzer or with an IBM compatible system. In the image analyzer, the tracking image provides a criterion for the continuation of a CFU with time. As 52 long as the routine finds a data point in the next image, within the same track, it will use it as the continuing point of the same CFU. If it finds two possible points for continuation, it selects the closer of the two to the last analyzed point, and labels the other as a potential daughter CFU (CFU-separation). Withip the image analyzer, this routine is relatively .slow since it requires frequent interactions with the image analyzer unit and multiple image handling. The routine within an IBM-compatible computer uses a less rigid criterion for the evaluation of the continuation. Instead of using the tracks, it uses a range <4 by 6 pm) within which a continuation is allowed. If it finds two possibilities to continue, it selects the closer one and labels the other a possible daughter-CFU (CFU-separation). Since this system can use a hard disk setup and a machine language version of the programs, this routine is much faster in an IBM-compatible system than in the Image Analyzer. Both systems reevaluate possible CFU-separations during the assembly process. If the mother-CFU does not decrease in size during a possible division, the separation will be rejected. 53 Other than the above differences, the sorting routiiie performs the same functions in the two systems. In addition to the three dimensional analysis this routine calculates the neighbor analysis, the dimensionless nearest neighbor distance, the influence number (not dimensionless), and the dimensionless influence number. Additionally, this routine calculates the movements and directions of the CFU at the surface and monitors changes in cell numbers per CFU. The latter will be used to determine the number of events of cell multiplications with time at the surface as well as erosion of CFU. The organization of these data files is listed in Appendix B. Since accumulation of both CFU and cells can be influenced by colonies moving into and out of the field, the program identifies those new appearances close to the image frame. The calculation by this routine can be summarized in the following way: 1. Calculation of the values for each CFU, including first and last observations. 2. Determination whether each CFU adsorbed, separated, or migrated into the field, and whether they desorbed, or migrated out of the field. 3. Calculation of movement and direction for each CFU. 4. Conversion of the area of each CFU into cells per CFU and calculation of the events of adsorption, desorption, multiplication and erosion in terms of cells at the surface. 5 5. Calculation of the neighborhood analysis during the first observation of each CFU. 54 Subsequently, the sorting routine builds, several data files with a summary of data obtained. These files are in form of ASCII - files which can be translated into a format for Super Calc spread sheets and other statistical software. Method of Analysis and Chemostat Operation Direct Cell Count Cell concentration in the bulk flow of the capillary tube was one of the main parameters of the experimental series. Therefore, it was necessary to use a fast and accurate method to determine, the cell concentration of the chemostat effluent. The method of Hobble et al. (1976) was adapted to use the Image Analyzer for counting. The filters used were evenly hydrophilic, so that surfactant treatment could be omitted. Thus, the filters retained the irgalan black much better under the high energy illumination than surfactant-treated filters. Counting the cells with the Image Analyzer facilitated and significantly improved the analysis. 10 fields on each filter were counted and the average of these counts used to determine the cell concentration. Standard errors of the counts per filter were in the range of 7 to 12%, significantly lower than the error by the manual method. Replicates of several filters with the same sample, (count of three filters per sample) 55 yielded for the average values per filter a standard error of less than 10%. Chemostat effluent samples were sonicated prior to the count to break up aggregation of the cells. A sub-sample (75 pi) was suspended in three ml 0.01% acridine orange (AO) for at least 5 min. It appears to be noteworthy to mention that cells from chempstat cultures appear mainly orange, whereas bacteria from natural environments (very low growth rate) are often green. Since orange cells are much better detected by the Image Analyzer than green ones (in contrast to direct count by eye) it can be necessary to heat the sample before staining to change green fluorescens to orange (denaturalizing of protein). Cell Size Distribution Cell size for single cells and the total population of the chemostat effluent were measured with the image analyzer prior to the experimental series to determine the cell number per adsorbed CFU in the capillary analysis. For this analysis white light phase contrast was used with a microscope magnification of 40*I.5. Single cells for the size distribution were selected manually, whereas all cells were accepted for the size distribution of the total population. 56 Mounting of Capillary Tube Capillary tubes (Wale Apparatus) were precleaned by combustion (SOO0C) for several hours (over night) to remove all organic contamination in e the inside. They were connected to iZza inch diameter high pressure nylon tubing (6 cm) with heat-shrink PVC tubing (2 cm, diameter nominally iZa inches). The connections were sealed and secured with silicon glue dispensed out of a tuberculin syringe (I ml), and then heat fitted with hot air. This procedure to connected the flat capillary tubes tightly to the round tubing (no leaks on the microscope stage). Chemostat Operation A New Brunswick Bioflow C30 with a volume of 330 ml and a flow rate of 1.0 ml min™1 was used as chemostat. Thus, the dilution rate and growth rate was 0.18 h™1. Temperature was maintained at ,25° ± C. Growth was carbon-limited with glucose as sole carbon source (44.4 mg l™*- as TOC) . C to N ratio was 10 and C to P ratio 15. Phosphorus was used to buffer the system at pH 6.8. Calcium concentration was 50 mg l™i as CaCO3 (added sterile after heat sterilization to prevent precipitation in form of calcium phosphate). 57 Magnesium chloride1 concentration was 7.5 mg I"1. Micronutrients were added according to Trulear (1983). The dilution liquid had the identical composition as the growth medium except that ^. . rio organic, carbon was present. The chemostat could be operated continuously for up to five days without heavy wall growth. Effluent glucose was measured colorimetricalIy with a specific enzyme reaction (Trulear, 1983). 58 RESULTS Progression of Experiments. The results are based on 15 experiments, 9 at 0.5 N m"1 ,and two each at 0.75, I.O1, and 1.25 N m~2 . CFU concentration in the bulk flow of the capillary tube ranged from 1.1"IOs to 11.2-10= CFU ml”*. Each experiment lasted 300 min for colonization, and images were taken at 5 min intervals. The extent of surface colonization by CFU under ^ ^ 1Sat conditions and the total surface coverage by tracks is displayed in Figures 5, 6, and 7 (not ' real tracks but artificial display of tracks; see "Image Collection"). The small dark areas are the colonies and the grayish, larger fields are the "tracks". The figures of the tracks were generated over a period of 300 minutes, and the colonies are the ones observed .at 300 minutes after beginning of the experiment. Figures 5 and 6 are from experiments at 0.5 N m~* with I.1-10= and 10-10= CFU ml-1 respectively. Shear stress during colonization in Figure 7 was 1.25 N m-2 and CFU concentration 12.2-10= CFU ml-1. 59 Figure 5. Tracking Image: 0.5 N m™1, I.I-IOs CFU ml”1, flow from left to right. The grayish areas are the tracks of the colonies and the dark within the tracks are the colonies (after 300 min). Size of observed area:150•150 pm. Area coverage by CFU: 0.35%, by tracks: 3.325% 60 % f ^ * w 4 $> ^ # % k l> * + '^t- # S a f IP *lv ^ 6 - W s C " . / A - ' ** st ‘ ^ * * * j? <* 4» * ®*> * * 4%'* # “» ;» " *** T «g» * *' " S Jtiili, Wf «» 5 usaiCTw - *% **% -?<, *p - «* ^ v v - » - # » H * S •** % t *.0» * , ' O % . - V ^ *»y »* < » * - S • . 1^ U A <• - * \ •„ .- i ' - S ^ v » . . X f - - > v f » * * »-. % r **'.. -. # ' ^ . A *» *! m *m> 4 » > T ■ypj <*= * » * • ' - 4 » + . V * m * * + , ' / - . C * # - * 4 * * 1» .J y -~ * .- -i 4. - # * * ♦ e , « r.* » V - , ' ^ ■ * \ *'- v * : & 5 j * JjTtS « /- & tr m^ — % - * V. V- *,- ** Figure 7. Tracking Image: 1.25 N m-', 12.2-IOg CFU mI™1, flow from left to right. The grayish areas are the tracks of the colonies and the dark within the tracks are the colonies (after 300 min). Size of observed area:150-150 pm. Area coverage by CFU: 1.9%, by tracks: 8.46% 62 The results can be grouped in three classes: 1. Kinetic measurements 2. Behavioral distributions 3. Spatial distributions Kinetic measurements describe the events at the substratum, i.e. events of adsorption, desorption, and growth related processes during the observation time interval (5 min) and their rates. The results describe the kinetics of substratum colonization. “Behavioral" characteristics of each CFU observed, include size during first and last observation, age during last observation, movement,' orientation, net growth, and , so on. These results are not useful for kinetic analysis but help to elucidate the processes involved. during the early colonization of a substratum. The third group, spatial distribution, determines the degree of interaction of each CFU during its first observation with other CFU already established. This analysis is uncommon but very powerful in establishing mechanisms of adsorption in terms of spatial distribution. 63 Kinetic Results The events o£ colonization on a glass substratum during the first 300 min can be presented in terms of CFU (Figure 8a), and areal coverage (Figure Sb). Adsorption kinetics can also be demonstrated in terms of cells (Figure Sc). Growth related processes are displayed in Figure Sc. Accumulation of biomass and areal coverage are presented as measured, but adsorption, desorption, and growth related processes are shown cumulative, i.e. the number of observed events were added to the number of the previous events. The slope of data displayed in this manner is equal to the rate. Thus, an increase of the slope indicates an increase of the rate. Directly Measured Results All results are presented in the Tables 9 to 23 (Appendix C). Each table represents an entire experimental series, whereas Figures 41 to 55 (Appendix D) represent the same results in graphic form. The summarized results are displayed in Tables I to 3. The nomenclature is in accordance to ones used in the conceptual model. Adsorption rate is a function of CFU concentration in the bulk flow AR EA C OV ER AG E BY C FU IN % CF U (N um be r/s qm m ) 64 ABI, 0.5 N/sqm, 5.0 • 10*6 cells/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CFU ------------------------ ----------------------------------------------------------- D ADSORPT. CUUUL X DESORPT. CUUUL v CFU SEP. CUUUL ■ ACCUUULAHON CFU 20000 10000- SOOO- TIME (min) AREA COVERAGE BY CFU IN % TIME (min) % AREA COVERAGE Figure 8. Typical progression of colonization in CFU (8a> and area coverage (8b) during 300 min. of glass substratum. Shear stress: 0.5 N m™2 terms of a smooth 65 ABI, 0.5 N/sqm, 5.0 . 10*6 cells/ml ___ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS 4 0 0 0 0 ---- ----------------------------------------------------------------------------- * ADSORPT. CUUUL » DESORPT. CUUUL ♦ ACCUUULAT10N CELLS 200 300 TIME (min) MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS ----------------------------- ------------------------- --------------------------- * UULT1PL. CUUUL A EROSION CUUUL ♦ ACCUUULAT10N CELLS 40000 *->30000 ■ g 20000 ■ O 10000- TIME (min) Figure 8. Typical progression of colonization in terms of cells. Adsorption related processes (8c) and growth related Processes (8d) 66 (Figure 9a and 9b). The linear regressions in these figures is calculated in Table I and presented as “Slope" and intercept . Thus, the assumption of a direct proportionality between adsorption rate and bulk CFU concentration as stated in Equations 3.2 and 3.16 is valid. Figure IOa displays the desorption rates at the same shear stress for CFU and Figure IOb for cells. Data from these figures suggest that all regressions of the rates with cell concentration have their origin through the zero points of the coordinate system. Growth related processes, such as CFU-separation, cell multiplication, and erosion for a shear stress of 0.5 N m~2 are displayed in Figure 11, 12a and 12b respectively. These first order rates do not show a correlation with cell concentration in the bulk flow, which is in accordance with Equations 3.8 and 3.18. 67 Shear Stress: 0.5 N nr2 ZERO ORDER KINETICS, Rate I# min-1 ram--2] Series # CFU/ral Adsorption CFU Desorption CFU Adsorption Cell Desorption Cell AAl LleS 8.18 i 2.46 7.54 + 4.17 14.38 + 2.46 11.37 ± 5.81 AB3 I.IeS 5.99 + 2.38 2.34 ± .90 10.43 + 4.28 3.73 + 1.47 AA4 1.92e6 13.52 + 4.53 10.07 ± 4.82 ' 16.20 + 5.5 10.92 ± 4.97 AB2. 2.45e6 19.34 ± 3.48 10.24 ± 4.63 ' 30.18 ± 3.62 15.26 + 6.80 AA3 2.75e6 20.50 + 6.28 11.11 ± 5.29 34.33 + 10.29 16.70 + 7.89 AC2 3. S4eS 27.29 t 3.75 11.11 ± 8.24 47.61 + 3.2 15.12 + 8.83 ACl 4.7e6 35.34 + 13.44 27.11 ± 23.95 46.29 + 16.75 27.11 + 23.95 ABl 5e6 43.45 i 5.51 36.81 ± 15.04 57.51 + 6.61 50.80 + 29.15 AA2 le7 71.68 + 26.40 57.20 + 31.75 135.66 + 47.48 107.03 + 58.56 Slope 7.39e-6 + 8.26e-7 5. ISe-S ± 1.54e-6 1.36e-5 + 1.86e-6 1.12e-5 i 2.BOe-S Intercept .423 i 2.16 -3.146 ± 4.03 -5.779 + 4.87 -12.122 + 7.33 FIRST ORDER KINETIC COEFFICIENT Ch-1] in respect to surface concentration Series # CFU/ral CFU-Separation Multipl. (Cells) Erosion (Cells) AAl . I. IeS .239 ± .225 .712 + .431 .474 + .386 AB3 I.IeS .015 ± .045 .306 + .204 .212 + .262 AA4 1.92e6 .074 + .107 .638 + .337 .482 + .397 AB2 2.45e6 .067 ± .061 .581 i .243 .394 + .129 AA3 2.75eS .055 i .071 .556 + .336 .290 + .130 AC2 3.64e6 .048 + .044 .392 + .084 .254 + .068 ACl 4.7e6 .039 ± .043 .433 + .238 .286 + .130 ABl ■ 5e6 .180 + .084 .550 + .208 .294 + .106 AA2 le7 .193 + .107 .593 + .191 .360 + .209 Average .099 + .076 .559 + .124 .391 + .104 T a b l e I. S u m m a r y o f d i r e c t l y m e a s u r e d r a t e s a t ID . 5 KI m " i s h e a r s t r e s s . S l o p e a n d i n t e r c e p t a r e t h e l i n e a r r e g r e s s i o n s u s e d i n F i g u r e s 9 a n d I O t o s h o w t h e p r o p o r t i o n a l i t y o f t h e r a t e s w i t h b u l k C F U c o n c e n t r a t i o n . 68 Shear Stress : 0.75 N ur* ZERO ORDER KINETICS, Rate [# mitr1 Series # CFU/ml Adsorption CFU Desorption CFU Adsorption Cell Desorption Cell AB4 AC3 2.65e6 6.3e6 18.82 + 6.99 42.61 + 15.93 10.21 i 4. 87 21.50 + 10.18 27.33 + 9.47 . 74.17 + 27.2 13.44 + 6.32 27.86 + 10.87 Slope Intercept 6.52e-6 1.548 3.09e-6 2.013 1.28e-5 -6.677 3.95e-6 2.971 FIRST ORDER KINETIC COEFFICIENT Ch-1] in respect to surface concentration Series # CFU/ml CFU-Separatioh Multipl. (Cells) Erosion (Cells) AB4 AC3 2.65e6 6.3e6 .065 + .061 .012 ± .030 .457 + .191 .431 + .097 .210 + .114 .321 + .081 Average .039 .444 .266 Shear Stress : 1.0 N rir* ZERO ORDER KINETICS, Rate [# ruin"1 mm-;] Series # CFU/ml Adsorption CFU Desorption CFU Adsorption Cell Desorption Cell AB5 6.75e6 31.75 + 4.01 - 22.17 ± 12.33 56.01 + 8.81 36.99 ± 21.22 AC4 B.71e6 41.33 + 16.86 26.78 ± 15.21 73.86 + 33.82 39.92 ± 20.38 Slope 4.89e-6 2.35e-6 9.lle-6 1.49e-6 Intercept - -1.242 6.294 -5.463 26.899 FIRST ORDER KINETIC COEFFICIENT Ch-1] in respect to surface concentration Series # CFU/ml CFU-Separation Multipl. (Cells) Erosion (Cells) AB5 6.75e6 .126 ± .098 .455 ± .199 .229 ± .132 AC4 8.7e6 ' .055 + .062 .433 + .132 .301 ± .099 Average .091 .444 .265 Table 2. Summary of directly measured rates at 0.75 and 1.0 N m"2. Slope and intercept describe the proportionality between the rates and the bulk CFU concentration. 69 Shear Stress : 1.25 N nr2 ZERO ORDER KINETICS, Rate I# mirr1 mnr2] Series # CFU/ral Adsorption CFU Desorption CFU Adsorption Cell. Desorption Cell AB6 AC5 6. SeB 1.2£e7 19.69 ± 2.71 51.76 ± 22.57 11.76 ± 3.56 17.36 + 10.76 30.42 ± 3.74 180.40 ± 30.38 15.69 ± 4.75 28.85 + 12.35 Slope Intercept 6.OSe-B -22.062 I.06e-6 4.469 9.43e-6 -34.648 2.48e-6 -1.443 FIRST ORDER KINETIC COEFFICIENT U r 1I in respect to surface concentration Series # CFU/ml CFU-Separation Multipl. (Cells) Erosion (Cells) ABB AC5 6.9e6 1.2067' .057 + .059 .034 ± .044 .563 + .234 .572 ± .247 .345 + .149 .370 + .183 Average - .046 .568 .358 Table 3. Summary of directly measured rates at 1.25 N m~2. Slope and intercept describe the proportionality between the rates and the bulk CFU concentration. 7 0 Adsorption CFU1 0.5 N/sqm 5.6 7.5.6 CFU-Concentration 1.25.7 AdeorpUon CFU Adsorption Cell, 0.5 N/sqm iso- CFU-Concentration AdMtpUon Cell Figure 9. Adsorption rates plotted against cell concentration in the bulk flow for CFU (9a) and for cells (9b). Shear stress: 0.5 N m- 2 . The slope and intercept of the regressions are presented in Table I. Ce ll [# /m in s qm m ] CF U [# /m in a qm m ] 7 1 Desorption CPU, 0.5 N/eqm 1.25.75.6 7.5.6 CFU-Concentration Dw orpU on CFU Desorption Cell, 0.5 N/sqm 150 100 7.5.6 CFU-Concentration Dw orpU on C d l Figure 10. Desorption rates plotted against cell concentration in the bulk flow for CFU (10a) and for cells (10b). Shear stress: 0.5 N m~2. The slope and intercept of the regressions are presented in Table I. 7 2 CRJ-Separatlon, 0.5 N/sqm OZ .2- 2.5.6 5.6 7.5.6 CFU—Concentration C FU -S ep a ra tio n Figure 11. CFU-separation as a first order rate plotted against cell concentration in the bulk flow. Shear stress: 0.5 N m”i. Average rate coefficient is 0.099 ± 0.076 h"1. 7 3 Call Multiplication, 0.5 N/sqm K .2- 5*8 7.5*6 CFU-Concentratlon 1.25*7 Multlpl. (CU.) Erosion Cells, 0.5 N/sqm 5*6 7.5*6 CFU-Concentration Ero.len (CM.) Figure 12. First order rate coefficient for cell multiplication (12a) and cell erosion (12b) plotted against cell concentration in the bulk flow. Shear Stress: 0.5 N m~"2 . 74 Derived Results Derived results cannot be measured . directly in the experiments, but are calculated from direct measurements, such as the probabilities for desorption and erosion, surface-particle capture factors, and offset time. The derived results are presented in Tables 24 to 38 in Appendix E, and rates are summarized in Tables 4 to 7: Shear Stress : 0.5 N n-i Series # CFU/ral Desorption Erosion Adsorption Transport CFU Offset Time S CFU 8 Cell 5 Cell € CFU E Cell Rate $ W (CFU) tv. (Cell) Afll I. IeS 92.81 79.04 76.68 .01125 .01991 964.06 .0085 48.99 53.52 AB3 I. IeS 39.02 35.73 75.69 .00822 .01438 964.06 .0062 48.58 51.11 AA4 1.92e6 74.50 67.61 63.50 .01065 .01278 1682.72 .0080 37.21 44.67 AB2 2.45e6 52.94 50.57 67.84 .01195 .01874 2147.22 .0090 69.93 78.66 AA3 2.75eS 54.22 48.65 58.32 .01128 .01900 2410.15 .0085 35.74 41.89 AC2 3.64eS 40.73 31.75 54.94 .01134 .01992 3190.16 .0086 50.21 65.38 ACl ■ 4.7eS 76.71 58.56 41.13 .01138 .01494 4119.16 .0086 42.41 55.50 ABl SeS 84.70 88.32 77.11 .01317 .01748 4382.09 .0099 35.81 44.83 AA2 1b7 79.35 78.90 74.21 .01087 .02067 8764.17 .0082 62.89 68.40 Average 66.11 59.90 65.49 .01112 .01754 .0084 47.97 56.00 Standard Error 8.90 6.38 3.74 .00004 .00079 .00004 31.42 11.28 Table 4. Summary of derived rates calculated for 0.5 N m" 75 Shear Stress : 0.75 N i t 2 Series # C F U M Desorption B CFU S Cell Erosion 5 Cell Adsorption E CFU € Cell Transport CFU Rate $ Offset Time tr (CFU) tr (Cell) AB4 2.65e6 54.25 49.71 61.30 .01073 .01563 2658.6 .0071 57.42 60.25 AC3 b. 3eb 50.54 37.56 47.71 .01021 .01787 6320.46 .0067 33.86 47.06 Average 52.40 43:64 54.51 .01047 .01675 .0069 45.64 53.66 Standard Error 1.32 4.29 4.83 .00018 ,00079 .00015 20.51 10.31 Table 5. Summary of derived rates calculated for 0.75 N m~2 Shear Stress : 1.0 N nr2 Series # CFU/ral Desorption S CFU B Cell Erosion 5 Cell Adsorption E CFU € Cell Transport CFU Rate I Offset Time tr (CFU) tr (Cell) AB5 6.75e6 70.82 66.05 74.81 .00699 .01254 7453.46 .0042 65.36 64.81 AC4 8.7e6 64.79 54.05 57.41 .00716 .01283 9606.68 .0043 52.12 62.66 Average Standard Error 67.81 2.15 60.05 4.24 66.11 6.17 .00708 .00006 .01269 .00010 .0043 .00005 58.74 25.54 63.74 7.82 Table 6. Summary of derived rates calculated for 1.0 N m~2. Shear Stress : 1.25 N nr2 Series # C F U M Desorption Erosion . Adsorption Transport CFU ' Offset Time S CFU B Cell 6 Cell € CFU € Cell Rate I V (CFU) tr (Cell) AB6 AC5 6.9e6 1.22e7 59.26 33.54 51.56 35.88 66.20 59.06 .00429 .00639 .00664 .00994 82707.4 14511 '.0024 .0036 34.03 55.05 32.56 66.43 Average Standard Error 46.40 9.10 43.72 5.54 62.63 2.60 .00534 .00074 .00829 .00117 .0030 .00043 44.54 11.02 49.50 12.39 m"2Table 7. Summary of derived rates calculated for 1.25 N 7 6 Probability of Desorption: --------- CFU: 0.661 ------— Cells: 0.599 * CFU Adsorption (0.5 N /sqm) Figure 13. Correlation between desorption and adsorption at 0.5 N/m'. The slope of the regression is equal to the probability of desorption in terms of adsorption. Probability of Erosion: Cells Erosion: 0.655 0.0 0.2 0.4 0.6 0.8 Uultiplication Rate Coefficient (0.5 N/sqm) Figure 14. Correlation between erosion and multiplication at 0.5 N/m2. The slope of the regression is equal to the probability of erosion in terms of multiplication 7 7 The probabilities o£ desorption and erosion as derived terms are directly related to their positive counter parts, adsorption and multiplication. The relatively good fit (Figure 13 and 14) indicates that these rates are rather dependent their positive counter rate than the bulk flow concentration. Offset time is calculated from the slopes and intercepts of adsorption and desorption. It is defined as the time difference between the beginning of adsorption and the "offset" beginning of desorption. This time interval is a function of the conditioning of the substratum and the residence time distribution, but it appears to be independent of the bulk CFU concentration (Figure 15). Offset Time of Desorption, 0.5 N/sqm S«6 7.5e6 CFU-Concentration Figure 15. Correlation between offset time and bulk CFU concentration. 78 Behavioral Distribution Results in this section represent measurements obtained from individual ■CFU and are not necessary related to the kinetics of colonization of substrata, i.e. events per unit time and area. The "behavioral" characteristics, measured and presented in this section, describe activities of CFU at the substratum such as movement, orientation of CFU during adsorption, cells per CFU, net growth, and more. The data, presented in distribution histograms, represent a defined subset of the data base. The criteria for the subset, depend on the specific behavioral characteristics. Data of individual CFU have been combined from several experiments and organized depending on shear stress. This reduces the number of distributions and increases the number ■ of samples per distribution. Distributions representing 0.5 N m~2 are presented in this section and a complete set in Appendix F. Eight distributions per shear stress have been calculated. 79 Residence Time Two different distributions for residence time have been calculated: I. Total residence time, and 2. finite residence time. The difference between the two is the criterion for rejecting a CFU. For the total residence time distribution all CFU have been incorporated where adsorption has been observed including those which exceeded the last image. Hence, the residence time for these CFU could have been longer since their desorption has not been observed prior to termination of the experiment (Figure 16 a). For the finite residence time distribution only those CFU have been included where adsorption and desorption has been observed. In contrast to the total residence time distribution, this distribution represents the residence time of the reversibly adsorbed CFU. since both adsorption and desorption of these CFU have been observed. The difference between reversibly adsorbed and total CFU is reflected in the level of acceptance: 371 of 884 CFU were characterized in the finite compared to 815 of 884 CFU in the total residence time distribution. The probability of remaining at the substratum decreases with time. For 8 0 Total CFU S e rie s AA 0 .5 N /sqm AVERAGE - 6 7 .2 6 3 8 STANDARD DEVIATION - 8 3 .9 0 2 8 4 o 23- TOTAL RESIDENCE TIME [min] ACCEPT. 813 OF 884 Total CFU Series AA 0.5 N /sqm AVERAGE - 13.9973 STANDARD DEVIATION - 27.11492 ^ ACCEPT. 371 OF 884 FINITE RESIDENCE TIME [min] Figure 16. Residence time distribution Series AA (0.5 N m—2). a: Total residence time distribution representing all CFU AA except the ones entering or exiting, b. Finite residence time of series AA. Only CFU were accepted where adsorption and desorption has directly been observed (no daughter-CFU, entering, exiting, or CFU exceeding last image of the experiments). This distribution represents for reversibly adsorbed CFU the probability in respect to time to remain at the substratum. /example, the probability of desorbing between zero and five minutes at 0.5 N m""1 is 48%, between five and ten minutes 'it reduces to 12% and so on. Orientation of CFU During Adsorption The distribution of CFU orientation at its first observation after adsorption is presented in ' Figure 17. Only CFU were included where adsorption was observed Cno entry and no daughter-CFU). This distribution shows two peaks, one at 0° degree and one at 90° (flow direction 90°). In some case CFU length orientation could not be measured unequivocally and the image analyzer reported their orientation as 0°. About 25 to 30% of the CFU with a 0° orientation were identified as being squared or round (no valid measurement of orientation). That leaves about 30 to 35% of the CFU with a true 0° orientation. Therefore, it can be concluded that CFU either adsorb perpendicular or parallel to the flow direction with a very small probability for any values in between (Figure 17). 81 8 2 Total CFU S e rie s AA 0 .5 N /s qm AVERAGE - 4 8 .3 3 9 7 1 STANDARD DEVIATION - 4 3 .2 5 2 8 3 223 43 673 80 1123 133 1373 ORIENTATION OF CFU IN I . FIELD Figure 17. Orientation of adsorbing CFU at substratum. Only adsorbing CFU have been accepted for this distribution. Direction of flow: 90* Motility at Substratum Motility at the substratum was measured for all CFU which were observed for at least 15 minutes (three images). Figure 18 a displays the rate of gliding on the substratum. Rates of gliding less that 0.1 pm min™1 do not necessarily express motility. They can represent a change of location of the center point due to growth or resolution of the image analyzer. Figure 18 b shows the distribution of direction of gliding. CFU which were stationary are represented with a direction of 0* (flow direction 90*). Moving CFU have a 83 aoccpt. are or a84 Total CFU S eries AA 0 .5 N /sqm >E - 2 .1 7 2 3 2 7 E —0 2 STANDARD DEVIATION - . 0 3 8 3 3 8 7 INTEGRATED RATE OF GUDING Cum/mlnl Total CFU Series AA 0.5 N /sqm AVERAGE - 103.4289 STANDARD DEVIATION - 102.7*22 ACCEPT. 870 or 884 as28|3|8ga35g=g INTEGRATED DIRECTION OF GUDING Figure 18. Integrated movement at substratum. a: Integrated rate of gliding of CFU in Series AA. Minimum residence time for this distribution is 15 min. b: Integrated direction of gliding of CFU at substratum. 0* degree direction is associated with no motion. Direction of flow: 90". 84 Total CFU S e rie s AA 0 .5 N /sqm AVERAGE - 1 .5 8 8 8 7 4 STANDARD DEVIATION - .7 1 5 1 5 8 8 CELLS PER CFU IN FIRST OBSERVATION ACCEPT. 737 OT 884 Total CFU Series AA AVERAGE - 2.027457 0.5 N /sqm - 1.333352 ACCEPT. 682 OF 884 Figure 19. Cells per CFU (Series A A ). a: Number of cells per CFU during first observation. b: Number of cells per CFU during last observation. 85 general gliding direction with the flow. This is also indicated in the tracking images (Figures 5 to 7). Cell Number per CFU The number of cells per CFU has been measured for both the first and the last observation (Figures 19 a and b). These values have been calculated from . area measurement of each CFU and division by standard single cell size (rounded to the next integer value). All CFU have been accepted for this requirement except for daughter-CFU, and entering/ exiting CFU. The comparison of the two plots indicates a growth of the CFU during their observed residence time. Spatial Distribution of CFU during Adsorption Spatial distribution has been calculated for all adsorbing CFU. Daughter-CFU and entering CFU have been excluded. Calculation of spatial distribution was made according to the analysis presented in Appendix A. Figure 20 displays the spatial distribution for adsorbing cells of the experimental series AA2. All results of experimentally measured spatial distributions are presented in Appendix G. 86 Spatial distributions of adsorbing CFU are calculated with the frequency of two Indices of interaction with established colonies: The relative neighbor distance is the index representing the width of "empty field" around the adsorbing CFU. Thus, the relative neighbor distance is an index describing non-interaction between the adsorbing CFU and the established colonies. The relative neighbor distance is a dimensionless number which is calibrated to be 1000 for a perfect uniform distribution. The dimensionless influence number is the index representing the influence of established colonies on the adsorbing CFU. The more dense the colonies„ the greater is the influence number. Thus, the influence number represents an index describing interaction between adsorbing CFU and established colonies. This number is dimensionless and has a value close to 10 for a perfect uniform distribution. This spatial distribution analysis results in a three dimensional graph of the two indices with frequency as the third dimension - The distributions of the experimental values (solid line's) are standardized with calibration distributions generated with computer simulations (dotted lines). The calibration distributions are presented in Figure 20 with dotted lines: uniform distribution (left,top), true random (center), and aggregated (bottom, right). The contour lines have been generated with the 10% to 90% values of the summations of the two indices. Therefore, the center represents the median value of the frequencies, and the contour lines enclose data point 87 frequencies in intervals of 20%. Thusr data of series AA2 can be interpreted as following: The median of adsorbing CFU has a spatial distribution similar to * 40% of true random with a trend to uniform distribution. 10% of adsorbing CFU have a spatial distribution similar to 25% of true random distribution with a trend to aggregated distribution. 10% of adsorbing CFU have a spatial distribution similar to the median of the calibration for uniform distribution. The entire distribution of adsorbing CFU of Series AA2 is a random distribution with a clear trend to uniform distribution. This three-dimensional frequency analysis allows a quantitative description of the distribution in terms of the median value, the width of distribution, and the extreme values. The figures of the spatial distributions (Appendix G) indicate that the distributions at low CFU concentration in the bulk flow and, thus, a low surface concentration have a wide range of variance. The higher the surface concentration the narrower will be the variance of distribution. At the same time the median shifts towards a uniform distribution. The measured distributions show a cIear trend towards uniformity compared with the calibration 88 distribution. This indicates, that the neighborhood of established colonies is blocked for new adsorption. T e s t S e r i e s M 2 , 0 . 5 N / s q m 1 0 * 1 0 e 6 c e l l s / m l V- 10 * - D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 20. Spatial distribution of adsorbing CFU of Series AA2. The measured distribution (solid lines) is superimposed on the calibration distributions (dotted lines). The calibration distributions in the upper left is for uniform, in the center for true random, and in the lower right for aggregated distributions. 89 DISCUSSION ? Sorption-Related Processes Sorption related processes comprise adsorption and desorption, hence processes which carry biomass from the bulk liquid to the substratum and vice versa. the Results section, it was noted that adsorption rates are proportional to the CFU concentration in the bulk flow and also a function of shear stress (Tables I to 3). Depending on two independent variables does not facilitate comparison of adsorption rates obtained under different conditions. Nevertheless, using the definition of Equation 3.2 in terms of CFU and Equation 3.16 in terms of cells, it is possible to separate a factor representing the surface- liquid interaction. In the experimental system used (two variables: CFU concentration in bulk flow, and shear stress) this surface-particle capture factor € depends on shear stress only. With Equation 3.25, it is possible to express a sticking efficiency $ as a function of € and the dimensionless length of the system. This sticking efficiency is the ratio of adsorption rate to flux to the substratum. In addition, this dimensionless factor can be recalculated for systems documented in literature. 90 S T I C K I N G E F F I C I E N C Y C o m p a r i s o n W i t h L i t e r a t u r e a Fletcher (1977) 10 & I S i,0*j o ° Powell and S later (1983) x ±X x - 0.1 Shear Stress (N /sqm) Figure 21. Sticking efficiency $ in comparison with data from Fletcher (1977) and Powell and Slater (1983). Figure 21 displays the sticking efficiency of the experiments in relation to values documented in literature. Data obtained by Fletcher (1977) are from a stagnant system, where sedimentation might have been the main contributing transport mechanism. Powell and Slater's (1983) data were obtained in a flow through system comparable to the one used. From Figure 21 it becomes evident that, indeed, shear stress is controlling the adsorption processes. This can also be seen from the Figures 22 and 23. These figures display the surface-particle capture factors € both in terms of CFU and cells at the substratum. 91 In the Results section it was shown that desorption can be expresses in terms of adsorption. Both rates were found to follow the characteristics of zero order kinetics. This indicates that these processes are, for the length of experiments <5 hours), independent of the accumulation of CFU at the substratum. The independence of desorption can be explained by the concept of reversible and irreversible adsorption. CFU adsorbing to the substratum have a distinct probability to desorb within some time or become irreversibly adsorbed. The probability of desorption, as opposed the rate of desorption, is independent of shear stress (65.9 ± 17.6%). Figure 24 displays probability of desorption in terms of CFU and Figure 25 in terms of cells. The slight trend of a lower probability with increased shear is statistically not significant. Hence, probability of desorption is independent of shear stress.. The solid line represents the mean and the dotted lines the 95% confidence interval. The time interval for reversible adsorption which is sometimes referred to as the "critical residence time" is not a fixed time of x minutes but rather a "critical residence time probability" (see Figure 14b). This time probability is a function of shear stress. Since the frequency is a power function of residence time, the product 9 2 S U R F A C E - P A R T I C L E C A P T U R E F A C T O R ( C F U ) o ; a. : (-0.707S) Shear Stress (N /sqm) Figure 22. Surface-particle capture factor in relation to shear stress. • -# S U R F A C E - P A R T I C L E C A P T U R E F A C T O R ( C E L L S ) Jbfrufffcm.- v = 0.0133 * * ^ °'B3a) Shear Stress (N /sqm) Figure 23. Surf ace-particle capture factor € in relation to shear stress. € for CFU for cells 9 3 PROBABIL ITY OF D E SOR PT IO N ( C F U ) j j s 8-O MO Q 5 Is I I . Ktffnaaion: v a 67 .8» + / - 17.84 0.5 1.0 U Shear Stress (N /sqm ) Figure 24. Probability of desorption of adsorption. of CFU in terms PROBABILITY OF DESORPTION (CELLS) IN 8- : o : COQJ Q 5: H— 'O ^ ^ : I°-o : si 8 : Q- : rtffrtMsion: y = 55.59 + /— 17.4 0.4 0.8 1.2 Shear Stress (N /sqm) Figure 25. Probability of desorption in terms of cell. 94 of residence time and frequency is constant (see Table 8) but varies with shear stress. This dependency is presented in Figure 26. Shear Stress [ N m-1 ] Residence Time Probability t%*min] Standard Error 0.5 59.6 ± 35.7 0.75 50.7 ± 29.8 1.0 39.3 ± 23.2 1.25 37.0 ± 26.4 Table 8. Residence time probability for reversibly adsorbed CFU under different shear stresses. 0.5 N/sqm 0.75 N/sqm 1.0 N/sqm 1.25 N/sqm I I I I I I | I I I I I I Residence Time Reversibly Adsorbed CFU (min) Figure 26. Comparison of residence time of reversibly adsorbed CFU as a function of shear stress. 95 >- Offset Time of Desorption The offset time has a very poor correlation with shear which indicates its independence of it. Data suggest that the offset time is neither a.function of the residence time of reversibly adsorbed biomass nor a function of bulk CFU concentration. The offset time is much longer than the average residence time of reversibly adsorbed CFU. Therefore, it must be the result of the conditioning of the substratum and, hence, a function of the probability to transform from reversible to irreversible adsorption, which might be much greater in the beginning of an experiment than -L^ tsr on. This is indicated by a "ramp" or a low desorption rate during the period of offset time (Figure 8). Indeed, CFU adsorbing very early (first 5 to 15 min) to an almost clean substratum have a probability of close to one to transform to irreversibly adsorbed CFU, whereas CFU's adsorbing later have a probability of about 0.4. This can be translated into the following assumption of two phases of conditioning: I. Conditioning by organic macromolecules, 2. Conditioning by colonies . established at substratum. Thus, the average values from Tables 4 to 7 are used to describe this time interval. 96 Growth Related Processes Growth related processes, such as CFU-separation, multiplication, and erosion, are processes restricted to the biomass immobilized at the substratum. CFU-Separation CFU-separation rates were found to follow a first-order kinetic in terms of CFU at the substratum. One could speculate that CFU-separation should depend on shear stress. CFU separation rate decreases slightly with increased shear stress (Figure 27). This might be the result of a weakening of bonding within the CFU, permitting daughter CFU to glide away from the mother CFU under low shear stress. Under increased stress, this frail connection can break and the disconnected part can reenter the bulk flow. The trend of decreased rates of CFU-separation with increased shear stress is not clearly significant. 97 C F U - S E P A R A T I O N R A T E S -0.00 • JU grw Ion.- y = 0.083 * *xp ( —0.484 * * ) -0.10 Shear Stress (N /sqm ) Figure 27. CFU-separation rates as a function of shear stress. Multiplication Rates Multiplication rates measured were in the range of 0.4 to 0.6 h~1, significantly higher than the growth rate in the chemostat (0.18 h"1) but within the range of maximum growth rate for P. aeruginosa ■ This increased rate can be attributed to several reasons: CFU adsorbing to the substratum are in the process of cell division during adsorption. Thus, the measured multiplication rate is not the growth rate but represents only the in situ observation of cells multiplying. In this case, the concept 98 of growth rate baaed on a generation time ia not fulfilled. Due to immobilization of the biomaaa and the flux of nutrients along the substratum, the organisms "see" more nutrients than they did in the chemostat (no diffusive boundary layer). Still, the observed rate is greater than the normally measured maximum growth rate <0.45 h-1). Due to the selective tprocess of adsorption (sticking efficiency SE 5. oi.008) only highly active cells are adsorbing. If "activity" is expressed in a higher motility, too, then these cells have an advantage over others to adsorb. Figure 28 displays the measured multiplication rates. The solid line represents the total experimental average and the dotted lines the 95% confidence interval. Erosion Erosion rates can be described best with a first order kinetic in terms of cells at the substratum. Data suggest that erosion rates of cells appear to be related to multiplication rates. The more new cells are formed within CFU, the larger the number of cells which can erode. Figure 29 displays the measured erosion rates. Erosion as a probability is displayed in Figure 30. The solid line represents the total experimental average and the doted lines the 95% confidence interval. 99 M U L T I P L I C A T I O N R A T E S ' 0 .6 - D'O -C L- parallel to the slope of the regression has been superimposed. All data 1 2 9 Calibration of Different Distributions D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 35. Frequency contour plot of the calibration distributions. points have been translated into the new coordinate system and the data sorted for a summation curve. This coordinate transformation allows a minimizing of the size of the frequency field. The 10%- through the 90% levels of both x'- and y' coordinates gave the coordinates in the initial coordinate system for the frequency contour plot. The circle formed by the 10%- and the 90% values defines a field containing 80% of all measured values. In Figure 35 this boundary line is called the 20% border line. The frequency 1 3 0 contour plot for each calibration distribution has been calculated and plotted in log-scale (Figure 35). Figure 36 displays the same values as Figure 35 in linear scale to show that transformation of the indices into their logarithms give a good linearization of the problem. Calibration of Different Distributions 1000 '0 100 150 200 250 D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 36. Frequency contour plot (Figure 35) linear scaling. displayed in 131 TEST OF THE SPATIAL DISTRIBUTION Several tests of the distribution analysis have been • First it has been tested whether the distributions are independent of particle (50) numbers per field. Ten fields with half the number of particles compared to the calibration have been generated and analyzed for both uniform and random distributions. No difference could be found compared to the calibration. This test suggest that the two indices are independent of the number of particles per field. Three test distributions with ten fields for each have been generated with a different pattern than the calibration distribution. One of the test distributions has been based on a uniform, and two on an aggregated distribution. Compared to the calibration distribution, they had a much greater degree of randomness. Hence, their frequencies of indices are between true random and the relative calibration distribution. Figures 37, 39, and 41 are examples of these distributions. 1 3 2 Uniform Teat Distribution This test distribution (Figure 37) has a 10 times higher degree of randomness than the uniform calibration distribution (Figure 33). In a visual comparison it appears that this distribution is closer to a random — than a uniform distribution except that a very short nearest neighbor distance for few particles, as found in true random patterns, is missing, but it has some "empty spots" in the field, too. Plotting the frequency contour plot (Figure 38) of this distribution shows that 20% of the points have distribution indices similar to the median of the uniform U N I F O R M D I S T R I B U T I O N S IM U L A T I O N 1 0 0 p p f , d * 1 7 5 % X COORDINATES Figure 37. Example of a uniform test distribution. 1 3 3 Test Uniform Distr. 100 ppf Random: d*175% L- 10 D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 38. Frequency contour plot of the uniform test distribution. calibration, and about 20% are similar to a true random. The median of the test distribution is between random and uniform but clearly not either one. ' V Aggregated Test Distribution I. This test has been generated with five centers and 20 particles per center (Figure 39). The degree of randomness 134 A G G R E G A T E D D I S T R I B U T I O N S IM U L A T I O N 5 * 2 0 p p f , 7 5 * I QceoOO > Figure 39. Example of aggregated test distribution I. around the centers of aggregates has been increased to 75% of the field width, and the centers have been placed randomly. Hence, it is possible that the aggregates can overlap each other. The randomness in this test distribution is clearly visible. However, the frequency of points close to each other is much greater than in a true random distribution. The comparison of the frequency contour plot with the calibration (Figure 40) shows that the median of this distribution is similar to 40% of the true random distribution. The entire distribution covers a wide range from nearly uniform to highly aggregated. X COORDINATES 135 Test Aggregated Distr 5*20ppf Rand: 7556 »_ 10 *- D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 40. Frequency contour plot of aggregated test distribution I. Aggregated Test Distribution 2. The generation of this distribution used 33 centers and three particles per field (Figure 41). In addition, the centers had to be 10% of the field width apart from each other, and the particles had the same random distance (10% of field width). Therefore, an overlap of the aggregates as it was found in Figure 39 was excluded. Each aggregate can 136 A G G R E G A T E D D I S T R I B U T I O N S IM U L A T I O N 3 3 * 3 p p f , 1 0% X COORDINATES Figure 41. Example of aggregated test distribution 2. easily be defined, but overall it appears that this distribution has a fairly even density of particles over the entire field. The frequency contour plot of this distribution (Figure 42) indicates that it is clearly an aggregated distribution, especially in terms of the index for non-interaction, the relative nearest neighbor distance. The median of the index of interaction, the dimensionless influence number, is about half of that of the calibration distribution, which is in good accordance with the number of particle per aggregate (three instead of eight). 1 3 7 Test Aggregated Distr 33*3 ppf Rand.: 10% Figure 42. Frequency contour plot of aggregated test distribution 2. Conclusion of the Test Distributions The tests show that the indices for the spatial distributions are to a large extend independent of the number of particles per field and the field dimension, and they are a useful tool to describe the characteristics of the distribution pattern. Some refinements can be included, such as variance analysis and others which would allow an 138 analysis of skewness or "double-humps" in the frequency contour plot. But the task of this part of the work was to define a base for a measurable system to describe spatial distributions during the process of adsorption. APPENDIX B ORGANIZATION OF DATA FILES 140 ORGANIZATION OF DATA FILES All flies. series. data files are comma separated ASCII sequential The file identifier determines the experimental The following files are created within the sorting routine: 1. 1SUMDATA.XXX 2. ICFUSUMM.XXX 3. 1CFUSEPA.XXX 4. 1CFUENDF.XXX 5. 1CFUDETA.XXX 6. 1CFUEXIT.XXX Summary of events per field. Summary of each observed CFU. Summary of CFU-separation. Summary of CFU observed in last field of the experiments. Summary of cell erosion of each CFU. Summary of CFU exiting the field. Data Organization 1SUMDATA.XXX: One line contains 21 entries. Each image analyzed will be represented in one line. It is a summary of the number of events observed during an experiment, containing the values of number of adsorptions, desorptions, multiplications, and so on. 1234567*9 1. experimental time (from beginning of experiment). 2. time interval between this and the earlier image. 3. counted events of adsorption in terms of CFU. 4. counted events of desorption in terms- of CFU. 5. counted events of entries in terms of CFU. 6. counted events of exits in terms of CFU. 7. counted events of CFU-separation in terms of CFU. S . number of CFU in this field (accumulation) 9. area coverage in this field. 141 H O counted cells. events of adsorption in terms of 1 1 . counted cells. events of desorption in terms of 1 2 . counted events of entries in terms of cells. 13. counted events of exits in terms of cells. 14. counted events of CFU-separation in terms of cells. 15. counted events of cell multiplications in terms of cells. 16. counted events of erosions in terms of cells. 17. number of cells in this field (accumulation). 18. counted events of total increase in terms of CFU. 19. counted events of total decrease in terms of CFU. 20. counted events of total increase in terms of cells. 21. counted events of total decrease in terms of cells. 1CFUSUMM.XXX One line has 15 entries, each CFU is represented in one line. It is a summary of each observed CFU, and contains all relevant data to describe the CFUzS "behavior". 1. CFU number. 2. CFU name index: I - normal, 2 - entry, 3- exit, 4 - daughter, 6 - daughter exit. 3. Field of first observation. 4. Field of last observation. 5. Age of CFU at last observation. 6. Relative nearest neighbor number during adsorption. 7. Areal density influence number during adsorption (non dimensionless). 8. Dimensionless areal density number during adsorption. 9. Orientation of length axis of CFU in first observation (flow direction: 90°). 10. Integrated rate of gliding at substratum from first to last observation Cpm/min] 11. Integrated direction of the gliding in 10 in degrees. 12. Cells per CFU during firs observation. 13. Cells per CFU in last observation. 14. Net growth (13-12), calculated as growth rate Eh"1 1]. 15. Total number of cells eroded from CFU. 142 1CFUSEPA.XXX Separation of CFU, in order of fields. Each line has 9 entries, and each event of separation has one line. CFU number of daughter CFU. Field number of separation. Dummy variable. Cells of "mother" CFU prior to separation. Cells formed in "mother" CFU prior to separation. Distance moved by "mother" CFU prior to separation. Time interval to 6 in min. Age of "mother" CFU prior to separation. Time "mother" CFU exceeds after separation. 1CFUENDF.XXX Summary for each CFU observed in the last field of the experiment. Each line has 4 entries and each CFU detected in the last field has I line. 1. CFU number. 2. Field number of the last field. 3. CFU index (I : normal, 2 : daughter) 4. age of CFU CminJ. ' 1CFUDETA.XXX Summary for each event of erosion of cells from a CFU in order of fields. Each line has 10 entries and each event of erosion has I line. 123456*890 1. CFU number. 2. Field number of observation. 3. Number of erosion events for this CFU prior to this erosion. 4. Number of cells eroded in this event. 5. Number of cells in this CFU prior to this erosion. 6. Net growth of CFU prior to this erosion. .7. Distance moved prior to this erosion. 8. Time interval to 7. 9. Age of CFU prior to erosion. 10. Age of CFU after erosion. 1. 2. 3. 4. 5. 6. 7. 8 . 9. 143 ICFUEXIT.XXX Summary of CFU exiting the Field. Each line has and each CFU exiting has I line. 1. CFU number. 2. Field number of exit. 3. index of CFU CI : normal, 2 : daughter) 4. Age of CFU at last observation. 4 entries 144 APPENDIX C TABLES OF DIRECTLY MEASURED RESULTS 145 Series: AAl Shear Stress: 0.5 N1Iii-2 Cell Concentration: 1.1 ■ 10s cells-ml-1 ZERO ORDER KINETICS RATE (slope) Y-INTERCEPT M 1Itiin-1Tnm-2] /-INTERCEPT CONFIDENCE INTERVAL (95%) ra ± Rate + Y-Interc. Adsorption CFU 8.18 -10.68 1.30 1.00 2.64 8.48 Desorption CFU 7.54 -379.40 50.30 1.00 4.17 39.61 CFU Separation 3.83 -347.50 90.62 1.00 1.70 31.23 Entry CFU 0.22 15.36 -69.00 0.46 0.07 3.74 Exit CFU 0.57 -24.32 42.39 0.88 0.20 5.10 Accumulation CFU 4.20 43.76 -10.42 0.99 . . 1.10 11.42 Adsorption Cell 14.38 64.20 . -4.46 1.00 2.46 11.10 Desorption Cell 11.37 -557.60 49.05 1.00 5.81 61.34 Entry Cell 0.60 27.76 -46.34 0.50 0.18 9.98 Exit Cell 1.18 -51.61 43.62 0.90 0.42 10.02 Multiplication Cell 18.38 -1289.65 70.16 1.00 8.97 122.11 Erosion Cell 10.06 -462.71 45.99 t o o 5.40 51.21 Accumulation Cell 10.50 -51.70 4.93 0.98 2.76 33.55 Area Coverage 0.0012 -0.0074 6.3122 0.9855 0.0003 0,0032 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) [ h-1 ] Rate ± Std. Dev. Multiplication Cell 0.712 0.431 Erosion Cell 0.474 0.386 Desorption CFU 0.766 0.701 Desorption Cell 0.587 0.673 CFU Separation 0.239 0.225 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS W3 Time Offset [min] Desorption CFU 92.18 48.99 Desorption Cells 79.04 53.52 ■ CFU Separation 89.31 Erosion Cell 0. Order 54.73 ■ -24.17 Erosion Cell t Order 76.68 Table 9. Directly measured results of series AAl. 146 Series: AA2 Shear Stress: 0.5 NTir-2 Cell Concentration: 10 • IO6 cells-ml-1 ZERO ORDER KINETICS [#’min-1-mm~2] RATE (slope) Y-INTERCEPT X-INTERCEPT re CONFIDENCE INTERVAL (95%) ± Rate ± Y-Intere. Adsorption CFU 71.86 -1311.83 ' 18.25 0.99 26.40 221.23 Desorption CFU 57.02 -4627.23 81.15 1.02 31.75 384.35 CFU Separation 27.97 -2112.11 75.51 1.03 19.22 169.44 Entry CFU 3.10 -222.38 71.70 0.98 , 1.33 23.51 Exit CFU 15.86 -998.97 62.99 1.02 10.16 89.47 Accumulation CFU 34.79 906.06 -26.04 0.92 ■: 9.14 226.81 Adsorption Cell 135.66 -2429.47 17.91 0.99 47.48 444.69 Desorption Cell 107.03 -9238.21 86.31 1.03 58.56 750.00 Entry Cell 4.97 -302.04 60.75 0.99 2.30 32.43 Exit Cell 30.97 -2394.30 77.31 1.02 17.17 204.13 Multiplication Cell 179.43 -12051.47 67.16 1.03 155.93 979.79 Erosion Cell 108.79 -7505.13 68.99 1.03 81.76 617.23 Accumulation Cell 88.73 1481.38 -16.69 0.94 23.31 530.78 Area Coverage 0.0096 0.1628 -16.8796 0.9342 0.0025 0.0582 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) C h-1 I Rate ± Std. Dev. Multiplication Cell 0.593 0.191 Erosion Cell 0.360 0.209 Desorption CFU 0.355 0.230 Desorption Cell 0.264 0.194 CFU Separation 0.193 0.107 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS M Time Offset CminI Desorption CFU 79.35, 62.89 Desorption Cells 78.90 68.40 CFU Separation 57.25 Erosion Cell 0. Order 60.63 1.83 Erosion Cell I. Order 74.21 Table 10. Directly measured results of series AA2 147 Series: Shear Stress: Cell Concentration: AA3 0.5 N1Hir* 2.75 ■ IO6 cells-ml-1 ZERO ORDER KINETICS RATE (slope) Y-INTERCEPT [#Tnin-1 viinr*] X-INTERCEPT CONFIDENCE INTERVAL (95%) re ± Rate ± Y-Interc. Adsorption CFU 20.50 -634.39 30.95 0.95 6.28 124.39 Desorption CFU 11.11 • -741.19 66.69 1.00 5.29 73.25 CFU Separation 1.86 -205.42 110.54 0.82 0.64 26.57 Entry CFU 0.12 ,40.58 -338.92 0.42 0.03 2.21 Exit CFU 0.55 -38.60 69.72 0.61 0.18 10.17 Accumulation CFU 11.55 -183.52 15.88 0.93 3.04 69.31 Adsorption Cell 34.33 -1109.24 32.31 0.93 10.29 239.13 Desorption Cell 16.70 -1239.08 74.20 1.00 7.89 116.74 Entry Cell 0.21 52.81 -246.84 0.18 0.06 4.61 Exit Cell 0.95 -58.47 61.83 0.54 0.30 19.45 Multiplication Cell 36.61 -2734.06 74.67 0.97 14.97 296.32 Erosion Cell 16.68 -991.49 59.43 0.98 7.17 113.57 Accumulation Cell 35.26 -1145.43 32.48 0.90 9.27 262.67 Area Coverage 0.0039 -0.1291 33.2004 0.8968 0.0010 0.0300 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) C h-1 ] Rate + Std. Dev. Multiplication Cell ■ 0.556 0.336 Erosion Cell 0.290 0.130 Desorption CFU 0.434 0.302 Desorption Cell 0.253 0.172 CFU Separation 0.055 0.071 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS rn Time Offset Emin] Desorption CFU 54.22 35.74 ■ Desorption Cells 48.65 41.89 CFU Separation - 79.59 Erosion Cell 0. Order 45.56 -15.24 Erosion Cell I. Order 58.32 Table 11. Directly measured results of series AA3 148 Series: AA4 Shear Stress: 0.5 NTir2 Cell Concentration: 1.92 ■ IO6 pells-nil-1 CONFIDENCE INTERVAL'(95%) ZERO ORDER KINETICS RATE (slope) Y-INTERCEPT X-INTERCEPT r* ± Rate ± Y-Interc. CSTiiin-1 ^mrr2I Adsorption CFU 13.52 -583.07 ' 43.14 0.97 4.53 73.50 Desorption CFU 10.07 -809.02 80.35 1.01 4.82 72.55 CFU Separation 1.56 -169.30 108.47 0.94 0.60 16.88 Entry CFU 0.00 0.00 0.00 0.00 0.00 0.00 Exit CFU 0.00 0.00 0.00 0.00 0.00 0.00 Accumulation CFU 5.77 -112.96 19.57 0.98 1.52 20.10 Adsorption Cell 16.20 -603.98 37.29 0.97 5.50 79.64 Desorption Cell 10.95 -897.49 81.96 1.00 4.97 83.07 Entry Cell 0.00 0.00 0.00 0.00 0.00 0.00 Exit Cell 0.00 0.00 0.00 0.00 0.00 0.00 Multiplication Cell 12.59 -798.68 63.45 0.98 5.36 89.44 Erosion Cell 7.17 -270.94 37.79 0.97 2.98 40.34 Accumulation Cell 10.86 -277.75 25.58 0.97 2.85 46.86 Area Coverage 0.0012 -0.0298 25.3751 0.9677 0.0003 0.0049 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) I h-1 I Rate ± Std. Dev. Multiplication Cell 0.638 0.337 Erosion Cell 0.482 0.397 Desorption CFU 0.683 0.282 Desorption Cell 0.434 0.189 CFU Separation 0.074 0.107 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS M Time Offset IminI Desorption CFU 74.50 37.21 Desorption Cells 67.61 44.67 CFU Separation 65.33 Erosion Cell 0. Order 56.95 -25.66 Erosion Cell I. Order 63.50 Table 12. Directly measured results of series AA4 149 Series: ABl Shear Stress: 0.5 N'iit2 Cell Concentration: 5.0 ■ IO6 cellsvnl-1 CONFIDENCE INTERVAL (950 ZERO ORDER KINETICS Cjhmin-liImr2] RATE (slope) Y-INTERCEPT X-INTERCEPT r° ± Rate ± Y-Intere. Adsorption CFU 43.45 1297.57 -29.86 0.99 5.51 56.81 Desorption CFU 36.81 -219.01 5.95 0.99 15.04 84.15 CFU Separation 10.86 -535.72 49.35 0.99 5.42 59.58 Entry CFU 3.24 -264.62 81.63 1.01 1.54 23.65 Exit CFU 4.50 -186.82 41.54 0.96 1.79 28.25 Accumulation CFU 14.22 1333.93 -93.82 0.95 . 3.74 71.20 Adsorption Cell 57.51 1818.27 -31.61 0.99 6.51 68.46 Desorption Cell 50.80 -671.08 13.21 1.00 '29.15 134.56 Entry Cell 6.37 -604.31 94.87 1.00 2.81 53.38 Exit Cell 7.65 -296.51 38.76 0.92 2.75 56.73 Multiplication Cell 68.05 -3596.03 52.84 1.01 45.76 342.15 Erosion Cell 34.94 -1852.42 53.02 1.00 19.53 187.49 Accumulation Cell 35.83 1300.59 -36.30 0.99 9.41 96.02 Area Coverage 0.0040 0.1384 -34.7387 0.9889 0.0010 0.0096 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) [ h-1 ] Rate ± Std. Dev. Multiplication Cell 0.550 0.208 Erosion Cell 0.294 0.106 Desorption CFU 0.649 0.326 Desorption Cell 0.500 0.294 CFU Separation 0.180 0.084 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS CO Time Offset [min] Desorption CFU 84.70 35.81 Desorption Cells 88.32 44.83 CFU Separation 79.21 Erosion Cell 0. Order 51.34 0.18 Erosion Cell I. Order 77.11 Table 13. Directly measured results of series ABl 150 Series: AB2 Shear Stress: 0.5 N tit2 Cell Concentration: 2.45 ■ IO6 cells-ml-1 CONFIDENCE INTERVAL (95%) ZERO ORDER KINETICS' CttTdin-1Tiim-2] RATE (slope) Y-INTERCEPT X-INTERCEPT rs ± Rate + Y-Interc. Adsorption CFU 19.34 372.78 -19.28 1.00 3.48 21.49 Desorption CFU 10.24 -518.58 50.65 0.98 4.63 61.28 CFU Separation 2.82 -165.07 58.56 0.99 1.34 17.45 Entry CFU 0.64 61.40 -96.29 0.71 0.17 5.95 Exit CFU 1.29 -96.01 74.24 0.79 0.44 17.10 Accumulation CFU 12.63 580.01 -45.93 0.97 3.32 52.23 Adsorption Cell 30.18 586.39 -19.43 0.99 3.62 29.66 Desorption Cell 15.26 -904.06 59.23 0.98 6.80 100.10 Entry Cell 1.19 54.44 -45.73 0.70 0.34 12.48 Exit Cell 2.34 -183.03 78.37 0.78 0.78 32.23 Multiplication Cell 50.53 -2561.46 50.69 1.01 34.23 248.35 Erosion Cell 35.58 -1976.76 55.55 1.00 18.20 204.35 Accumulation Cell 31.02 658.29 -21.22 0.98 8.15 87.63 Area Coverage 0.0034 0.0653 -19.1055 0.9895 0.0009 0.0080 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) [ h-1 ] Rate ± Std. Dev. Multiplication Cell 0.581 0.243 Erosion Cell 0.394 0.129 Desorption CFU 0.228 0.154 Desorption Cell 0.155 0.112 CFU Separation 0.067 0.061 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS [« Time Offset [min] Desorption CFU 52.94 69.93 Desorption Cells 50.57 78.66 ■ CFU Separation 77.83 Erosion Cell 0. Order 70.41 4.87 Erosion Cell I. Order 67.84 Table 14. Directly measured results of series AB2 151 Series: AB3 Shear Stress: 0.5 N1Hr2 Cell Concentration: 1.1 ■ IO6 CellsTfll-1 CONFIDENCE INTERVAL (95S) ZERO ORDER KINETICS Eft'min-1‘mm-2] RATE (slope) Y-INTERCEPT X-INTERCEPT ra ± Rate ± Y-Interc. Adsorption CFU 5.99 -76.87 12.84 1.00 2.38 13.93 Desorption CFU 2.34 -143.54 61.42 0.94 0.90 18.84 CFU Separation 0.23 -28.31 123.59 0.74 0,08 3.99 Entry CFU 0.39 -38.18 98.34 0.88 0.14 4.69 Exit CFU 0.39 -5.47 13.92 0.91 0.13 2.63 Accumulation CFU 3.89 2.95 -.76 ' 0.99 1.02 8.68 Adsorption Cell 10.43 -129.94 12.46 1.00 4.28 23.22 Desorption Cell 3.73 -236.81 63.57 0.95 1.47 29.29 Entry Cell 0.58 -58.50 100.63 0.87 0.21 7.16 Exit Cell 0.61 -.53 0.86 0.85 0.19 4.86 Multiplication Cell 9.24 -817.75 88.48 1.01 4.31 71.26 Erosion Cell 7.51 -734.60 97.88 0.99 3.17 66.90 Accumulation Cell 8.35 -22.80 2.73 0.99 2.19 18.71 Area Coverage 0.0009 -0.0061 6.5659 0.9893 0.0002 ' 0.0022 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) [ h-1 ] Rate ± Std. Dev. Multiplication Cell 0.306 0.204 Erosion Cell 0.212 0.262 Desorption CFU 0.240 0.239 Desorption Cell 0.181 0.186 CFU Separation 0.015 0.045 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS [%] Time Offset [min] Desorption CFU 39.02 48.58 Desorption Cells 35.73 51.11 CFU Separation • 110.75 Erosion Cell 0. Order 81.20 9.40 Erosion Cell I. Order 75.69 Table 15. Directly measured results of series AB3 152 Series: AB4 Shear Stress: 0.75 N1 nr-2 Cell Concentration: 2.65 ■ 10* cells-ral-1 ZERO ORDER KINETICS Cihmin-1Tmir2] RATE (slope) Y-INTERCEPT X-INTERCEPT r= CONFIDENCE INTERVAL (95%) ± Rate + Y-Intere. Adsorption CFU 18.82 -104.36 ' 5.54 - 1.00 6.99 31.00 Desorption CFU 10.21 -642.99 62.97 1.00 4.87 65.34 CFU Separation 2.92 -315.09 107.98 0.96 1.14 30.54 Entry CFU 0.71 84.31 -118.10 L 12 0.13 2.44 Exit CFU 0.30 -16.60 54.89 0.88 0.11 2.88 Accumulation CFU 12.44 211.74 -17.02 0.99 3.27 27.44 Adsorption Cell 27.33 -150.87 5.52 1.00 9.47 49.79 Desorption Cell 13.44 -883.78 65.77 0.99 6.32 88.74 Entry Cell 1.78 98.73 -55.48 0.90 0.39 8.35 Exit Cell 1.08 -70.43 65.04 0.90 0.39 10.49 Multiplication Cell 37.24 -2490.26 66.87 1.02 22.14 218.94 Erosion Cell 17.66 -1136.92 64.37 1.00 8.83 110.66 Accumulation Cell 33.95 -318.93 9.39 0.99 8.92 56.81 Area Coverage 0.0037 -0.0322 8.7605 0.9952 0.0010 0.0058 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) [ h-1 I Rate ± Std. Dev. Multiplication Cell 0.457 0.191 Erosion Cell 0.210 0.114 Desorption CFU 0.251 0.127 Desorption Cell 0.154 0.096 CFU Separation 0.056 0.061 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS [fl Time Offset. CminI Desorption CFU 54.25 57.42 Desorption Cells 49.17 60.25 CFU Separation 102.44 Erosion Cell 0. Order 47.42 -2.49 Erosion Cell I. Order 61.30 Table 16. Directly measured results of series AB4 153 Series: AB5 Shear Stress: 1.0 N T r 2 Cell Concentration: 6.75 ■ IO6 cells-iul"1 CONFIDENCE INTERVAL (95%) ZERO ORDER KINETICS Ohmin-1Vflm"2] RATE (slope) Y-INTERCEPT X-INTERCEPT ra ± Rate ± Y-Interc. Adsorption CFU 31.31 288.62 -9.22 0.99 4.01 23.00 Desorption CFU 22.17 -1244.63 56.14 1.01 12.33 122.70 CFU Separation 9.65 -959.98 99.52 1.01 4.30 81.89 Entry CFU 0.35 -3.76 10.65 0.48 0.11 7.06 Exit CFU 3.27 -133.07 40.68 0.99 1.58 16.64 Accumulation CFU 16.63 525.60 -31.60 0.98 4.37 49.81 Adsorption Cell 56.01 406.98 -7.27 1.00 8.81 48.33 Desorption Cell 36.99 -2128.77 57.54 1.01 21.22 204.56 Entry Cell 0.67 -45.01 66.88 0.52 0.21' 14.48 Exit Cell 4.89 -185.52 37.90 0.99 2.34 24.27 Multiplication Cell 60.68 -4144.98 68.31 1.00 30.12 393.41 Erosion Cell 29.11 -1844.55 63.37 1.00 13.91 186.48 Accumulation Cell 46.08 405.67 -8.80 0.99 12.11 ’ 113.64 Area Coverage 0.0051 0.0326 -6.4000 0.9873 0.0013 0.0131 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) [ h"1 I Rate ± Std. Dev. Multiplication Cell. 0.465 0.199 Erosion Cell 0.229 0.132 Desorption CFU 0.394 0.174 Desorption Cell 0.295 0.174 CFU Separation 0.126 0.098 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS [%] Time Offset CminI Desorption CFU 70.82 65.36 Desorption Cells 66.05 64.81 CFU Separation 108.74 Erosion Cell 0. Order 47.97 -4.94 Erosion Cell I. Order 74.81 Table 17. Directly measured results of series AB5 154 Series: AB6 Shear Stress: 1.25 N‘in-2 Cell Concentration: 6.9 ■ IO6 cells-ml""1 ZERO ORDER KINETICS RATE (slope) Y-INTERCEPT [#"min-i'mm-2] X-INTERCEPT CONFIDENCE INTERVAL (95%) re ± Rate ± Y-Interc. Adsorption CFU 19.69 681.43 -34.60 0.98 2.71 30.81 Desorption CFU 11.67 6.65 -.57 . 0.97 3.56 37.47 CFU Separation 2.47 -201.91 81.63 1.01 1.17 18.09 Entry CFU 0.00 0.00 0.00 0.00 0.00 0.00 Exit CFU 1.22 -3.50 2.87 0.93 0.38 6.53 Accumulation CFU 9.17 493.03 -53.75 0.95 2.41 46.18 Adsorption Cell 30.42 1024.93 -33.69 0.98 3.74 40.64 Desorption Cell 15.69 17.70 -1.13 0.97 4.75 52.06 Entry Cell 0.00 0.00 0.00 0.00 0.00 0.00 Exit Cell 2.15 -80.35 37.36 0.78 0.70 24.68 Multiplication Cell 49.62 -3206.28 64.61 1.02 33.81 274.91 Erosion Cell 32.37 -2263.54 69.92 1.01 17.43 203.00 Accumulation Cell 29.28 285.62 -9.75 0.99 7.69 63.31 Area Coverage 0.0032 0.0261 -8.1012 0.9913 0.0008 0.0068 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) [ Ir1 ] Rate + Std. Dev. Multiplication Cell 0.563 0.234 Erosion Cell 0.345 0.149 Desorption CFU 0.507 0.419 Desorption Cell 0.336 0.377 CFU Separation . 0.057 0.059 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS M Time Offset [mini Desorption CFU 59.26 34.03 Desorption Cells 51.56 32.56 CFU Separation 116.23 Erosion Cell 0. Order 65.24 5.31 Erosion Cell I. Order 66.20 Table 18. Directly measured results of series ABG. 155 Series: ACl Shear Stress: 0.5 N v r 2 Cell Concentration: 4.7 ■ 10s cellsvnl-1 ZERO ORDER KINETICS [Jtmin-liImr2] RATE (slope) Y-INTERCEPT X-INTERCEPT r* CONFIDENCE INTERVAL (95X) ± Rate ± Y-Intere. Adsorption CFU 35.34 -885.48 25.06 0.99 13.44 120.26 Desorption CFU 27.11 -1821.57 67.19 ■ 1.03 23.95 145.73 CFU Separation 1.71 -153.12 89.66 1.00 0.76 13.84 Entry CFU 0.00 0.00 0.00 0.00 0.00 0.00 Exit CFU 1.72 -184.83 107.32 0.97 0.69 17.14 Accumulation CFU 10.71 415.93 -38.85 0.99 2.81 27.65 Adsorption Cell 46.29 -541.26 11.69 0.99 16.75 114.63 Desorption Cell 27.11 -1821.57 67.19 1.03 23.95 145.73 Entry Cell 0.00 0.00 0.00 0.00 0.00 0.00 Exit Cell . k 2.29 -247.34 107.94 0.95 0.89 24.16 Multiplication Cell 33.39 -1297.31 38.85 1.00 17.59 157.63 Erosion Cell 22.55 -925.91 41.06 1.00 12.29 107.70 Accumulation Cell. 30.90 518.28 -16.77 1.00 8.12 41.56 Area Coverage 0.0034 0.0526 -15.3664 ' 0.9969 0.0009 0.0044 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) r h"1 ] Rate + Std. Dev. Multiplication Cell 0.433 0.238 Erosion Cell 0.286 0.130 Desorption CFU 0.623 0.219 Desorption Cell 0.256 0.087 CFU Separation 0.039 0.043 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS CM /Time Offset [min] Desorption CFU ■ 76.71 42.14 Desorption Cells 58.56 55.50 CFU Separation 64.60 Erosion Cell 0. Order 67.52 2.21 Erosion Cell I. Order 41.13 Table 19. Directly measured results of series ACl 156 Series: AC2 Shear Stress: 0.5 N th-2 Cell Concentration: 3.64 • IO6 cellsTnl-1 ZERO ORDER KINETICS [# iDiin-1-mrr2] RATE (slope) Y-INTERCEPT X-INTERCEPT CONFIDENCE INTERVAL (95%) re ± Rate ± Y-Interc. Adsorption CFU 27.29 348.02 -12.75 0.99 3.75 25.82 Desorption CFU 11.11 -416.25 37.45 1.01 8.24 45.96 CFU Separation 3.48 -312.51 89.90 0.99 1.50 29.03 Entry CFU 0.00 0.00 0.00 0.00 0.00 0.00 Exit CFU 1.58 -136.02 85.93 0.93 0.60 15.66 Accumulation CFU 18.70 446.52 -23.88 0.98 . 4.91 54.60 Adsorption Cell 47.61 604.98 -12.71 0.99 3.20 19.69 Desorption Cell 15.12 -796.17 52.67 1.01 8.83 79.40 Entry Cell 0.00 0.00 ■ 0.00 0.00 0.00 0.00 Exit Cell 3.57 -357.11 99.95 0.95 ' 1.37 36.73 Multiplication Cell 64.77 -5088.74 78.57 1.01 31.87 . 452.85 Erosion Cell 36.33 -2554.09 70.30 1.00 17.66 ' 242.22 Accumulation Cell 54.76 -212.62 3.88 1.00 14.39 78.85 Area Coverage 0.0060 -0.0325 5.3753 0.9959 0.0016 0.0089 FIRST ORDER KINETICS RATE COEFFICIENT (in terras of accumulation) t h-1 3 Rate ± Std. Dev. Multiplication Cell 0.392 0.084 Erosion Cell 0.254 0.068 Desorption CFU , 0.214 0.103 Desorption Cell 0.118 0.056 CFU Separation 0.048 0.044 , i NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS BI Time Offset train] Desorption CFU 40.73 50.21 Desorption Cells 31.75 65.38 CFU Separation 102.65 Erosion Cell 0. Order • 56.10 -8.27 Erosion Cell I. Order 54.94 Table 20. Directly measured results of series AC2. 157 Series: AC3 Shear Stress: 0.75 N v r 2 Cell Concentration: 6.3 ■ 10G cells'ml-1 CONFIDENCE INTERVAL (95%) ZERO ORDER KINETICS [Svnin-1Viirr2] RATE (slope) Y-INTERCEPT X-INTERCEPT + Rate ± Y-Interc. Adsorption CFU 42.61 -1301.42 30.54 0.99 15.93 163.32 Desorption CFU 21.50 -1384.53 64.40 1.00 10.18 139.74 CFU Separation 1.12 -142.49 127.56 0.65 0.37 22.75 Entry CFU 2.68 -136.85 51.05 1.00 1.43 14.42 Exit CFU 3.19 -153.58 48.14 0.98 1.41 19.04 Accumulation CFU 22.99 -325.63 14.16 0.99 . 6.04 50.89 Adsorption Cell 74.17 -2057.54 27.74 0.99 27.20 277.71 Desorption Cell 27.86 -2083.92 74.80 0.95 10.87 241.76 Entry Cell 4.58 -250.45 54.73 0.94 1.76 34.77 Exit Cell 6.36 -483.03 75.92 — 0.96 2.53 53.95 Multiplication. Cell 62.05 -4760.64 76.73 0.98 26.55 481.95 Erosion Cell 46.69 -3670.48 78.62 0.99 20.37 359.70 Accumulation Cell 61.44 -1063.57 17.31 0.99 16.14 138.07 Area Coverage 0.0068 -0.1245 18.2354 0.9895 0.0018 0.0160 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) C h-1 ] Rate .+ Std. Dev. Multiplication Cell 0.431 0.097 Erosion Cell 0.321 0.081 Desorption CFU 0.432 0.148 Desorption Cell 0.206 0.075 CFU Separation 0.012 0.030 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS [%] Time Offset CminI Desorption CFU 50.45 33.86 Desorption Cells 37.56 47.06 CFU Separation 97.02 Erosion Cell 0. Order 75.25 1.89 Erosion Cell I. Order 47.71 Table 21. Directly measured results of series AC3. 158 Series: AC4 Shear Stress: 1,0 N t i t 2 Cell Concentration: 8.7 ■ IO6 cellsTiil-1 CONFIDENCE INTERVAL (95%) ZERO ORDER KINETICS [fl'inirr1 Tiinr2] RATE (slope) Y-INTERCEPT /-INTERCEPT re ± Rate ± Y-Interc. Adsorption CFU 41.33 -979.86 23.71 0.99 16.86 127.66 Desorption CFU 26.78 -2030.40 75.83 1.02 15.21 170.63 CFU Separation 3.75 -375.35 100.17 0.86 1.32 47.73 Entry CFU 0.33 49.21 -150.49 0.84 0.07 2.52 Exit CFU 2.46 -146.61 59.66 0.84 0.84 26.94 Accumulation CFU 19.16 211.87 -11.06 ' 0.99 . 5.03 45.19 Adsorption Cell 73.86 -1333.04 18.05 1.00 33.82 183.44 Desorption Cell 39.92 -3221.78 80.71 1.01 20.38 276.62 Entry Cell 0.72 176.64 -243.83 -1.87 0.09 2.94 Exit Cell 5.52 -486.64 88.22 0.86 1.95 65.37 Multiplication Cell 64.47 -4251.10 65.94 1.03 50.1.1 350.52 Erosion Cell 47.90 -3363.67 70.23 1.03 33.88 274.10 Accumulation Cell 52.60 281.19 -5.35 0.98 13.82 162.50 Area Coverage 0.0058 0.0304 -5.2725 0.9834 0.0015 0.0170 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) [ h-1 ] Rate ± Std. Dev. Multiplication Cell 0.433 0.132 Erosion Cell 0.301 0.099 Desorption CFU 0.410 0.163 Desorption Cell 0.236 0.122 CFU Separation 0.055 0.062 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS [%] Time Offset [min] Desorption CFU 64.79 52.12 Desorption Cells 54.05 62.66 CFU Separation 76.46 Erosion Cell 0. Order 74.29 4.29 Erosion Cell I. Order . 57.41 Table 22. Directly measured results of series AC4 159 Series: AC5 Shear Stress: 1.25 N tit2 Cell Concentration: 12.2 IO6 cells'inl-1 CONFIDENCE INTERVAL (95*) ZERO ORDER KINETICS [STiiin-liEir2] RATE (slope) Y-INTERCEPT /-INTERCEPT re + Rate ± Y-Interc. Adsorption CFU 51.76 -469.66 9.07 1.00 22.57 93.98 Desorption CFU 17.36 -1113.17 64.12 1.02 10.76 98.49 CFU Separation 2.26 -227.69 100.66 0.93 0/86 24.04 Entry CFU 0.22 -29.35 133.12 0.43 0.07 6.60 Exit CFU 2.30 -44.32 19.28 0.95 0.63 12.08 Accumulation CFU 17.30 226.30 -13.08 0.98 4.54 52.43 Adsorption Cell 80.40 -1022.70 12.72 0.99 30.38 196.42 Desorption Cell 28.85 -2283.35 79.15 0.98 12.35 227.42 Entry Cell 1.07 -142.13 132.62 0.45 0.34 30.93 Exit Cell 4.49 -136.30 30.32 0.94 1.64 28.50 Multiplication Cell 73.07 -5104.62 69.85 1.00 35.68 484.20 Erosion Cell 47.79 -3213.26 67.24 1.00 23.26 311.29 Accumulation Cell 56.23 -626.34 11.14 0.99 14.77 144.90 Area Coverage 0.0062 -0.0745 12.0275 0.9883 0.0016 0.0153 FIRST ORDER KINETICS RATE COEFFICIENT (in terms of accumulation) C h-1 ] Rate ± Std. Dev. Multiplication Cell 0.572 0.247 Erosion Cell 0.370 0.183 Desorption CFU 0.336 0.157 Desorption Cell 0.198 0.125 CFU Separation 0.034 0.044 NEGATIVE RATES IN TERMS OF THEIR POSITIVE EQUIVALENTS m Time Offset [mini Desorption CFU 33.54 55.05 Desorption Cells 35.88 ' 66.43 • CFU Separation 91.59 Erosion Cell 0. Order 65.39 -2.61 Erosion Cell I. Order 59.09 Table 23. Directly measured results of series AC5 160 ■ APPENDIX D FIGURES OF KINETIC RESULTS AR EA C OV ER AG E BY C FU IN X CF U (N um be r/s qm m ; 161 AAI, 0 .5 N / s qm , 1.1*1 Oe6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CFU 20000 .13000 10000 3000- □ x V ADSORPT. CUMUL DESORPT. CUUUL CFU SEP. CUMUL ACCUMULATION CFU 0 SO 100 ISO 200 230 300 TIME (m in) AREA COVERAGE BY CFU IN X 2.3- TlME (m in) X AREA COVERAGE Figure 43. Progression of colonization terms of CFU (a) and area coverage (b). (Series AAD in 162 40000 g 30000 I *§ 20000 3 AM, 0 .5 N / s qm , 1 .1 -IOeS CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS I10000 - . .... 0 SO 100 ISO 200 250 300 ADSORPT. CUUUL DES0RPT. CUUUL A C C U U U U m O N CELLS TIME (m in) MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS • UULTtPL CUUUL A EROSION CUUUL ♦ ACCUUULATtON CELLS Figure 44. Progression in terms of cells (Series AAl). Sorption related processes (a) and growth related processes (b) . 163 20000 AA2, 0 .5 N / s qm , 10 • 10e6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CFU ADSORPT. CUUUL | S g . 1 3 0 0 0 10000 SOOO - O X DESORPT. CUUUL CFU SEP. CUUUL ACCUMULATION CFU 100 ISO 200 TIME (min) 250 300 AREA COVERAGE BY CFU IN X W 1.3- TlME (min) X AREA COVERAGE Figure 45. Progression o£ colonization . CE LL S (N um be r/s qm m ) CE LL S (N um be r/s qm m ) 164 AA2, 0 .5 N / sqm , 10 • 10e6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS Mt ArtCfiDDT CADSORf3T. CUMUL DESORPT. CUMUL ACCUMULATION CFllS MULTIPLICATION, EROSION AND ACCUMULATION ♦0000 20000 - 10000 - TIME (min) OF CELLS UULT1PU CUUUL EROSION CUMUL ACCUMULATION CELLS Figure 46. Progression in terms of cells (Series AA2). Sorption related processes (a) and growth related processes (b) . AR EA C OV ER AG E BY C FU IN % CF U (N um be r/s qm m ) 165 20000 13000 10000 3000 - AA3, 0 .5 N / s qm , 2 .7 5 • IOeG CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CFU a AOSORPT. CUUUL X DESORPT. CUUUL V CFU SEP. CUUUL ■ ACCUU ULAT10N CFU 100 130 200 TIME (min) 230 300 AREA COVERAGE BY CFU IN % TIME (min) X AREA COVERAGE Figure 47. Progression of colonization (Series terms of CFU (a) and area coverage (b). AA3) in 166 MULTIPLICATION. EROSION AND ACCUMULATION 40000 30000■ g 20000 ■ O 10000- TlME (min) OF CELLS UULTlPU CUUUL EROSION CUUUL ACCUMULATION CELLS Figure 48. Progression in terms of cells (Series AA3). Sorption related processes (a) and growth related processes (b) . 167 AA4, 0 .5 N / s qm , 1 .92 • 10^6 c e l l s /m l ADSORPTION, DESORPTION AND ACCUMULATION OF CFU 20000 JQ 10 0 0 0 - O 3000 - ISO TIME (min) ADSORPT. CUUUL DESORPT. CUUUL CFU SEP. CUUUL ACCUUULATION CFU AREA COVERAGE BY CFU IN X 2.3 - TIME (min) X AREA COVERAGE Figure 49. Progression of colonization (Series AA4) in terms of CFU (a) and area coverage (b). CE LL S (N um be r/s qm m ) CE LL S (N um be r/s qm m 168 AA4, 0 .5 N / s qm , 1 .92 * 10^*6 c e l l s /m l ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS 40000■ 30000• 20000 - 10000 - * o ♦ 50 100 150 200 250 300 TIME (min) ADSORPT. CUUUL DESORPT. CUUUL ACCUUULAT10N CELLS 40000 MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS 30000 - 20000 10000 * UULTIPL. CUUUL A EROSION CUUUL ♦ ACCUUULATION CFIIS 100 150 200 TIME (min) 250 300 Figure 50. Progression in terms of cells (Series AA4). Sorption related processes (a) and growth related processes (b) . AR EA C OV ER AG E BY C FU IN % CF U (N um be r/s qm m ; 169 20000 ABI, 0 .5 N / s qm , 5 .0 • 1 0 e6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CFU .1 0 0 0 0 ■ 10000 0000 - O ADSORPT. CUUUL X DESORPT. CUUUL T CFU SEP. CUUUL ■ ACCUU ULMlON CFU 00 100 100 200 200 300 TIME (min) AREA COVERAGE BY CFU IN X TIME (min) X AREA COVERAGE Figure 51. Progression of colonization (Series terms of CFU (a) and area coverage (b). ABl) in 1 7 0 MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS ------------------ --------------- ---------------- ♦ UULT1PL CUUUL A EROSION CUUUL ♦ ACCUUUIXnON CELLS 40000 20000 ■ O 1 0 0 0 0 - TIME (min) Figure 52. Progression in terms of cells (Series ABl). Sorption related processes (a) and growth related processes . 171 SERIES AB2; 0 .5 N / s qm , 2 .45 . 10 e6 CFU/ml AnsnPDTiriKl n c - c - — ..... ........... ..... • V ■ ADSORPT. CUUUL DESORPT. CUUUL CFU SEP. CUUUL ACCUUULABON CFU area coverage by CFU in X TIME (min) X AREA COVERAGE Figure 53. Progression of" colonization (Series AB2) in terms o£ CFU (a) and area coverage (b). 172 0 .5 N / s qm , 2 .45 40000 5 30000 g 20000 - 10000 - TIME (min) MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS - — -- --------- ♦ UULTIPL. CUMUL A EROSION CUMUL ♦ ACCUMULATION CELLS 40000 g 20000• O 10000 - TIME (min) Figure 54. Progression in terms of cells (Series AB2). Sorption related processes (a) and growth related processes (b) . 173 20000 AB3; 0 .5 N / s qm , 1.1 . 10e6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CFU 13000 -1 JD 1 0 0 0 0 3 5. 2O 0000 - O X V ■ ADSORPT. CUUUL DESORPT. CUUUL CIrU SEP. CUUUL ACCUUULAT10N CFU 60 100 150 200 250 300 TIME (min) 2 .5 - g ^ fS y 1.3 8 H I .5 AREA COVERAGE BY CFU IN X ♦ X AREA COVERAGE 100 ISO 200 250 300 TIME (min) Figure 55. Progression of colonization (Series AB3) in terms of CFU (a) and area coverage (b). 174 AB3; 0 .5 N / sqm , 1.1 . 10e6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS -------------------------- * ADSORPT. CUUUL o DESORPT. CUUUL ♦ ACCUUULATION CELLS 40000 g 20000■ 10000 ■ TIME (min) 40000 MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS II 30000 - 20000 IO 10000 UULTIPL CUUUL A EROSION CUUUL ♦ ACCUUULATION CELLS 100 ISO 200 TIME (min) 250 300 Figure 56. Progression in terms of cells in terms of CFU (a) and area coverage (b). CE LL S (N um be r/s qm m ) 176 AB4; 0 .7 5 N / s qm . 2 .6 5 • 10e6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS * ADSORPT. CUUUL O DESORPT. CUMUL ♦ ACCUMULATION CELLS MULTIPLICATION, EROSION AND ACCUMULATION 40000 20000 ■ 10000 • TIME (min) OF CELLS M U L H P L CUMUL EROSION CUMUL ACCUMULATION CELLS Figure 58. Progression in terms o£ cells (Series AB4). Sorption related processes (a) and growth related processes (b) . AR EA C OV ER AG E BY C FU IN % CF U 177 AB5; 1 .0 N / s q m , 6 . 7 5 . IOeG C FU /m l ADSORPTIONT-SESORPTION AND ACCUMULATION OF CFU --------------- --------------------- ---------------- n ADSORPT. CUUUL X DESORPT. CUUUL V CFU SEP. CUUUL ■ ACCUMULATION CFU 20000 10OOO - SOOO ■ TIME (min) AREA COVERAGE BY CFU IN X TIME (min) % AREA COVERAGE Figure 59. Progression of colonization (Series terms of CFU (a) and area coverage (b). AB5) in CE LL S (N um be r/ sq m m ) CE LL S (N um be r/ aq m m ) 178 AB5; 1.0 N / s qm , 6 .75 • 10e6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS ADSORFT. CUMUL O DESORPT. CUUUL ♦ ACCUMULATION CELLS MULTIPLICATION, EROSION AND ACCUMULATION 40000 30000 - 20000 - 10000 - TIME (min) OF CELLS UULTlPL CUUUL EROSION CUUUL ACCUMULATION CEU-S Figure 60. Progression in terms of cells (Series AB5). Sorption related processes (a) and growth related processes ( b ) . 179 AB6; 1 .25 N / s qm , 6.9 • 10e6 CFU/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CFU 20000 13000 - 10000■ 3000 - 130 TIME (min) ADSORFrT. CUMUL DESORPT. CUUUL CPU SEP. CUUUL ACCUMULATION CFU AREA COVERAGE BY CFU IN X W 1.3- TlME (min) X AREA COVERAGE Figure 61. Progression of colonization (Series AB6) in terms of CFU (a) and area coverage (b)] 180 AB6; 1 . 2 5 N / s q m , 6 .9 • 1 0 e 6 ADSORPTION, DESORPTION AND ACCUMULATION 40000 g 20000■ 10000 - TIME (min) MULTIPLICATION, EROSION AND ACCUMULATION 40000 20000 - O 10000- TIME (min) OF CELLS ADSORPT. CUUUU DESORPT. CUUUL A C C U U U U m O N CELLS C FU /m l OF CELLS UULT1PL. CUUUL EROSION CUMUL ACCUMULATION CELLS Figure 62. Progression in terms of cells (Series AB6). Sorption related processes (a) and growth related processes . 181 A C I ; 0 . 5 N / s q m , 4 . 7 • 1 0 e 6 C FU /m l OF CFU ADSORPT. CUUUL DCSORPT. CUUUL CFU SEP. CUUUL ACCUUULM10N C m AREA COVERAGE BY CFU IN X TIME (m in) % AREA COVERAGE Figure 63. Progression of colonization (Series AC1) in terms of CFU (a) and area coverage (b). 182 ACI; 0 .5 N /sqm , 4 .7 * 10e6 CFU/m l ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS g 20000 • 10000 ■ TIME (min) ADSORPT. CUUUL DE30RPT. CUUUL ACCUUULAT10N CELLS MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS -------------- ------------- * UULTlPL CUUUL A EROSION CUUUL ♦ ACCUUULAHON CELLS 40000 30000■ g 20000 ■ O 10000 TIME (min) Figure 64. Progression in terms of cells (Series ACl). Sorption related processes (a) and growth related processes (b) . 183 AC2; 0 . 5 N / s q m , 3 . 6 4 ' 1 0 e 6 C F U /m l D ADSORPT. CUUUL X DESORPT. CUUUL V CfU SEP. CUUUL ■ ACCUUULATION CFU AREA COVERAGE BY CFU IN % TIME (min) * AREA COVERAGE Figure 65. Progression of colonization (Series AC2) in terms of CFU (a) and area coverage (b). CE LL S (N um be r/s qm m ) CE LL S (N um be r/a qm m ) 184 AC2; 0 .5 N /sqm , 3 .6 4 • 10e6 CFU/m l ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS 40000 20000 - 10000 - TIME (min) ADSORPT. CUMUL DESORPT. CUUUL ACCUMULATION CELLS MULTIPLICATION, EROSION AND ACCUMULATION 20000- ioooo- TIME (min) OF CELLS UULTLPU CUUUL EROSION CUMUL ACCUMULATION CELLS Figure 66. Progression in terms of cells (Series AC2). Sorption related processes (a) and growth related processes (b) . BY C FU IN % CF U (N um be r/s qm m ) 185 I 20000 10000 10000- 0000 AC3; 0 .7 5 N /sqm , 6 .3 • IOeG CFU/m l ADSORPTION, DESORPTION AND ACCUMULATION OF CFU D ADSORPT. CUUUL X DESORPT. CUUUL V CFU SEP. CUUUL rn ACCUU ULXTl ON CFU 100 100 200 TIME (min) 200 300 AREA COVERAGE BY CFU IN X TIME (min) X AREA COVERAGE Figure 67. Progression of colonization (Series terms of CFU (a) and area coverage (b). AC3) in 186 ADSORPTION. DESORPTION AND ACCUMULATION OF CELLS -------------- ----------------------- ------------- • ADSORPT. CUUUL O DESORPT. CUUUL ♦ ACCUUULAHON CELLS C3; 0 . 7 5 N / s q m , 6 . 3 • IOeG C FU /m l 40000 10000■ TIME (min) MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS --------------------------------------------------- * UULT1PL. CUUUL A EROSION CUUUL ♦ ACCUUULATION CELLS 40000 g 20000■ O 10000- TlME (min) Figure 68. Progression in terms of cells (Series AC3). Sorption related processes (a) and growth related processes (b) . 187 AREA COVERAGE BY CFU IN X TIME (min) % AREA COVERAGE Figure 69. Progression of colonization (Series AC4) in terms of CFU (a) and area coverage (b). 188 1.0 N /sqm , 8 .7 adsorption, desorption an d a c c u mulation o f cells ♦ ADSORPT. CUUUL ♦ DESORPT. CUUUL ♦ A C C U U U U m O N CELLS 40000 E joooo E 20000 - 10000 - TIME (min) MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS ' ------------ * UULTIPL. CUUUL A EROSION CUUUL ♦ ACCUU ULATION CELLS 40000 E 20000 - O 10000 - TIME (min) Figure 70. Progression in terms of cells . AC5) in 1 9 0 ADSORPTION. DESORPTION AND ACCUMULATION OF CELLS 4 0 0 0 0 -------------------------------------------------------- -------------------------------------- • ADSORPT. CUUUL ACS; 1 . 2 5 N / s q m , 1 2 . 2 • IOeG C FU /m l » DESORPT. CUUUL ♦ ACCUUULATION CELLS 100 150 200 250 300 TIME (min) MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS ----- --------------------------------------------- ♦ UULT1PL. CUUUL A EROSION CUUUL ♦ ACCUUULATION CELLS 40000 .30000 - 20000 - O 10000 - TIME (min) Figure 72. Progression in terms of cells (Series AC5). Sorption related processes (a) and growth related processes . 191 APPENDIX E TABLES OF DERIVED RESULTS 192 Analysis of Adsorption Series AAl CFU Cone, [#/mll ( • 10G ) I.10 Shear Stress [NTr-2J: .50 Observed Adsorption CFU [tt'iror'-nin-1] 8.18 Observed Ads. Cells [S1InirliInin-1] 14.38 Other Important Parameters: Geometry of tube [mml: Width: 4.00 Half Height: .09 Transport Parameters: Diffusivity [mm2is-13 10-3 Viscosity [N1S1In-1] 10-3 Adsorption and Transport CFU Adsorption coefficient €: .01125 Transport rate: 964.06 Ratio Transp./ Adsorpt. [jC] .85 Adsorption and Transport Cells Adsorption coefficient €: .01991 Transport rate: 964.06 Ratio Transp./ Adsorpt. M] 1.49 Table 24. Derived results of series AAl. Analysis of Adsorption Series AA2 CFU Cone. [#/ml] ( 1 IO6 ) 10.00 Shear Stress [NTn--2O: .50 Observed Adsorption CFU [STnrn- 1Tnin- 1 ] 71.86 Observed Ads. Cells [STnrn- l i Inin- 1 ] 135.66 Other Important Parameters: Geometry of tube CmrnO: Width: 4.00 Half Height: .09 Transport Parameters: Diffusivity Cmm2iS-1] 10-3 Viscosity CN1S1In-1] 10-3 Adsorption and Transport CFU Adsorption coefficient €: .01087 Transport rate: 8764.17 Ratio Transp./ Adsorpt. M .82 Adsorption and Transport Cells Adsorption coefficient 6: .02067 Transport rate: 8764,17 Ratio Transp./ Adsorpt. [Jt] 1.55 Table 25. Derived results of series AA2 193 Analysis of Adsorption Series AA3 CFU Cone. [#/ral] ( - 10*) 2.75 Adsorption and Transport CFU Shear Stress CNiIir*]: 5 0 ■ Adsorption coefficient €: .01128 Observed Adsorption CFU C S 1Iiim"1 "nin-1] 20.50 Transport rate: 2410.15 Observed Ads. Cells C# 1Hinr'11min"1] 34.33 Ratio Transp./ Adsorpt. CM .85 Other Important Parameters: Adsorption and Transport Cells Geometry of tube Cmm]; 4.00 Adsorption coefficient €: .01900Width: Half Height: .09 Transport rate: 2410.15 Ratio Transp./ Adsorpt. CM 1.42 Transport Parameters: Diffusivity CmmeiS"1] 10"3 Viscosity CN1S1Iir1] 10"3 T a b l e 2 6 . D e r i v e d r e s u l t s o f s e r i e s A A 3 . Analysis of Adsorption Series AA4 CFU Cone. C#/ml] ( • IO6 ) Shear Stress CN1Ir*]: 1.92 .50 Adsorption and Transport CFU Adsorption coefficient €: .01065 Observed Adsorption CFU C#'mrii"1■min"1] 13.52 Transport rate: 1682.72 Observed Ads. Cells Ctt1Iiim-liIiiin"1] 16.20 Ratio Transp./ Adsorpt. CM .80 Other Important Parameters: Adsorption and Transport Cells Geometry of tube Cmm]: 4.00 Adsorption coefficient €: .01278Width: Half Height: .09 Transport rate: 1682,72. Transport Parameters: Ratio Transp./ Adsorpt. CM .96 Diffusivity CrnmeiS"1] IQ"3 Viscosity CN-s-m"1] IQ-3 Table 27. Derived results of series AA4. 194 Analysis of Adsorption Series ABl CFU Cone. [#/ml] ( ■ IO6 ) 5.00 Adsorption and Transport CFU Shear Stress tM'ir2]: .50 Adsorption coefficient €: .01317 Observed Adsorption CFU [#-nm_1 tHiin-1] 43.45 Transport rate: 4382.09 Observed Ads. Cells CAtMm-ltMin-1] 57.51 Ratio Transp./ Adsorpt. C%] .99 Other Important ParaMeters: ' Adsorption and Transport Cells Geometry of tube Cmm]: Width: 4.00 Adsorption coefficient G: .01748 Half Height: .09 Transport rate: 4382.09 Ratio Transp./ Adsorpt. C%] 1.31 Transport Parameters: Diffusivity Cmm2tS-1] !Cr2 Viscosity CNtStM-1] 10-3 T a b l e 2 8 . D e r i v e d r e s u l t s o f s e r i e s A B l . Analysis of Adsorption Series AB2 CFU Cone. CAM] ( - IO6 ) 2.45 Adsorption and Transport CFU Shear Stress CNtM-2!: .50 Adsorption coefficient €: .01195 Observed Adsorption CFU CAtMm-1•min-1] 19.34 Transport rate: 2147.22 Observed Ads. Cells CAtMm-1-min-1] 30.18 Ratio Transp./ Adsorpt. CW .90 Other Important Parameters: Adsorption and Transport Cells Geometry of tube Cmm]; Width: 4.00 Adsorption coefficient €: .01874 Half Height: .09 Transport rate: 2147.22 Ratio Transp./ Adsorpt. Cti 1.41 Transport Parameters: Diffusivity Cmm2tS-1] IQ-3 Viscosity CNtStM-1] IQ-3 Table 29. Derived results of series AB2. 195 Analysis of Adsorption Series AB3 CFU Cone. ( • IO6 ) 1.10 Shear Stress [N-ir^]: .50 Observed Adsorption CFU Cft1IEi-1-min-1] 5.99 Observed Ads. Cells Cft1Mm-liMin-1] 10.43 Other Important Parameters: Geometry of tube Crum]: Width: 4.00 Half Height: .09 Transport Parameters: Diffusivity CmmeiS-1] 10-3 Viscosity CN'S'm-1] 10-3 Adsorption and Transport CFU Adsorption coefficient €: .00822 Transport rate: 964.06 Ratio Transp./Adsorpt. CU] . .62 Adsorption and Transport Cells Adsorption coefficient €: .01438 Transport rate: 964.06 Ratio Transp./ Adsorpt. DG 1.08 Table 30. Derived results of series AB3. Analysis of Adsorption Series AB4 CFU Cone, [ft/ml] ( 1 IO6 ) 2.65 Shear Stress CN1Iir2]: .75 Observed Adsorption CFU Cft1Mm-liMin-1] 18.82 Observed Ads. Cells Cft1Mm-liMin-1] 27.33 Other Important Parameters: Geometry of tube Crnrn]: Width: 4.00 Half Height: .09 Transport Parameters: Diffusivity Cmm2iS-1] 10-3 Viscosity CN1S1M-1] 10-3 Adsorption and Transport CFU Adsorption coefficient €: .01073 Transport rate: 2658.60 Ratio Transp./ Adsorpt. DG .71 Adsorption and Transport Cells Adsorption coefficient €: .01563 Transport rate: 2658.60 Ratio Transp./ Adsorpt. DG 1.03 Table 31. Derived results of series AB4. 196 Analysis of Adsorption Series AB5 CFU Cone. [#/ml] ( - 10*) Shear Stress [Ntii--Z]: 6.75 Adsorption and Transport CFU I nn Observed Adsorption CFU [#-min-1-min-1] Observed Ads. Cells [STiim-1Tiiin"1] Adsorption coefficient €: 31.33 Transport rate: 56.01 Ratio Transp./ Adsorpt. K] .00699 7453.46 .42 Other Important Parameters: Geometry of tube [mm]: Width: Half Height: Transport Parameters: Adsorption and Transport Cells 4.00 .09 Adsorption coefficient €: Transport rate: Ratio Transp./ Adsorpt. [%] .01254 7453.46 .75 Diffusivity [KimeiS-1] Viscosity [N1S1M"1] 10"3 !Cr= T a b l e 3 2 . D e r i v e d r e s u l t s o f s e r i e s A B 5 . Analysis of Adsorption Series AB6 CFU Cone. [#/nl] ( • IO6 ) Shear Stress [N1M-Z]; 6.90 1.25 Adsorption and Transport CFU Adsorption coefficient €: .00429 Observed Adsorption CFU Hhmm-liInin-1] 19.69 Transport rate: 8207.42 Observed Ads. Cells [Whmm-liMin"1] 30.42 Ratio Transp./ Adsorpt. [%] .24 Other Important Parameters: Adsorption and Transport Cells Geometry of tube [rum]: Width: 4.00 Adsorption coefficient 6: .00664 Half Height: .09 Transport rate: 8207.42 Ratio Transp./ Adsprpt. [%] .37 Transport Parameters: Diffusivity ImmeiS"1] IQ"3 Viscosity [N1S1M"1] JO"3 Table 33. Derived results of series AB6. 197 Analysis of Adsorption Series ACl CFU Cone. r#/ml] ( ■ IO6 ) 4.70 Adsorption and Transport CFU Shear Stress IN-im2]: .50 . Adsorption coefficient €: .01138 Observed Adsorption CFU [S1Hira-1‘min-1] 35.34 Transport rate: 4119.16 Observed Ads. Cells [S-imr1,■min-1] 46.29 Ratio Transp./ Adsorpt. [#] .86 Other Important Parameters: Adsorption and Transport Cells Geometry of tube ImraI: Width: 4.00 Adsorption coefficient €: .01494 Half Height: .09 Transport rate: 4119.16 Ratio Transp./ Adsorpt. [%] 1.12 Transport Parameters: Diffusivity [mmai5-1] !Cr= Viscosity [N1S1Iir1] 10-a T a b l e 3 4 . D e r i v e d r e s u l t s o f s e r i e s A C l . Analysis of Adsorption Series AC2 CFU Cone. [#/ml] ( - IO6 ) Shear Stress IN1HT*I: 3.64 .50 27.29 47.61 Adsorption and Transport CFU Observed Adsorption CFU [ S 1Iiira-1 Tiiin-1] Observed Ads. Cells [S'lrar^ rain-1] Adsorption coefficient €: Transport rate: Ratio Transp./Adsorpt. [%] .01134 3190.16 .86 Other Important Parameters: Geometry of tube [mm]: Width: Half Height: Transport Parameters: Adsorption and Transport Cells 4.00 .09 Adsorption coefficient €: Transport rate: Ratio Transp./ Adsorpt. Ift .01992 3190.16 1.49 Diffusivity IramaiS-1] Viscosity [N-s-ir1] IQ"3 IQ-3 Table 35 Derived results of series AC2. 198 Analysis of Adsorption Series AC3 CFU Cone. [#/rnl] ( • IO6 ) 6.30 Shear Stress [N*ir23: .75 Observed Adsorption CFU'[S-mnr^nin”1] 42.61 Observed Ads. Cells [tt’innr1 iHiin-1] 74.17 Other Important Parameters: Geometry of tube [mm]: Width: 4.00 Half Height: .09 Transport Parameters: Diffusivity Emm21S-1] 10-3 Viscosity CN'S'm-1] 10-3 Adsorption and Transport CFU Adsorption coefficient €: .01021 Transport rate: 6320.46 Ratio Transp./ Adsorpt. W] .67 Adsorption and Transport Cells Adsorption coefficient €: .01787 Transport rate: 6320.46 Ratio Transp./ Adsorpt. K] 1.17 Table 36. Derived results of series AC3. Analysis of Adsorption Series AC4 CFU Cone. [#M ] ( ■ IO6 ) 8.70 Shear Stress [N1Ir2I: 1.00 Observed Adsorption CFU Hf-mm-1-min-1] 41.33 Observed Ads. Cells [S'rnm-1iInin-1] 73.86 Other Important Parameters: Geometry of tube [mm]: Width: 4.00 Half Height: .09 Transport Parameters: Diffusivity [mm2is-1] 10-3 Viscosity [N-s-m-1] 10-3 Adsorption and Transport CFU Adsorption coefficient €: .00716 Transport rate: 9606.68 Ratio Transp./ Adsorpt. [%] .43 Adsorption and Transport Cells Adsorption coefficient €: .01283 Transport rate: 9606.68 Ratio Transp./ Adsorpt. [%] .77 Table 37. Derived results of series AC4. 199 Analysis of Adsorption Series AC5 CFU Cone. [#/ml] ( • IO6 ) 12.20 Shear Stress CMTir2]: 1.25 Observed Adsorption CFU [St e t 1 iHiin-1] 51.76 Observed Ads. Cells CS-mm-'-minr1] 80.40 Other Important Parameters: Geometry of tube [ram]: Width: 4.00 Half Height: ,09 Transport Parameters: Diffusivity CmmeiS-1] 10“3 Viscosity [N1STr1] 10-3 Adsorption and Transport CFU Adsorption coefficient €: .00639 Transport rate: 14511.67 Ratio Transp./ Adsorpt. HG .36 Adsorption and Transport Cells Adsorption coefficient 6: .00994 Transport rate: 14511.67 Ratio Transp./ Adsorpt. CH .55 Table 38. Derived results of series AC5. 200 APPENDIX F DISTRIBUTIONS OF "BEHAVIORAL" •1 CHARACTERISTICS 201 Total CFU Series AA 0.5 N /sqm AVERAGE - 67.2638 STANDARD DEVIATION - 83 .90284 SS3SSSSS828SSSSRSS|2ggSSSS8| ACCEPT. 813 OF 884 TOTAL RESIDENCE TIME [min] Total CFU Series AA 0.5 N /sqm AVERAGE - 15.9973 STANDARD DEVIATION - 27 .11492 ACCEPT. 371 OF 884 FINITE RESIDENCE TIME [min] Figure 73. Residence time distribution Series AA <0.5 N m""1). a: Total residence time distribution representing all CFU except the ones entering or exiting, b. Finite residence time of series AA. Only CFU were accepted where adsorption and desorption has directly been observed (no daughter-CFU, entering, exiting, or CFU exceeding last image of the experiments). This distribution represents for reversibly adsorbed CFU the probability in respect to time to remain at the substratum. 202 Total CFU 0.75 N/sqm AVERAGE - 80.74246 STANDARD DEVIATION - 0SSSS88R8S85gS5S8R8Sge§gS88S8| 91.41666 ACCEPT. 431 OT 476 TOTAL RESIDENCE TIME [mini Total CFU 0.75 N /sqm AVERAGE - 8.411765 STANDARD DEVIATION - 0”258a83S38383RK838883228883S38 FINITE RESIDENCE TIME [mini 19.78005 ACCEPT. 170 or 476 Figure 74. Residence time distribution <0.75 N m™1). Q- Total residence time distribution representing all CFU except the ones entering or exiting. b: Finite residence time. Only CFU were accepted where adsorption and desorption has directly been observed (no daughter-CFU, entering, exiting, or CFU exceeding last image of the experiments). This distribution represents for reversibly adsorbed CFU the probability in respect to time to remain at the substratum. 2 0 3 Total CFU 1.0 N/sqm ■ 71.1368 STANDARD DEVIATION - 81.6892 ACCEPT. 31 AVERAGE =2SS938RgS828SS8SRS2 TOTAL RESIDENCE TIME CmtnJ Total CFU 1.0 N /sqm AVERAGE - 9.336283 STANDARD DEVIATION 0”2S8aS33SS38SRR838S88528aS3SS8 22.64219 ACCEPT. 226 OF 338 FINITE RESIDENCE TIME [mini Figure 75. Residence time distribution (1.0 N m~i). a: Total residence time distribution representing all CFU except the ones entering or exiting. b: Finite residence time. Only CFU were accepted where adsorption and desorption has directly been observed (no daughter-CFU, entering, exiting, or CFU exceeding last image of the experiments). This distribution represents for reversibly adsorbed CFU the probability in respect to time to remain at the substratum. 204 T o t a l C F U 1 . 2 5 N / s q m 75.72207 ----------------AVERAGE STANDARD DEVIATION - 94.07856 ACCEPT. 367 or 3 M S8SS88R8S8e8RS88g88|S§8S3|g|8 TOTAL RESIDENCE TIME [mini T o t a l C F U 1 . 2 5 N / s q m AVERAGE - 9.036144 STANDARD DEVIATION - 228S83SSS38SeRSS888S5S8888S5S FINITE RESIDENCE TIME [mini 21.2126 ACCEPT. I M or 363 Figure 76. Residence time distribution (1.25 N ). a: Total residence time distribution representing all CFU except the ones entering or exiting. b: Finite residence time. Only CFU were accepted where adsorption and desorption has directly been observed (no daughter-CFU, entering, exiting, or CFU exceeding last image of the experiments). This distribution represents for reversibly adsorbed CFU the probability in respect to time to remain at the substratum. 205 Total CFU Series AA 0.5 N /sqm AVERAGE - 48.53971 STANDARD DEVIATION - 43 .25285 2Z5 43 67J 60 1123 133 1373 ORIENTATION OF CFU IN I . FIELD OF 884 Figure 77. Orientation o£ CFU after adsorption. Shear stress: 0.5 NZm2. Direction of flow: 90*. Total CFU 0.75 N/sqm - 44.82351 ACCEPT. 401 OT 476 Figure 78. Orientation of CFU after adsorption, stress: 0.75 NZm2. Direction of flow: 90". Shear 2 0 6 T o t a l C F U 1 . 0 N / s q m AVERAGE - 45.10967 STANDARD DEVIATION - 44.12158 60 I lZ S 133 137J ORIENTATION OF CFU IN I . FIELD Figure 79. Orientation of CFU after adsorption. Shear stress: 1.0 N/m'. Direction of flow: 90*. T o t a l C F U 1 . 2 5 N / s q m AVERAGE - 34.73514 STANDARD DEVIATION - 42.38683 ^ ACCEPT. 341 o r 393 Figure 80. Orientation of CFU after adsorption. Shear stress: 1.25 NZm2. Direction of flow: 90*. 207 Total CFU Series AA 0.5 N /sqm :E - 2 .17Z527E—02 STANDARD DEVIATION - .0385397 ^ ACCEPT. 870 Of 884 INTEGRATED RATE OF GUDING tum /m lnl INTEGRATED DIRECTION OF GUDING Figure SI. Integrated movement at substratum (Series AA, 0.5 N m™2). a: Integrated rate of gliding of CFU in Series AA. Minimum residence time for this distribution is 15 min. b: Integrated direction of gliding of CFU at substratum. 0’ degree direction is associated with no motion. Direction of flow: 90°. 208 Total CFU 0.75 N /sqm AVERAGE - 1 .147112E—02 STANDARD DEVIATION - ^R ~ 3.034939E-02 ACCEPT. 474 OT 476 INTEGRATED RATE OF GUDING [um /m lnl Total CFU 0,75 N/sqm AVtitAte - 7S.96 STANDARD DEVIATION - 96.3457 INTEGRATED DIRECTION OF GUDING Figure 82. Integrated movement at substratum (0.75 N m~2). a: Integrated rate of gliding of CFU in Series AA. Minimum residence time for this distribution is 15 min. b: Integrated direction of gliding of CFU at substratum. 0* degree direction is associated with no motion. Direction of flow: 90". 2 0 9 Total CFU 1.0 N /sqm AVERAGE - 2 .21B445E-02 STANDARD DEVIATION - 4 .616306E-02 ^ ACCEPT. M O or ase INTEGRATED RATE OF GUDING [um /m lnl Total CFU 1.0 N/sqm AVERAGE - 75.1928 STANDARD DEVIATION - 82.9351 3 9 2 8 i 3 I 8 I 8 I S I INTEGRATED DIRECTION OF GUDING Eisj ACCEPT. S M or M e Figure 83. Integrated movement at substratum (1.0 N m~* >. a: Integrated rate of gliding of CFU in Series AA. Minimum residence time for this distribution is 15 min. b: Integrated direction of gliding of CFU at substratum. 0* degree direction is associated with no motion. Direction of flow: 90*. 210 Total CFU 1.25 N /sqm AVERAGE 2.063443E -02 STANDARD DEVIATION 4.331108E—02 ACCEPT. 362 OT 303 INTEGRATED RATE OF GUDING [um /m tnl Total CFU 1.25 N/sqm AVERAGE - 74.4631 STANDARD DEVIATION - 89.85924 ^ ^ r P fT1 r P rP 1T1 rP rP fT1 INTEGRATED DIRECTION OF GUDING Figure 84. Integrated movement at substratum (1.25 N m--2 ) . a: Integrated rate of gliding of CFU in Series AA. Minimum residence time for this distribution is 15 min. b: Integrated direction of gliding of CFU at substratum. O’ degree direction is associated with no motion. Direction of flow: 90". 211 Total CFU Series AA 0.5 N /sqm *A0E - 1.588874 STANDARD DEVIATION - .7151388 ACCEPT. 737 OT 884 CELLS PER CFU IN FIRST OBSERVATION Total CFU Series AA 0.5 N /sqm AVERAGE - 2 .027457 STANDARD DEVIATION - 1.333332 ACCEPT. 692 OT 884 o — ce»o«-cjK>4pin CELLS PER CFU IN LAST OBSERVATION Figure 85. Cells per CFU (Series AA, 0.5 N m” 2). a: Number of cells per CFU during first observation. b : Number of cells per CFU during last observation. 212 Total CFU 0.75 N /sqm AVERAGE - 1.643705 STANDARD DEVIATION - .8898312 ACCEPT. 421 or 476 Total CFU 0.75 N /sqm AVERAGE - 2.107981 STANDARD DEVIATION - 1.34692 1^3 ACCEPT. 426 OT 476 CELLS PER CFU IN LAST OBSERVATION Figure 86. Cells per CFU < 0.75 N m~1). a : Number of cells per CFU during first observation. b : Number of cells per CFU during last observation. 213 Total CFU 1.0 N /sqm AVERAGE - 1.784067 STANDARD DEVIATION - g K CELLS PER CFU IN FIRST OBSERVATION .8001561 ACCEPT. 477 or 65« Total CFU 1.0 N/sqm AVERAGE - 2.112832 STANDARD DEVIATION - 1.173663 ^\] ACCEPT. 432 OT 65« CELLS PER CFU IN LAST OBSERVATION Figure 87. Cells per CFU < 1.0 N m"2). a : Number of cells per CFU during first observation. b : Number of cells per CFU during last observation. 214 Total CFU 1.25 N /sqm AVERAGE - 1.736264 STANDARD DEVIATION - r n I s PER CFU IN FIRST OBSERVATION .9856844 ACCEPT. 364 OT 363 Total CFU 1.25 N/sqm AVERAGE - 2.374269 STANDARD DEVIATION - 1.753165 ACCEPT. 342 OT 363 CELLS PER CFU IN LAST OBSERVATION Figure 88. Cells per CFU < 1.25 N nr-1). a : Number of cells per CFU during first observation. b : Number of cells per CFU during last observation. 215 APPENDIX G RESULTS OF SPATIAL DISTRIBUTIONS 216 T e s t S e r i e s A A I , 0 . 5 N / s q m I . I * 1 0 e 6 c e l l s / m l L- 10 I I I I I I D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 89. Spatial distribution of adsorbing CFU, Series AAl. The measured distribution is superimposed on the calibration distributions (dotted lines). The calibration distribution in the upper left is for uniform, in the center for random, and in the lower right for aggregated. 217 T e s t S e r i e s A B 3 , 0 . 5 N / s q m 1 . 1 * 1 0 e 6 c e l l s / m l Figure 90. Spatial distribution of adsorbing CFU, Series AB3. The measured distribution is superimposed on the calibration distributions (dotted lines). The calibration distribution in the upper left is for uniform, in the center for random, and in the lower right for aggregated. 218 T e s t S e r i e s M 4 , 0 . 5 N / s q m 1 . 9 2 * 1 0 e 6 c e l l s / m l --1 T TTTTTT 10 1 0 * D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 91. Spatial distribution of adsorbing CFU, Series AA4. The measured distribution is superimposed on the calibration distributions CO O J3 -C *(U z : CU > O CD CU « I I I I I I I | I I I--1— I I I I I-------- T 10 IO1 D i m e n s i o n l e s s I n f l u e n c e N u m b e r I ill 10 3 Figure 96. Spatial distribution of adsorbing CFU, Series ABl. The measured distribution is superimposed on the calibration distributions I I i I I I I D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 102. Spatial distribution of adsorbing CFU, Series AB6. The measured distribution is superimposed on the calibration distributions (dotted lines). The calibration distribution in the upper left is for uniform, in the center for random, and in the lower right for aggregated. 2 3 0 T e s t S e r i e s A C 5 , 1 . 2 5 N / s q m 1 2 . 2 * 1 0 e 6 c e l l s / m l I- 10 D i m e n s i o n l e s s I n f l u e n c e N u m b e r Figure 103. Spatial distribution of adsorbing CFU, Series AC5. The measured distribution is superimposed on the calibration distributions (dotted lines). The calibration distribution in the upper left is for uniform, in the center for random, and in the lower right for aggregated. MONTANA STATE UNIVERSITY LIBRARIES 3 1 7 6 2 1 0 0 1 5 2 4 5 1