Organic carbon degradation in the East Gallatin River with biofilm kinetics by Subramaniam Srinanthakumar A thesis submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Civil Engineering Montana State University © Copyright by Subramaniam Srinanthakumar (1982) Abstract: The importance of sessile microbial populations in aquatic environments has been recognized for many years especially the heterotrophic slimes under polluted conditions. The extensive literature included in this dissertation review indicated that models proposed by previous researchers to predict substrate degradation in streams have been based on assumptions of first order or saturation kinetics incorporating mainly the substrate utilization by suspended biomass. The goal of this research is to determine substrate utilization and growth kinetics of heterogeneous river biofilms in multi-substrate environments. The East Gallatin River in Bozeman, Montana was chosen for the study because of its proximity, and the dense biofilm growth below the sewage outfall. A preliminary study was conducted in 1979 to evaluate the status of the river below the sewage outfall and formulate hypotheses. The detailed investigation carried out subsequently looks at two important aspects of organic carbon degradation in a shallow stream: (1)It determines the kinetics of organic carbon utilization by river biofilms using a pilot plant channel and compares the effectiveness of suspended microbial population in removing organic carbon with the biofilm community. (2) It verifies the mathematical models formulated for application to river water quality under steady state conditions for the substrate and biomass. River data collection included hydraulic, water quality and biofilm parameters over the summers and fall of 1979, 1980 and 1981. The preliminary study results showed that all the water quality parameters measured returned to background levels within seven miles below the outfall and that biofilm growth controlled the organic degradation below the sewage outfall. The results of the kinetic studies done established first order kinetics for soluble organic carbon utilization by river biofilms in a specified range of substrate concentrations, flow velocities and temperature. The measured and predicted values of the proposed models for describing organic carbon degradation and biomass changes showed good agreement. Sensitivity analyses of hydraulic and biofilm parameters were also carried out to determine the impact of the variability of the parameters on the substrate decay.  ORGANIC CARBON DEGRADATION IN THE EAST GALLATIN RIVER WITH BIOFILM KINETICS by SUBRAMANIAM SRINANTHAKUMAR A thesis submitted in partial fulfillment of the requirements for the degree Of DOCTOR OF PHILOSOPHY in Civil Engineering Approved: Chairperson, Graduate Ccqpmittee Head, Major Department Graduate Dean MONTANA STATE UNIVERSITY Bozeman, Montana April, 1982 ACKNOWLEDGMENTS I wish to express my sincere appreciation and gratitude to my advisor, Dr. A. Amirth- arajah, for the guidance, encouragement and suggestions during the entire course of this study and the preparation of this dissertation, Dr. W. G. Characklis for his contribution in using the concepts in biofilm kinetics in stream modeling and for the time he spent in connection with this study, Dr. G. A. McFeters for his comments and suggestions on th e . microbiological aspects of the study, Professor T. T. Williams for his encouragement in conducting the study and efforts in allocating funds and Dr. W. A. Hunt for his comments on organizing the dissertation. I am very grateful to some of my fellow graduate students, Michael Rubich for his contribution during the preliminary study, Phillip Stark for his assistance in the con­ struction of the experimental channel and river measurements, Jack Martin for assisting in the operation of the experimental channel, Tracy Boyd, Bryan Suprenant, Tom Engleson and Mike Trulear for their contributions during the study. Contributions of Don Noyes and his staff of the Bozeman Wastewater Treatment Plant for their excellent cooperation during the experimental channel study, the Engineer­ ing Experiment Station at Montana State University for supporting the author during the entire program and May Mace for typing this thesis are gratefully acknowledged. To God, parents and other members of my family, my sincere thanks for the moral support and encouragement during my entire academic career. Last but not the least, I will be failing in my duty if I do not thank my wife for her moral support, strength and for helping in several ways during the entire academic pro­ iii . gram. TABLE OF CONTENTS Page V IT A ... ................ .................................................................................................. ............. ; . . . ii ACKNOWLEDGMENTS........... ffi TABLE OF CONTENTS . ............................................................................................................. iv NOTATIONS......................... .................................. ........... ! .................................... ............. . . v i i ABBREVIATIONS......................................................................... xi LIST OF TABLES. ......................................................................................................................... xiii LIST OF FIGURES............: ................................. ........................................... ...........................xv ABSTRACT.............................................. ................................' . : ...............................................xix INTRODUCTION.............................................................................. I GOAL, OBJECTIVES AND SCOPE OF STUDY......... Theoretical................................................................ Field and Pilot Plant Scale Experimental Studies LITERATURE REVIEW.............................................. ........................ Backgrourid Information....................... ...................................... Nature and Significance o f Microbial Adhesion......... Composition and Organisms of Slimes.............................. . Functional Aspects o f Biofilms Including Their Activity Mechanisms o f Microbial Adhesion........................................ ................................. 10 Factors Affecting Attachment, Growth and Nutrient Removal . 1 4 Effect of the attaching solid surface......................................................... .. 14 Effect of shear forces and velocity .............. ............. i ................................i . . 15 Effect of pH and t e m p e r a t u r e ......................................................... 16 Effect of dissolved oxygen (DO)................ ....................................................: . 17 Effect of substrate and nutrients.............................. ...........................................18 Effect of film thickness......................... ............................................................... 19 Substrate-Biofilm Kinetics and River Modeling....................................................... 20 Theoretical Developments on Substrate-Biofllm Kinetics.....................................20 Reactor Studies of Substrate Kinetics and Biofilm Dynamics..............................27 <0 O O N V i U i W W W Page V Water Quality Modeling of Rivers ...............................................................................29 A Summary and Critique................................................................ .................................... 31 THEORETICAL CONSIDERATIONS......... ............., ........................................................... 37 Mathematical Models.............................................................................................................. 37 Conceptual Description................................................................. 37 Specification of Interactions......................................................................................... 37 Assumptions and Conditions.............................. : .............................................................40 Modeling Organic Carbon in Streams.............................. ...................... ...........................41 Formulation of Models..............................................; ................................................41 Pilot-Plant Channel Study......................................................................... ; . . . . . . . . . . 43. EXPERIMENTAL INVESTIGATION....................... ........., ....................: .................... .........45 Experimental Apparatus: Pilot Plant Channel S tudy...................................................45 General Layout......... .................... ..............................................................................45 Details o f Reactor Channel and Appurtenances................................ ...................... 45 Channel description.................................... 45 Channel design considerations......................................... 48 Influent feeding system...................... .4 9 Effluent recycling system . ....................... ...........................................................50 Pumps, motor, generator and watermeter.................................................... 50 Reactor Start-Up.................... 51 Experimental Observations............................................................................................52 General description of runs.....................................................................................52 Observations during a run ....................................................................................... 53 Field Studies—River Measurements................................ 53 Study Area Description......................... ............................................... ................. , . 53 River Flows and Morphology...................... 54 Description o f Sites.................................................. 55 Preliminary stu d y .....................; .................... ................................................... . 5 5 Detailed investigations...................... . . 5 5 Field Measurements................................ 55 Field Sampling and Laboratory Analytical Procedures . ...................................... .. 59 Measurement o f Water Quality Parameters.................... 59 Hydraulic Measurements................................................................., ...........................65 Measurement o f Biofilm Parameters........................................................................... 66 RESULTS AND ANALYSIS........................... 71 Preliminary Study.............................................. 71 Hydraulic Parameters.................. 71 Page Water Quality and Biofilm Parameters. ..................................................................... 73 Major Conclusions from the Preliminary Study....................................................... 82 Kinetic Studies................................ i................................................................................... 84 Pilot Plant Channel Study..................................................... ...................................... 84 Determination o f and Relationships for Rg, Rq and ..................................... 94 Determination of Rg, Rq and ................ ............... .................. ..................94 Relationships o f Y ^ with S and ( S j - S ) ................................ .................... 96 Temperature Relationships for R g ..................................................... ......................104 Determination o f Relationships Between Rg and S ................................................ 106 Other Possible Relationships.............. ..; ............. ............................................. .109 Specific biomass production rate vs. substrate concentrations.................................................................. 109 Soluble organic carbon removal and loading rate.......................................... .113 Summary Statistics for Important Parameters Developed.................................... 115 Field Investigations in the R iver.....................................................................................116 River Data Collection and Modeling............................................................ .............116 Hydraulic and physical parameters in the study reach..................................... 117 Water quality parameters......... ........................................................... .123 Biofilm d a ta ............................................................................................................ 134 Electron m icroscopy..........................................................................................134 Biofilm characteristics......................................................... 134 Autotrophic Index (A l) ..................................................................................... 145 ATP measurements.................................................... 145 . Model Verification............................................. 151 Sensitivity Analysis................................ 156 DISCUSSION................................................................ .162 Diffusipnal Limitations.................. .162 Steady and Unsteady State Models........................................................... 164 Kinetic Expressions........................ .161 Characterization of Mixed River Biofilms . ....................................................................169 Limitations of the Proposed Models ................................ ......................................— .172 Original Contribution of This Research................................ 174 Significance of Some Results in This Study to the Bozeman Sewage Treatment Plant Expansion........................................................... 174 SUMMARY AND CONCLUSIONS. . ; ......................... .176 APPENDICES ......................... .182 LITERATURE CITED.................................................................................. 192 v i VU NOTATIONS Units L2 l* :• • L2 a = area of viable organisms per unit volume Lr1 B = coefficient describing a boundary effect by slime layers . r p - l SQ = diffusivity coefficient o f electron acceptor L2T-I 0 C d = diffusivity coefficient of electron donor . L2t - i De = effective diffusivity coefficient o f S in the film L2T-I d L = longitudinal dispersion coefficient L2x -I Do = diffusivity o f oxygen in the slime L2T-' Ds = diffusivity o f glucose in the slime L2t -I F = flow rate in the channel L3t -» F C = constant factor relating the quantities o f glucose and oxygen utilized in the aerobic metabolism — f = an empirical coefficient in determining longitudinal dispersion coefficient — H = mean flow depth in the stream L j = flux given by Djj (dS/dZ) - U.S ML-2T-' KD = coefficient for overall stream deoxygenation rJ-I k O = coefficient for overall BOD removal T-' ^sc = coefficient for sedimentation rJ-I Symbol 1 ■ i A = plan area of biofilm Ac = area of cross-section of flow Ap = plan area of study reach viii Symbol Units KS = Monod half-velocity coefficient ML"3 ki = biological rate equation coefficient k2 = biological rate equation coefficient Ir1 k3 = biological rate equation coefficient ' M"1 L3 K ' = laboratory determined BOD rate coefficient rJi-I kF = rate coefficient in R]}20 = kp S LT"1 kV = rate of substrate uptake defined by M1/2L"3/2T'1 . (2De ‘ S / 2 Thc = kKV L = length of study reach L M = total attached biomass ML"2 mA = heterotrophic fraction of attached biomass ML"2 MWa = molecular weight o f the electron acceptor M MWd = molecular weight of the electron donor M N = rate o f substrate consumption per unit interfacial area ML"2 T"1 NrsITiax = maximum rate o f substrate uptake ML"2 T"1 n . = Mannings coefficient — O = oxygen concentration in the film ML"3 P = descriptive level of . significance — Q = stream flow L3T"1 RB = attached biomass production rate ML-2T"1 ix Symbol Units r D = detachment rate ML-2T '1 r H = hydraulic radius ' L RS = suspended biomass production rate ML-3T '1 r = local rate of substrate uptake per unit area of viable organisms ML-2T '1 rc = individual cross-sectional area in a stream L2 rj = sources and sinks of S; MU3T '1 rv = rate o f substrate consumption per unit film volume ML-3T '1 S = substrate concentration ML"3 t̂ia = concentration o f electron acceptor within the film ML'3 ^cd = concentration of electron donor within the film ML'3 Se = effluent substrate concentration ML'3 Si = influent substrate concentration ML'3 si = concentration of a water quality variable ML'3 Soa = concentration o f electron acceptor in bulk liquid ML'3 Sod = concentration of. electron donor in bulk liquid ML'3 Ss . = substrate concentration at the top o f biofilm ML'3 T = water temperature . °C Th = biofilm thickness L The = critical film thickness L t = time T tf = time o f travel T X Symbol Units U = mean flow velocity LT-1 U sje = shear velocity . LT"1 V = volume of reactor L3 W = width o f stream L x = distance measured into the slime from the interface L X = concentration o f suspended biomass ML"3 Xf = cell concentration in. the slime ML"3 Xj = influent concentration of suspended biomass ML"3 - .biofilm yield coefficient . , - xi ABBREVIATIONS Ashfree Dry Weight AFW Centimeter " cm Cubic Feet cuft or ft3 Cubic feet per second . cfs or ft3 /s Degree(s) Celsius °C Dry Weight DW Feet ft Feet per second fps or ft/s Gallon(s) . gal. Gallon(s) per minute gpm Gram(s) g Hour(s) h Inch(es) in. Micrometer(s) jum Milligram(s) per liter mg/1 Milliliter(s) ml Minute(s) . min. Pound(s) . lb. Second(s) s Soluble Organic Carbon ' SOC Standard Stdi . xii Standard Deviation S.D. Standard Error S.E. Square meter(s) m2 Square feet sq.ft or ft2 Suspended solids SS Total Organic Carbon TOC Versus . vs Volatile Suspended Solids , VSS LIST OF TABLES Table Page 1. Analytical Procedures for Water Quality Parameters....................................................60 2. Mean Values for Sewage Effluent Characteristics................................ 73 • 3. Biofilm Characteristics During the Preliminary Study................................................. 80 4. Determination o f Rg, Rq and Under Steady State Conditions.................. 95 5. Biofilm Growth on Plexiglass Plates-Biomass Measurements.................................... 91 6. Chlorophyll a Measurements on Plexiglass Plate Growths........................................100 7. Measured Yield Coefficients.................................................................. 102 8. Regression Statistics in the Determination o f 6 ...........................................................104 9. Regression Statistics for Rg vs. S .............................................................. 106 10. Testing the Significance of Intercept in Rg20 vs. S ......................................... .107 11. Relationships of Rq and M with Statistical Analysis..................................................110 12. Calculation o f Soluble Organic Carbon Loading Rates ....................... 113 13. Hydraulic Measurements, 1980............ ........................... ............................................. 118 14. Hydraulic Measurements, 1981.................................................... . . . 119 15.. Summary of Measured Steady State Values for Hydraulic Parameters During the Study Period....................... ............................................... 120 16; Measured Average Water Temperature in the Study Reach During Sampling Period, 1980 and 1981................................. .122 17. Summary of Steady State Values for Hydraulic and Physical Parameters in the Study Reach Used as Input to the Model ..................................................................... ............................... 123 xiii Table Page 18. Mean Values for Nitrogen During Steady State Flow Period, 1980 ........................................................................... 133 19. Steady State Biofilm Thickness and Biomass, Biomass Productivity and Biodensity at Various Sites, 1980..............................................143 20. Steady State Biofilm Thickness and Biomass, Biomass Productivity and Biodensity at Various Sites, 1981..............................................144 21. Mean Biodensity Below Sewage Outfall................................................................. .146 22. Determination of Autotrophic Index (Al) for Cobble Growths, 1980 .............................. ............. : ............................................................. 146 23. Determination of Autotrophic Index (Al) for Slide Growths, 1980 and 1981................................................................ 147 24. Comparison of ATP and Ash-free Weight (AFW) for Cobble and SUde Growths, 1981............................................................................. 151 25. Parameters Required as Input to the Steady State Models..................... 155 26. Methods for Estimating Longitudinal Dispersion Coefficients................................155 27. Organic Carbon Estimates and ViabiUty Index .............................. ...........................171 xiv LIST OF FIGURES I . Schematic Diagram of the Model Frame W ork................................ ...........................38 2. CMF Reactor with Recirculation............................................. .................... ..................43 3. Schematic Diagram of the Field Channel Experimental Set U p................................ 46 4. (a) A View of Channel Set Up, (b) Plan View o f Channel, (c) End View o f Channel, (d) Recirculation Pump, (e) 2 in. Water Meter, (f) Plexiglass Plate with Biofilm Used in the Channel......................... 47 5. Confluence o f Sewage Outfall and East Gallatin R iver..............................................54 6. East Gallatin Study Area and Sampling Sites, 1979..................................................... 56 7. East Gallatin Study Area and Sampling Sites, 1980 and 1981.................................. 58 8. Solid Sampling with the Depth Integrating Sampler at Site 2 ......... ...................... , .................................................... ............... : ...................... 64 9. Current Meter Measurements at Site 2 . ....................................................................... . 64 10. Stream Flow vs. Distance, PreUminary Study, 1979 ........... ....................................... 72 11. Water Temperature and pH Variation with Distance, Preliminary Study, 1979.............................................................................................. 74 12. Stream DO and BOD Profiles During Steady State Flow Regime, Preliminary Study, 1979 ......... ...................................... ............................. 75 13. Mean Chemical Parameters vs. Distance During Steady State Flow Regime, Preliminary Study, 1979 ................................ ........................ 77 14. Steady State Distribution of Solids with Distance, Preliminary Study, 1979 ..................................... ........... ............................................ 79 15. Biofilm Depth vs Time, Preliminary Study, 1979 ....................................................... 81 16. River Biofilm Profile, Preliminary Study, 1979.................................. ........................ 83 17. Organic Carbon, Channel DO and VSS Variation with Time for (a) Run 2 and (b) Run 4 ............................................................; ............... 85 Figure Page 18. Organic Carbon, Channel DO and VSS Variation with Time for (a) Run 8 and (b) Run 9 ............................................................................. 86 19. Organic Carbon, Channel DO and VSS Variation with Time for (a) Run 10 and (b) Run 12.............. ........................................................ 87 20. Organic Carbon, Channel DO and VSS Variation with Time for (a) Run 13 and (b) Run 14....................... i ...............................88 21. Organic Carbon, Channel DO and. VSS Variation with Time for (a) Run 16 and (b) Run 1 7 . . . . .................. ........................... ................. 89 22. Organic Carbon, Channel DO and VSS Variation with Time for (a) Control Run 11 and (b) Control Run 1 8 . . . ..................................... 90 23. Typical Variations of Organic Carbon, Channel DO and VSS Variation with Time for (a) a regular and (b) a Control R u n .............................................. ............................................. ......................91 24. Variation o f Channel DO and VSS with Time Using Tap Water for Run 2 0 ......... .. . ; ......................... ........................... ..................... 92 25. Plots of pH and Temperature, with Time for Runs 17 and 20 . . ; . . . .............. .. 93 26. Variation of Yield Coefficient with Organic Carbon Removed and Reactor Organic Carbon Concentrations......................................... 98 27. A Plot o f Measured and Calculated Yield Coefficients................. .............................103 28; Plot o f In Rg vs. Temperature..................................................................... ....................105 29. Variation in Attached Biomass Production Rate with Reactor Soluble Organic Carbon Concentrations.. . . :............................................108 30. Biofilm Detachment Rate Variation with Biom ass.................................... ...............111 3 1. Variation of Specific Biomass Production Rate with Reactor Soluble Organic Carbon.Concentrations. ....................................... .112 32. Plot o f Soluble Organic Carbon Removal vs. Loading R ates................ ............... . .114 33. Distribution o f Soluble and Total Organic Carbon Under Steady State Flow Conditions, 1980 .............................................. ............. 124 xvi Figure Page 34. Distribution o f Soluble and Total Organic Carbon Under Steady State Flow Conditions, 1 9 8 1 .............. ................................. ...........125 35. Distribution of Soluble and Total BODl Under Steady State Flow Conditions, 1980 .......................................................................................126 36. Plots o f Steady State DO and pH at the Chosen Sites in the River, 1980.................................................................................... 128 37. Plots of Steady State DO and pH at the Chosen Sites in the River, 1981 . ............................................................................ 129 38. Distribution o f Solids Under Steady State Flow Conditions, 1980............................ 130 39. Distribution o f Solids Under Steady State Flow Conditions, 1981 .................................................... .131 40. Diumal Variation of Organic Carbon and Sewage Outfall Discharge at Selected Sites, 1980 ......... ............................... ...................... 132 4 1. Diurnal Variation o f DO and pH at Selected Sites, 1980................................. 135 42. (a) Algal Community at Site I . (b) Magnified View of D iatom s...............................136 43. (a) Attachment of Bacterial Rods at Site 2. (b) Magnified View of the Rods .................................. 136 44. Algal Community at Site 2 ...............................................................................................137 45. (a) Attachment of Bacterial Rods to Diatoms at Site 3, (b) Magnified View o f an Attached Rod to a D iatom ......... ...................................... 137 46. Variation o f Biomass at Selected Sites, 1 980 ................................. ........:................... 138 47. Variation o f Biomass at Selected Sites, 1 9 8 1 . . . . ......... ............................. ; .............139 48. Plot o f Mean BiofUm Thickness at Various Sites vs. Time, 19 8 0 ................................141 49. Plot o f Mean Biofilm Thickness at Various Sites vs. Time, 1 9 8 1 . . . .......................:142 50. Compositional Variation o f Biomass Below the Sewage Outfall, 1980......... ............................................. ...................... , ........................... : . .148 xvii Figure Page xviii Figure Page 5 1. Compositional Variation o f Biomass Below the Sewage Outfall, 1981;......... . . . 149 52. Variation and Comparison of ‘AF and Biomass for Cobble and Slide Growths at Site 2, 1980.................................................................. ' . . . .150 53. Measured and Predicted Distributions for Organic Carbon, Suspended Biomass and Biofilm Thickness Below Sewage Outfall, 1980 ..................................... 153 54. Measured and Predicted Distributions for Organic Carbon, Suspended Biomass and Biofilm Thickness Below Sewage Outfall, 1981.............................................. 154 55. Sensitivity o f Hydraulic Parameters in the Model for Substrate Decay, 1980 ........................................... .157 56. Sensitivity of Biofilm Parameters in the Model for Substrate Decay, 1980 ....................................................................................................................158 57. Sensitivity of Hydraulic Parameters in the Model for Substrate Decay, 1 9 8 1 .............................................. ; ..................................................................159 58. Sensitivity of Biofilm Parameters in the Model for Substrate Decay, 1 9 8 1 . . ............................................................................................................... 160 59. Unsteady State Model Results Using Program ‘DECAY 4’ (a) Diumal Variation o f SOC at Site 2, (b) Diurnal Variation o f SOC at 4 Km below Site 2, (c) Diurnal Variation o f SOC at 10 Km below Site 2 . . : ................ ; ............................. .. 166 Appendix Figures A l . Organic Carbon, Channel DO and VSS Variation with Time for (a) Run I and (b) Run 3 ........................................................................................ 184 A2. Organic Carbon, Channel DO and VSS Variation with Time for (a) Run 5 and (b) Run 6 .................................. i ..................................................185 A3. Organic Carbon, Channel DO and VSS Variation with Time for Run 7 .................................. 186 ABSTRACT xix The importance of sessile microbial populations in aquatic environments has been recognized for many years especially the heterotrophic slimes under polluted conditions. The extensive literature included in this dissertation review indicated that models proposed by previous researchers to predict substrate degradation in streams have been based on assumptions of first order or saturation kinetics incorporating mainly the substrate util­ ization by suspended biomass. The goal of this research is to determine substrate utilization and growth kinetics of heterogeneous river biofilms in multi-substrate environments. The East Gallatin River in Bozeman, Montana was chosen for the study because of its proximity, and the dense biofilm growth below the sewage outfall. A preliminary study was conducted in 1979 to evaluate the status o f the river below the sewage outfall and formulate hypotheses. The detailed investigation carried out subsequently looks at two important aspects of organic carbon degradation in a shallow stream: ( I ) I t determines the kinetics o f organic carbon utilization by river biofilms using a pilot plant channel and compares the effectiveness of suspended microbial population in removing organic carbon with the biofilm community. (2) It verifies the mathematical models formulated for application to river water quality under steady state conditions for the substrate and biomass. River data collection included hydraulic, water quality and biofilm parameters over the summers and fall of 1979, 1980 and 1981. The preliminary study results showed that all the water quality parameters measured returned to background levels within seven miles below the outfall and that biofilm growth controlled the organic degradation below the sewage outfall. The results o f the kinetic studies done established first order kinetics for soluble organic carbon utilization by river biofilms in a specified range o f substrate concentrations, flow velocities and temperature. The measured and predicted values o f the proposed models for describing organic carbon degradation and biomass changes showed good agreement. Sensitivity analyses of hydraulic and biofilm parameters were also carried out to determine the impact of the variability of the parameters on the substrate decay. INTRODUCTION Mathematical models have been used widely in the past decade in simulating water quality and ecological interactions. The increased use and development o f water quality models may be attributed to the Water Pollution Control Act amendments of 1972 (PL:92-500) which call for areawide wastewater planning across the United States. The Government Affairs Committee’s Criteria and Standards Task Group, while recognizing the heed for the re-evaluation of the goals of the 1972 Water Pollution Control Act, emphasized the importance of using calibrated models for realistic waste load allocations. Mathematical simulation techniques are useful as long as the physical mechanisms involved are accurately reflected in the model. In this respect, river systems can be ex­ pected to behave differently depending on the category they belong to. They can be tidal, non-tidal, swift moving, shallow or sluggish deep streams. The significant physical and biological mechanisms involved in water quality modeling can be quite different in each class of river system. Shallow rivers for example, present problems in modeling quite different from that of deep rivers. The microbial population, sessile or suspended, domi­ nating water quality modeling in various categories of rivers can be different. The impor­ tance of sessile microbial populations in aquatic environments has been recognized for many years. Natural biofilms growing on a river bed are composed primarily of algae and bacteria, appearing as a mass of slime. Under polluted conditions below a sewage outfall, the slimes are predominantly heterotrophic. In modeling organic carbon, biological slimes covering the stream bed play a major role; especially in shallow turbulent streams. The kinetics o f substrate uptake may vary depending on the range of substrate concentrations encountered in a study. In most studies involving modeling of natural systems, researchers arbitrarily assume the kinetics o f substrate uptake, as it is difficult to determine it in each case. However, the critical problem is to determine which microbial population, suspended, attached or both play the dominant function in substrate assimilation. The appropriate kinetic expression may then be utilized in the stream model. Thus, identifying the appro­ priate kinetics of the processes becomes imperative in modeling any system. This research is multidisciplinary in the areas o f water quality and microbial ecology, elucidating biofilm effects on stream water quality. The study was designed to make use of the advances made in biofilm kinetics and couple it with mathematical modeling of river systems. The research approach was to carry out an artificial stream study to determine the kinetics o f the substrate uptake and then use such information in the proposed stream models to study the applicability of such models in predicting organic carbon and biomass variations below a point source of pollution. The East Gallatin River which receives a par­ tially treated sewage effluent from the Bozeman Wastewater Treatment Plant was used for field studies. The results of the study provide useful information in terms of assessing the important microbial population in shallow streams and the order o f kinetics of substrate uptake by river films in a specified range of substrate concentrations. 2 GOAL, OBJECTIVES AND SCOPE OF STUDY The research carried out encompasses theoretical, as well as field and pilot plant scale phases of study. Modeling substrate and biomass in natural environments is complicated by the com­ plex microbial communities and the presence o f an undefined substrate. The goal of this research is to determine the growth and substrate utilization kinetics of river biofilms in multi-substrate natural environments. The theoretical objectives were to provide an extensive and critical review of the literature giving a background on microbial adhesion in natural environments, reactor kinetic studies done on microbial films and past modeling efforts, complete with a sum­ mary and a critique, and to: formulate substrate-biomass models based on theoretical considerations for organic carbon use and biomass variations below a sewage outfall in a stream. An artificial channel was constructed on the river bank for the pilot plant scale study: (I) To determine the kinetics of organic carbon uptake rate by river biofilms under field conditions, (2) To compare the importance of the suspended microbial population to the sessile organisms in predicting the organic carbon uptake in shallow turbulent streams. Several runs were made, each for five hours to establish steady state conditions with attached biomass grown on plexiglass plates. Control runs at high and low substrate con­ centrations were made without using the attached biomass to assess the importance of suspended microbial populations. The following parameters were measured during each 4 run: pH, DO, temperature, TOC, SS, VS8. Chlorophyll, biomass and thickness measure­ ments were also made on the attached films. The information obtained from the experimental study and the field data collected were used to verify the substrate biomass models formulated under steady state conditions. The river data collected for the validation of the model included water quality and biofilm growth kinetic parameters measured at six sites, one above and five below the sewage outfall over three summers. The first summer period was used as a preliminary study period to formulate hypotheses. The general structure o f the biofilms was also studied using electron microscopy. LITERATURE REVIEW The review o f the pertinent literature is categorized into three main sections. The first section deals with background information on bacterial adhesion mechanisms and the role of attached bacteria as a major component of the assimilative capacity in river systems. Substrate kinetic studies of suspended biomass and biofilms, the transfer and transfor­ mation processes related to modeling distributions o f substrates are reviewed in the second section in addition to published water quality models. The final section gives a summary and a critique of the relevant literature described in the previous sections. Several terms such as slimes, sewage fungus, periphyton, aufwuchs have been used in the literature to refer to the attached microbial growths in streams. In this study, for simplicity and convenience, the terms biofilm or slime layer will be used which refer to the gelatinous film formed on submerged surfaces such as rocks and includes both living and non-living materials. Background Information The occurrence of excessive biological growths in streams is of increasing concern to environmentalists because of their effect on aquatic life and oxygen resources. The micro­ organisms in rivers and streams can be attached to the streambed or suspended in the overlying water. The logical question to be asked at this point is why do microorganisms attach to a surface and how do they achieve attachment? It is imperative to understand the nature and the mechanisms by which microorganisms especially bacteria attach to the cobbles and rocks in streams before analyzing their effects on water quality. 6 Nature and Significance o f Microbial Adhesion A review o f recent literature throws considerable light on the advantages that sessile microorganisms more specifically bacteria and algae have, compared to the suspended organisms in extracting food from fast flowing streams especially in nutrient limited conditions. Costerton (24) found that a square centimeter of an immersed surface might typically have as many as a million attached bacteria whereas a cubic centimeter o f water flowing over that surface contained only a thousand bacteria. This was also revealed by Geesey (42) who demonstrated the significance o f sessile bacteria over those free floating in unpolluted mountain streams. The attachment makes life easier for bacteria in a station­ ary location from where they could easily extract the organic molecules and nutrients from the passing water. Characklis (19) concluded from his review that sessile bacterial growths are an essential part o f the assimilative capacity of rivers. Sanders (HO) compared sus­ pended and attached organisms in a river to batch and continuous cultures. The population that adheres, forms a thick slime layer on rocks in the stream bed especially when there is organic enrichment. The East Gallatin River downstream of the sewage outfall in Bozeman, Montana with its cobbly bed was shown to have dense slime layers for a considerable distance (78,105). The nature of these slime layers above and below the sewage outfall varied, due to the organic enrichment below the outfall. Costerton (25) found planktonic organisms favoring the “adherent growth habit” in aquatic systems. Hendricks (51) used respiratory and enzymatic data to establish that sessile microorganisms were more active than those suspended. The major role in recycling of substrates by slime layers has been long suspected by Zobell (150). 7 Composition and Organisms of Slimes Composition and colonization. Due to its hydrated nature which contains as much as 98% water, the capsular material surrounding bacteria is slimy and has almost the same refractive index as the medium (143). The slime composition has been reported to be predominantly carbohydrate with small amounts o f nitrogen (19). Mackie (70) reported that the slimy material surrounding bacteria was composed mainly of polysaccharides and that the thickness varied according to nutritional and environmental requirements. Ward and Berkeley (133) reported that most of the bacterial polysaccharides are composed of more than one type o f sugar residue often containing uronic acids and/or pyruvyl ketal groups which are responsible for the polymer having an overall negative charge. Using phase contrast and electron microscopy, Geesey (41) examined the in-situ distribution of cells revealing that they were enmeshed in an extensive “fibrous matrix.” It was further determined that this material surrounding the bacteria was produced by the bacteria themselves. Using staining procedures on slime, Fletcher (38) and Jones (58) determined that it was composed of an anionic polymer with the characteristics of polysaccharides. Several studies reported micro-colony development in slime layers (24,41) formed by a mass of tangled polysaccharide fibers suggesting that the glycocalyx may group bacteria in a somewhat organized community with several niches for different species. Such adher­ ent populations tend to respond uniquely to changes in nutrient or environmental con­ ditions. Most o f the natural bacterial films are interspersed among algae forming a mixed attached population which was evident from several electron micrographs (25). Algae have polysaccharide fibers similar to bacteria and the initial colonization may be accomplished by either bacteria or algae. There is not enough evidence in the literature to determine 8 which of the two, algae or bacteria, colonize first in natural environments. Geesey (42) on the basis o f electron microscopy showed that the attached algae provided a suitable surface for bacterial colonization. Algae would provide the surface and nutrients for bacterial growth. The electron micrographs obtained in this study support this finding as shown subsequently. Hendricks (51) considered a primary layer of bacterial growth as necessary for subsequent colonization by higher life forms. Baier (7) believed that the primary layer of bacterial growth changes the critical surface tension o f the monolayer, helping higher life forms to colonize subsequently. Marshall (77) suggested zymogenous chemoorgano- trophs to be the initial colonizers followed by oligotrophs and other higher forms. What­ ever group o f organisms colonize first, it certainly helps subsequent colonization by others. In general, only viable cells can colonize first as suggested by Meadows (83) because of their ability to withstand stresses. Organisms of slime layers. In general, a slime layer would have micro and macro organisms consisting of procaryotes, eucaryotes and macroinvertebrates. In the context of this study, the macroorganisms are not considered. Aquatic biofilms generally are com­ posed of phototrophs, heterotrophs and reducers (126). Sanders (109) reported that even though slimes in natural streams are composed of predatory, phototrophic and chemo- trophic microorganisms, the main population was the heterotrophs. All these organisms live together in niches forming an interacting ecological community. The most prominent and important filamentous bacteria found in slimes was Sphaero tilus which grew as a chain of ceils encased in filamentous sheaths (26,31). 9 The occurrence o f Sphaerotilus natans in the East Gallatin River as far as six miles below the sewage outfall has been reported (78,105). It is not entirely certain what envi­ ronmental factors allow Sphaerotilus to grow massively in competition with other organ­ isms. Dias (31) found that Sphaerotilus would grow even at reduced DO levels whereas such an environment was less favorable to other attached bacteria in a mixed population. Curtis and Curds (26) examined and compared the. composition of the slimes in different polluted habitats. The slimes were dominated by Sphaerotilus natans which require a continuous flow of nutrients and at least I mg/1 DO, or zoogleal bacteria. The bacteria Thiotrix, Beggiotoa and the Zoogleal bacteria were found to become abundant with the development o f slime (52), Most sewage fungus outbreaks were caused in situations when the soluble organic carbon concentrations were in the range of 6 to 20 mg/1 and where daytime DO exceeds 8 mg/1 (59). Nitrifying bacteria have been found in slimes in the presence of ammonia in rivers. Based on field measurements in shallow streams, Tuffey (130) concluded that the drastic decay of ammonia nitrogen was caused by nitrification by the attached population o f nitrifying bacteria. The findings from this study and Curtis (28) indicated that substantial numbers of nitrifying bacteria were found on the mud surface on the river bed throughout the river with a considerably lesser concentration in the waterphase contributed by scour from the slimes. Functional Aspects of Biofilms Including Their Activity A natural biofilm because o f autotrophic and heterotrophic groups o f organisms mixed together present difficulties in compartmentalizing, in order to obtain quantitative information on the heterotrophs. Under polluted conditions, the heterotrophic fraction of the biomass is much higher than the autotrophic fraction. Common measurements of 10 periphyton involved: species diversity; indices of community structure; dry weight (DW) arid ashfree dry weight (AFW); phytopigments; biovolume. Recent papers in the literature showed the interest of researchers to study the functional aspects of natural biofilms through the analysis of oxygen production and 14C assimilation (59,88,103). More recently, there has been a trend towards the measurement o f adenosine triphosphate (ATP) as an indication of the viable biomass (2 1,139). More realistic estimates o f bacterial counts have also been reported using Epi-illuminated fluorescence microscopy (15,54). Heterogeneous natural populations may be partitioned by use o f estimates of dry weight, ash-free dry weight, Chlorophyll a and ATP (21). Weber and McFarland (135) emphasized the importance o f Chlorophyll a as the primary photosynthetic pigment, the only form found in all algae and suggested a method of estimating the algal biomass. Geesey et al. (42) used a conversion factor of 60 to estimate cellular carbon from chloro­ phyll measurements. Others have provided methods for organic carbon estimates from chlorophyll measurements (73,79). Commonly employed values for ratios of mg cellular carbon to mg Chi. a range from 30 to 60 (21). By carefully combining the organic carbon estimates based on these different methods, the sample may be partitioned into auto­ trophic and heterotrophic components and viable and nonviable organic carbon. Problems of direct measurement of organic carbon in hetergeneous microbial communities have been mentioned by some investigators (21,42). Mechanisms of Microbial Adhesion The methods by which microbes adhere to surfaces have been o f concern and con­ sideration in the past few years. The problem of destruction and shearing of slimes, 11 especially the latter, requires a thorough knowledge of the modes o f microbial attachment to surfaces. Experiments have demonstrated that due to some strong mechanisms of attachment, even extensive washing would not remove these attached growths (150). Biocontact theories are presently based mostly on colloid stability theory (or DLVO theory). The colloid stability theory involves complex calculations of ionic double layer interactions and Van der Waals’ forces. Pethica (96) reviewed the relationship of DLVO theory as applied to biocontact and presented a general theory based on the. recent thermo­ dynamic description o f cell adhesion. Hall (47) presented a specimen calculation based on thermodynamic considerations which showed that changes in chemical composition are important variables as particles approach one another. This may mean that a shift in chemical composition would dominate the interaction. The attachment of bacteria to surfaces is influenced by the adsorbed organic substances which condition the surface for further attachment (75,76). However, some proteins have been found to inhibit attach­ ment of bacteria to surfaces (96). The movement of the flagellates help overcome the potential barrier and contribute to their attachment. The use of pili extending from many organisms into the environment have been implicated in certain bacterial adhesion to inert surfaces (133). There is, however, no clear demonstration in the literature of the general involvement of these surface appendages in the attachment process. Tadros (124) made a distinction between the two processes o f particle attachment, namely deposition and adhesion. The difference between these two is determined by whether they are governed by short-range or long-range forces. Rutter and Vincent (107) described the long-range surface forces involved in particle deposition: (I) Double layer interactions 12 (2) London—Van der Waals forces (3) Steric interactions (4) Bridging interactions Deposition would be based on the balance o f forces involved. Steric interactions predomi­ nate only when the surface and particle are highly covered with polymers. The long- and short-range forces were classified into various types by Tadros (124): (1) Long-range attractive forces due to Van def Waals and electrostatic forces. (2) Short-range forces are: (a) chemical bonds (b) dipole interactions (c) hydrophobic bonding (3) Interfacial reactions Based on the phenomena o f hydrophobic interactions, Rutter and Vincent (107) showed that microorganisms being hydrophilic adsorb to a hydrophilic clean glass surface stronger than to a hydrophobic teflon. Interfacial reactions are important with microorganisms capable of secreting polysaccharides which would condition the attaching surface. Ward and Berkeley (133) mentioned the possibility of the polysaccharides being produced only , I after the microbial adhesion had occurred. II Fletcher (39) divided the accumulation of microorganisms onto a surface into three stages: (a) Adsorption of the organisms to a surface; (b) Attachment by forming polymer bridges. 1 (c) Growth and division of organisms'on the surface. 13 At the usual pH range found in natural habitats, Marshall (77) determined a net negative charge associated with most bacteria on the basis of electrophoretic studies. Marshall (77) and Scheraga (1 13) described two different types of sorption in the adhesion process: Reversible sorption where application of a shear force or flagellar action would remove the bacteria and irreversible sorption caused by the extracellular polymers pro­ duced by bacteria and anchoring them to the surface. Bacteria and natural solid surfaces have been shown to be predominantly negatively charged which causes electrostatic repulsion. However, the Van der Waals attractive forces operate when the cells get close to the surface and may provide a weak net attraction at the secondary minimum. It is possible therefore for the cells in the initial reversible attachment to be held at a finite distance from the surface in equilibrium by the balancing of attractive and repulsive forces. At this point, irreversible attachment is accomplished by the organisms excreting extracellular polymers which overcome the electrostatic repulsion barrier and attach by bridging directly to the surface (75). This has been further supported by ZobelTs work (150) and by bacteria forming colonies on submerged surfaces (41,58). Wardell and Brown (134) looked at another aspect of colonization. Under limitations of carbon, the free receptor sites available on the surface and cells can be used by cells to adsorb with the small amount of polymer produced. When there is an excess carbon, large amounts of polymer may be produced which would cover all the available binding sites and possibly hinder attachment (74). The importance of this aspect can be readily seen in aquatic environments with low nutrients. During the adhesion random or perpendicular orientation of the bacteria de­ pends qn whether the extracellular polymers were produced around the entire bacteria or only at one pole. Costerton (24) found the polymeric fibers termed glycocalyx to be 14 negatively charged. The mechanism of attachment of these glycocalyx to the surface appear to be similar to the bridging mechanism of the polyelectrolytes in coagulation (64,137). The attachment bond is stronger than the connecting fibers because shearing off the organisms on a surface leaves a print o f attached polymers (66). Fletcher (39) defined passive and active bacterial attachment. Passive attachment is caused by molecular adsorp­ tion. Two types of physiological activity required for active bacterial attachment are: (a) mobility (b) synthesis of polymers required for bridging Motility helps increase the momentum and the statistical chance with which the bacteria can reach the surface. This shows clearly that attachment is dependent on physiological processes. Factors Affecting Attachment, Growth and Nutrient Removal Effect of the attaching solid surface. Many cells do not divide unless in contact with biological or non-biological surfaces (96). Several surface properties are important in the formation o f a primary film (52). The influence of solid surfaces on attachment and growth have been reported by many researchers (42,51,75,150). The solid surfaces concen­ trate nutrients and thus enhance attachment. The relationship between the surface area of a laboratory container and bacterial activity was demonstrated by Zobell (150). Solid surfaces in addition to concentrating nutrients aid in controlling the diffusion of exoen­ zymes from the cell. However, low molecular weight nutrients that are concentrated are not responsible directly for attachment (150). Dexter et al. (29) listed the effects of several parameters of solid surfaces other than toxicity on the microbial attachment growth: 15 (a) The surface texture of the surface (b) The surface charge (c) Wettability of the substrate After analyzing the influence of substrate wettability on the attachment o f marine bacteria to various surfaces including microscope slides, polystyrene and polyvinyl fluoride (PVF) 5 they found the “bioadhesive range” in terms of surface tension. If the surface tension of . ' ' ' r these materials was greater than a critical surface tension, they were defined to be in the ‘bioadhesive range’. Usually natural substrates like cobbles and artificial substrates like glass slides were found to be in this range. They described the formation of a film in two stages initiated by an organic conditioning film, which meant that it was unlikely that the wettability o f pure clean surfaces and the texture had any direct influence on the attach­ ment process after formation of the conditioning film. The difference between low-energy surfaces such as teflon and high-fenergy surfaces such as clean glass in bioadhesion was demonstrated by Weiss and Blumenson (138). There are several examples found in the literature in agreement with the critical surface tension concept. In natural environments, the attaching surfaces of microbes are rough and therefore there will be several zones of contact. Short-range forces such as chemical and hydrophobic bonding become stronger in these contact zones compared to long-range interactions such as Van der Waals and electro­ static forces which make adhesion sensitive to the detailed geometry o f the surfaces near contact (124). This may give rise to a range of adhesive strengths even for an apparently uniform population. Effect of shear forces and velocity. The influence of flow velocity is seen in trans­ porting nutrients to the attaching surface and in shearing the biomass building up. Higher 16 velocities over film surfaces enhanced slime growths due to better transfer of nutrients from the overlying water to the surfaces o f bacterial cells (52,109). This was also sup­ ported by Hartmann (50) in his study on the influence of turbulence on bacterial activity. Since very high velocities would promote high scour rates and low velocities would be unable to transfer food molecules adequately, an optimum range o f velocities for growth can be delineated. Experimental investigation in this connection by Sanders (109) and Characklis (18) on biofilms grown in the velocity range of 0.1 to 1.0 fps showed a velocity around I fps giving maximum growth. Sanders (109) showed that high velocities produced a dense and tough slime in contrast to the low density and more fragile slime mass at low velocities. Characklis (18) showed that biofilms can withstand high shear forces exceeding 15 dyn cm-2 . Shear forces become very important in determining film thicknesses because of the physical removal and the transfer of nutrients to the film. Trulear and Characklis (129) supported the assertion that increased shear stress caused greater scour rates. Effect of pH and temperature. Reid (99) suggested an optimum pH of 7.2 for slime growth. Close to neutral pH, maximum production of polysaccharide occurred (143). This meant that a pH range of 6.5-8 would be optimum for bacterial growth. Environments more acidic than pH 3 to 4 or pH greater than 10 are not common. The different species of microorganisms isolated at various extreme pH environments and their life have been reported by Langworthy (6 8 ). Green (45) reported that the percentage of dry matter in slimes varied between 3.5 to 6.5%, in the temperature range of 5 to 30°C; but higher temperatures increased the dry weight. The bacterial polysaccharides are synthesized at a larger rate at temperatures lower 17 than the optimum for bacterial growth (36). This may explain the lower optimum temper? atiire for dime growths compared to suspended growth. E. coli was reported to produce about 25 times the amount o f polysaccharide material at a temperature 15 to 20°C than at the optimum temperature of 37°C. Fletcher (39) suggested it was difficult to make any general prediction of the temperature effects on physiology other than their basic influ­ ence on reaction rates. Only a few reports are available on the activity o f river microorgan­ isms at very low temperatures such as below 5°C. Baross and Morita (10) summarized stream data showing the effect o f temperature on microbial growth rates which indicated that 8 to 20 times higher generation times are needed during the winter (0 to 5°C) com­ pared to the summer (16 to 2 1°C). Effect of dissolved oxygen (DO). DO is obviously an important factor from the point of view of metabolism of organisms. Depending on the diffusion o f oxygen, there will be aerobic and anaerobic zones in the biofilm. The cells in the anaerobic zone or below the limiting thickness for the diffusion of oxygen die or metabolize anaerobically (109). The mass of organisms in the top aerobic zone is considered to be active. Sanders (109) re­ ported that the maximum nutrient removal occurred when the slime thickness reached the limiting thickness which had a minimum value o f 21 microns. The active film thickness was found to be independent of DO (63). Tomlinson and Snaddon (127) and Komegay and Andrews (62) have shown that the active film depth is about 100 ^m. The extent to which oxygen would penetrate the film depends on the diffusivity coefficient, the type of film and the stoichiometry of the reaction. In the presence of anaerobic conditions in the lower part of slime layers, product formation in those layers become important. It is however, difficult to establish the role of these anaerobic decomposition products in varying the substrate concentrations by dif­ fusing through the top aerobic layer. Sanders (109) showed an indication o f a reduction in BOD removed from the supernatant substrate after reaching the limiting depth due to either the anerobic. products released or the utilization of these products by the organisms in the top layer. Oxygen was found below the active layer in some studies showing that it was not rate limiting (111,141). Using a nutrient broth of 20 mg/1 and a heterotrophic film, Whalen (141) found high concentration o f oxygen throughout the slime mass stabil­ izing at 75 pm depth. However, when a 500 mg/1 nutrient broth was used, the DO profile stabilized at 0.25 mg/1 below 150 jum. Variations in DO did not produce chemical com­ positional variations in the slimes (63). Effect of substrate and nutrients. Substrate and nutrients being directly involved in the metabolism of the cells have a very significant effect on attachment and growth. It has been suggested in several studies (8,75,129) that an organic film is formed initially on the attaching surface. This would be influenced by the chemical composition of the liquid media. The organic film, which Baier (7) suggested as a prerequisite for attachments, conditions the surface by enriching it with organics and latering the surface tension. The organic substances in the medium were found to promote attachment and in some cases inhibit the attachment process (39). Warded and Brown (134) based on their study of a continuous flow culture found increased adsorption of cells to a surface under carbon limitation due to the larger number o f free receptor sites available on the cell envelope and the surface. When there was glucose limitation, a small amount o f polymer was found to be sufficient to act as an adhesive between those receptor sites on the cell envelope and the surface. This factor may become very significant in natural environments with low 19 nutrients. Excessive carbon promoted larger polymer production and by covering all binding sites inhibited attachment (74). This would mean that, with carbon excess there will be more polymer coated to the surface than the number of bacteria attached. The concentration of nutrients in general has been found to vary the amount o f slime directly (99). Easily sloughing films were found to be characteristic o f growths in liquids having high amounts of oxidizable material (52). Effects of film thickness. In the literature, there has been a striking similarity in the concepts of film development, even though there have been disagreements on other aspects (33,63,109). Biofilm thickness is an important parameter in the metabolism of the slime community. McKinney (81) stated that the trickling filter efficiency would be maximal with a thin layer o f organisms. This was supported by several investigators (63,108,127) who showed that the effective depth of film ranged up to 120 jam. There was disagree­ ment, however, among these investigators on the changes in nutrient removal rates be­ yond the effective film depth. A literature review indicated two different theories, one based on Sander’s work (109) and the other on Komegay and Andrews (63) and Tomlin­ son and Snaddon (127). According to the. first theory, the nutrient uptake rate is reduced after the limiting biofilm thickness had been reached due to the fermentation products from the bottom layers diffusing into the aerobic layer and providing additional nutrition. The second theory postulated that there was a limiting thickness corresponding to a maximum nutrient removal rate but this rate became constant with increasing thicknesses. This condition remained until sloughing occurred with higher thicknesses. The anaerobic layer forming at the bottom is assumed not to change the nutrient utilization rates of the 20 films. Hoehn and Ray (55) made a comparison o f these two theories by studying the nutrient removal capacities of films in relation to their thicknesses and attempted to corre­ late these data with changes in physical characteristics. They reported that (he two theories were not mutually exclusive because as films grew, there was a limiting thickness when the nutrient removal rates declined. However, with more time the films adjusted to the changes in the internal environmental conditions after which they recovered, giving the original nutrient removal capabilities. When the films were about 300 to 400 pm thick, a steady : state nutrient utilization rate was achieved. These results were supported by Komegay and Andrews (63) Tomlinson and Snaddon (127) and Lamotta (6 6 ). The pattern of varia­ tion for biodensity was similar to nutrient removal with film thickness.' The density in­ creased up to the limiting thickness and declined reaching a steady density beyond about 300 pm thickness (55). This variation was found not to have been caused by the succession ' " • i . of bacterial types, 1 Substrate-Biofilm Kinetics and River Modeling Theoretical Developments on Substrate-Biofilm Kinetics ' Attempts have been made by several researchers to elucidate the mechanisms of substrate removal by biofilms and study its kinetics in reactor systems. Emphasis in sani­ tary engineering research was directed towards developing a better understanding o f the kinetics o f growth and substrate utilization o f biofilms. In the previous section, the studies by several investigators on biofilm growth and nutrient removal characteristics have been described. These experimental conclusions provided an impetus for the models developed subsequently; This section will describe the theoretical considerations which formed the 21 basis of substrate-biofilm models. The reaction scheme in these models involve substrate and nutrients, biomass, an exogenous electron acceptor and products. Organic substrate in homogenous systems flows through the microbial population enabling reaction with cells at all the points in the liquid phase whereas in a heterogeneous system it flows over the biofilm with reaction taking place only at the biomass surface. In a series o f publications, Atkinson (I) described the process firstly as a pseudo-homogeneous reaction system which is reaction rate limited and secondly as a heterogeneous system in which substrate dif­ fusion in the liquid phase or reaction rate became rate limiting (123). Considering only the rate limitation by dissolved organic matter and unlimited by the exogenous electron acceptor oxygen, Atkinson (2) subsequently incorporated diffusional resistances in both liquid and microbial mass. Considerable theoretical developments backed by experimental investigation followed (18,63,66,84,112). In all these cases, only one reactant was con­ sidered to be rate limited. Three major steps may be identified in describing the overall process o f substrate uptake by. bio films: (a) Diffusion of substrate from bulk liquid to the interface between the liquid and biofilm. (b) Diffusion within the bio film. (c) Biochemical reaction within the film. Lamotta (65) studied step (a) in detail by experimentally defining the reaction controlled region. The true kinetics of reaction can be studied by the proper choice o f a fluid velocity. This would eliminate the external diffusional resistances. Muller (90) and Baillod (9) after studying steps (b) and (c) demonstrated, that internal diffusion became very significant at low oxygen concentrations or carbonaceous concentrations. For diffusion and oxygen 22 consumption Bungay (17) and Whalen (141) treated the film as a homogeneous mass. For carbonaceous substrates, some investigators restricted the analysis to qualitative descrip­ tions o f the effects of film thickness on substrate uptake (55,109). The effect of mass transfer resistances have been well documented by several investigators (2,48,67). Williamson and McCarty (146,147) and Williamson and Chung (145) studied substrate utilization by bacterial films and defined conditions for limitations o f electron donor or acceptor. The bio film model they presented could be used only when either the electron donor or acceptor is both substrate and flux limiting across the entire film. It is possible to have one of the species, electron donor or acceptor flux limiting and the other substrate limiting over a certain portion of the film, which cannot be described by the model. This is probably the situation in trickling filters or in natural environments. If only one of the parameters is limiting throughout the film, the following relation­ ship holds when the electron acceptor is substrate limiting ( 146): s c a < ( W c d 0 ) where Scd>.SCa = Respective concentrations of the electron donor and acceptor at a specified film depth in mg/1 Kscj, Kga = Monod half-velocity coefficients for the electron donor and acceptor, respectively, in mg/1. Similarly for flux limitation which was based on a general metabolic reaction and Pick’s Law, the following condition holds when the electron acceptor is flux limiting, Soa < Dcd^aMWa (2) Dca"dM*d 23 where Sna, SnJ = electron acceptor and donor concentrations respectively in mg/1 in the bulk liquid. "d’ "a " respective stoichiometric reaction coefficients for electron donor and acceptor. MWa, MWcJ = molecular weights o f the electron acceptor and donor respectively in g. Dca, Dcd = diffusivity coefficient of electron acceptor and donor respectively in the film. Common examples of electron donor and acceptor are glucose and oxygen respectively. Neglecting convective terms, Lamotta (6 6 ) used the following material balance to analyze simultaneous diffusion and reaction. ^e ^ ^ca + rv where . Sca = substrate concentration at any point within the film. De = effective diffusivity coefficient o f S in the film. ry = rate o f substrate consumption per unit film volume. Assuming a zero order kinetics based on experimental evidence in the literature and under steady state conditions, he provided two rate expressions for the substrate uptake depending on the film thickness. For this purpose, a critical film thickness Thc was defined. (2De S.)‘A 1X - = — <4» where Icy = rate of substrate uptake (constant). Sg = substrate concentration at the top of biofilm. 24 In the case of incomplete substrate penetration, the observed substrate uptake was found to be dependent on the magnitude of the depth o f penetration and independent of the total thickness (66,129). For this case a correction factor called the effectiveness factor (X) was defined as follows to account for internal diffusional resistances: Atkinson and Daoud (3) presented the biological rate equation based on diffusion with biochemical reaction. Several subsequent publications by Atkinson’s research group (4,5) reviewed and showed how the biological rate equation presented earlier could be extended and used in the design of microbial film fermenters (5) and trickling filters (6 ). The complete biological rate equations* for microbial films were given ssrlw X = Thc/Th (6) where Th = total film thickness. N = XN, (k3 S ) max l+k3S (6) where Ianhk2Th ^p k2Th tanh - I) for ^p < I (7) tanh k2Th k2Th (8) _ (k2 T h(k 3 S) 0 ----------- —------ v V 2(l+k 3 S) [k3 S - ln(l+k 3 S ) r 1/2 (9) ( 10) k3 = 1 /KS (H) 25 S = substrate concentration in the solution. Th = biofilm thickness. a = area o f viable organisms/unit volume a ,Ks = rate coefficients defined by the expression: r = aS/(Ks+S) r = local rate o f substrate uptake per unit area of viable microorganisms. De = effective diffusion coefficient within the microbial mass. N = rate of substrate consumption/unit interfacial area. Nmax = maximum rate of substrate uptake = kt Th/k3 kx ,k2 ,k3 = biological rate equation coefficients. The advantage o f these models is that they take into account the diffusional resis­ tances in the slimes. The models, however, assume discrete viable organisms dispersed in limitations in the film. Harris and Hansford (49) emphasized the importance of this factor and formulated models to establish whether the performance of the microbial film is affected by limitation o f oxygen, organic carbon or both simultaneously. They used two material balance expressions and a modified Monod expression to incorporate two reactants as given below: the slime which is not true for filamentous organisms. Besides they do not consider oxygen ( 12) (13) 26 where Dg = diffusivity o f glucose in the slime. Dq = diffusivity o f oxygen in the slime. Sca = substrate concentration in the slime. 0 = oxygen concentration in the film. Kg5K0 = half-velocity coefficients for substrate and oxygen respectively. JLtm = maximum growth rate of organisms Xf = cell concentration in the slime, x = distance measured into the slime from the interface. = cell yield. Fc = constant factor relating the quantities of glucose and oxygen utilized in the aerobic metabolism. Kinetic parameters used in the model were taken from the literature. Below organic load­ ings of 300 mg/1 COD, the oxygen profile remained positive while the substrate concen­ tration profile dropped to zero. Within the loading range of 300 to 500 mg/1 COD5 both profiles fell to low levels. This was defined as the transition range before the limitation changed from substrate to oxygen. Using an annular reactor Trulear and Characklis (129) developed material balance relationships giving rate expressions for substrate removal, biofilm detachment and accrual. Low fluid velocities were found to limit the transfer of glucose from the bulk liquid to the liquid film interface. This becomes diffusion limited. Biofilm detachment increased with fluid velocity and attached biomass. 27 Due to the complexity o f the analysis involved and lack of parameter values the models of Williamson and McCarty (146,147) were not used widely as biofilm models in reactor designs. Meunier and Williamson (86,87) presented a simplified model so that these models could be used in the design o f certain biofilm reactors. The model which could be solved in a programmable calculator first computes the limiting species o f either the elec­ tron donor or acceptor and the flux. The design volume of the reactor is then determined on the basis of the calculated flux. Reactor Studies o f Substrate Kinetics and Biofilm Dynamics Experimental channels or artificial streams have been used to study the impact of pollutants and organic enrichment on the structure and function o f the periphytic com­ munities. The idea of these channels and streams is to simulate the natural system in the best possible way and provide the controlled environment a complex system would require to study its responses to several perturbations. The successful application o f continuous flow laboratory reactor systems in studying mixed populations has been reported by several investigators (3 1,43,66,94,149). Most o f these studies have given considerable infor­ mation on self-purification o f streams even though they provided inadequate data for quantitative analyses. Steady state conditions for biomass growth and substrate consump­ tion rates have been indicate in these studies. One study (94) concluded that substrate util­ ization was proportional to nutrient loading but at steady state, attached growth rate was limited by the available surface. Lamotta (6 6 ) found substrate uptake and biofilm growth rate to be defined by the initial substrate concentration during the early stages of growth and were zero order with respect to the subsequent concentrations. 28 Studies o f microbiofilms in natural environments have been limited in scope. Investi­ gations were carried out on kinetic studies of Sphaerotilus natans and related species in organic enriched waters as these organisms are predominant in river biofilms under pol­ luted conditions (27,31,97,102). Based on these studies, Sphaerotilus natans was found to have a competitive advantage over other organisms especially at low DO, nitrogen, and high flow rates. Dias and Heukelekian (30) showed the utilization of inorganic nitrogen com­ pounds by Sphaerotilus natans as readily as the organic nitrogen. Phaup and Gannon (97) determined the optimum concentration of sucrose for heavy growth o f Sphaerotilus natans as 5 mg/1 at a velocity range o f 0.58 to 1.49 ft/s in the temperature range of 20 to 28° C. One mg/1 organic carbon was found as a limiting concentration for the formation of slime by Curtis (27). Above this limit the slime growth was proportional to the concentration of organic carbon. By not accounting for sloughed material, they reported low yield coef­ ficients., Stumm-Zollinger (122) discussed the implications with respect to the procedures in assessing in a laboratory the matabolic activity o f a natural community. He concluded that laboratory mixed cultures grown on nonselective multisubstrate medium do not simu­ late natural populations. It can be inferred from his study that it is difficult, if not impos­ sible, to grow and maintain a natural microbial population in the laboratory without any alteration. He concluded that bacteria in natural environments can utilize certain sub­ strates concurrently. Clark et al. (22) successfully used artificial streams to study the structural and func­ tional responses o f the attached biological communities to disturbances. Benthic commun­ ity photosynthesis and respiration and the effects o f some important environmental factors such as light intensity, CO2 supply, DO and temperature were studied in some laboratory 29 streams by McIntire (80). Several other studies using a controlled environment in artificial streams to study the physical variations and toxicants on biological communities have been reported (72,95,144). Based on an extensive literature review, it can be said that artificial streams provide a very useful means o f studying natural microbial communities as long as the limitations are clearly recognized. Water Quality Modeling o f Rivers Water quality models. A general framework in the formulation and application of simple mathematical models to water quality analysis is described in Hydroscience (57) for EPA water programs. Several processes govern the degradation of organics discharged into rivers and other water bodies. The basic mechanisms o f self-purification have been described qualitatively in the literature (98,132). DO and BOD have been used as the two overall parameters of water quality for a long time. In addition to biooxidation, several factors such as sedimentation, scour and biological extraction have been reported as important in studying in-stream BOD removal rates (32,92,125,148). The overall removal of BOD may be given as: Ko = k D + k Sc + B (14) where Kq = coefficient for overall BOD removal. Kq = coefficient for overall stream deoxygenation. Kg0 = coefficient for sedimentation. B = coefficient describing a boundary effect by slime layers. Overall observed deoxygenation coefficients (K0) for 23 river systems were reported by S 30 Wright and McDonneI (148) which varied from 0.08/day to 4.25/day under steady state flow conditions. In order. (o estimate stream deoxygenation coefficients associated with oxidation o f carbonaceous BOD, empirical relationships were developed relating them to stream hydraulic geometry; The main point to note from this study was that the ob­ served in-stream deoxyge^afion rates were much higher than the laboratory BOD reaction rates, especially when stre^p flows were less than 800 cfs. Velz and Gannon (131) intro­ duced the coefficient B for which Bosko (14) and Novotny and Krenkel (92) subsequently formulated expressions tp account for BOD removal by slime layers in European and American streams. Models have been proposed and used by several investigators for DO and BOD (12,89,93,101,114) since the original Streeter-Phelps model (120). These models were modifications of the single term first order kinetic model. The schemes required for parameter estimation o f these models have been reported over the last few years (13,101). Several researchers have criticized the first order models which are based on a number of simple biochemical reactiqns (34,40,100). In the most recent stage of development, models utilizing saturation kinetig expressions have come into use (34,40,106). They successfully used Monod kinetic expressions in defining the utilization of substrate uptake by sus­ pended biomass and shqwed their application in streams. Gates (40) concluded that laboratory batch reactors popld be used with considerable advantage in studying biological processes in a river. The problem with using Monod type expressions in river modeling lies in the difficulties of selecting and using the appropriate coefficients. Rutherford and O’Sullivan (106) used curve fitting procedures to determine the coefficients to be used. Several water quality parameter compilation and modeling techniques for water bodies from small shallow streams to larger rivers in different geographic regions have been 31 reported in the literature by various investigators ( 11,23,53,60,61,71,89,92,114 ,117 ,142). The important observatiqp to be made from these modeling efforts is the emphasis placed on the sessile microbial communities in small, low flow streams (92,114) even though some . studies did not consider t^ppi (11,71). Transfer processes, general, advection and dispersion are the major transport processes in rivers. Adveptipn is very important in streams and rivers whereas dispersion becomes predominant in estuaries (57). A very useful parameter is the longitudinal dis­ persion coefficient, wjiich combines the effect of diffusion and dispersion; diffusion in this respect refers to mixing produced by turbulence and Brownian motion and dispersion by the variation of velocity across the stream. This parameter provides an easy method of determining the spread of pollutant over long distances in streams. The useful application of this parameter and its determination for modeling efforts have been discussed in the literature (35,37,69,82,IO(S). A Summary and Critique In general, microbial adhesion in streams provides the microorganisms especially the bacteria with a stationary location exposed to a continuous supply of nutrients and pro­ tection against many sourpes of stress in aquatic habitats. The sessile microorganisms were found to be enmeshed ip a polysaccharide matrix. There was no clear agreement on whether algae or bacteria polonize first even though there was evidence to show that attached algae provided a suitable surface for subsequent bacterial colonization. Massive growths of Sphaerotilus pytyps were found predominating under polluted conditions even 32 at reduced DO levels, possibly by their successful competition with other organisms. Often heterotrophs predominate the slime layers in polluted areas. Several theories have; been presented by. researchers on the mechanisms of microbial adhesion. The accumulation o f microorganisms onto a surface may take place in three stages: (a) Adsorption o f organisms to the surface (b) Attachment by polymer bridges (c) Growth and division of organisms on surface There has been no clear demonstration in the literature o f the general involvement of pili and flagellates in the adsorption process, even though obviously the hydrodynamics of organisms with these surface appendages should contribute in some way to the attachment process. Two types of sorption, reversible and irreversible have been identified in the literature depending on whether the application o f shear force would remove the bacteria or whether the adhesion y/as by extracellular polymers anchoring them to the surface. The organisms in the bottom %yer o f river biofilms must be irreversibly bound as they can only be removed by scraping with a blade. The organisms have to adhere to surfaces in low nutrient environments for survival. If this is so, why should organisms under polluted conditions with excessive nutrients attach to surfaces? Wardell and Brown (134) suggested that when there is excess, carbon, large amounts o f polymer would be produced which I - would cover all available binding sites thus hindering attachment of organisms. Under low nutrient conditions, there would be plenty o f binding sites available. But then, how will it be possible to find larger concentration of attached organisms under polluted conditions . compared to unpolluted conditions? This may be because of the “adherent growth habit” 33 suggested by Costerton (24) which would require the organisms to adsorb to . surfaces before metabolizing the substrates. Besides many organisms would divide only if they are attached to a surface. Various factors affecting the attachment, growth and nutrient removal capabilities of the organisms have beeq discussed. Surface properties of surfaces may dictate the for­ mation of the conditioning film initially. In this respect a rougher surface typical of natural environments should promote better initial colonization due to several zones of contact in forming a conditioning film. However, the surface texture and wettability should not interfere with the subsequent attachment process. The role of the flow velocity is in transporting the organisms food molecules and nutrients to the surfaces besides shearing the attached biomass. Higher velocities would promote the transfer process and increase scour rates while maintaining the kinetics in a reaction controlled region. This would reduce or eliminate the liquid phase diffusional limitations. Shear forces prevent biofilms from building up excessively so that a condition o f steady state is possible, exhibiting an oscillatory behavior corresponding to growth and scour. The prevention o f excessive build up may help maintain aerobic conditions in the film, more so in a mixed film with algae and bacteria. In thick films, the. bottom may become anaerobic causing product forma­ tion. However, the role of these products in changing the substrate concentration in the overlying water is unclear. Two different theories are hypothesized to explain the nutrient removal capabilities of the films. According to the first theory, the nutrient removal rates decreased after limiting thicknesses were reached whereas they reached a maximum and remained constant based oq the second theory. The decrease was found to be only tempo­ rary and a constant nutrieqt removal rate has been observed in many studies. It was evident from the literature that a considerable amount o f theoretical work backed by experimental investigations were carried out on microbial film reactors in the sixties and seventies. In most cases, however, rate limitation was restricted to only one reactant and assumed to pccur due to mass transfer in the liquid, solid phase diffusion in the slime or biochemical reaction. Subsequently, studies were done to define conditions under which an organic sq^strate (electron donor) or the oxygen (electron acceptor) may become limiting within a microbial film. This information could be used in the design of several biofilm reactors including trickling filters. It may be pointed out, however, that most o f these studies did not consider oxygen limitations or active film depth. This may be very important in reactors treating wastewaters having high concentration of organics with thick microbial films. A few studies in the past few years have considered the concept of active film depth in their formulations. Simple material balances have been used recently in establishing the kinetics o f substrate removal and biofilm growth. This is very useful considering the ease with which the model parameters can be determined. In all cases, the assumptions used in the mqdels should be studied carefully before application. Due to the complexity in functioning o f the slime layers, the low concentration of organics and the fact o f . continuous flow, reaction schemes in streams have not been fully explained. Several investigators reported the successful application of continuous flow • ■ I reactors in. the study of mixed populations. The reasons for using a CSTR reactor were that the flow characteristics are well known and simple material balance expressions can be formulated. By a rigoroug control of the experimental systems, less variable and replicable data may be obtained, bpt extrapolating these results to natural environments may be misleading. Artificial stream designs in this respect are more helpful because of its yersatil- 34 35 ity. They can be designed as systems enclosed in environmentally controlled chambers to semi-controlled open out-of-doors systems.. Artificially seeded organisms or naturally . colonized films may be ugecl. These designs can be tailored to fit the required experimental needs o f the investigator concerned. Therefore, artificial streams are, as reported recently very useful in studying q&tural populations. Problems o f using laboratory mixed cultures growing on non-selective piutli-substrate media in simulating natural populations have been discussed in the literature. Probably, an easier and cheaper method of obtaining a natural population would be to grow the organisms in the natural environment to be simulated and transfer them to an artificial stream system. In this case however, there will be several autotrophic and heterotrophic organisms making it a fairly complex microbial community presenting problems of isolation and identification. Several water quality models have been developed in different situations based on first order or saturation kinetics. In most modeling efforts, kinetics had to be assumed since information defining the rates of reactions was lacking. Recently, first order models have been criticized based on new developments on bacterial kinetics. Numerous theo­ retical refinements have ]?een made to the saturation kinetic expressions to account for various factors. Incorporating these refined expressions would theoretically give rise to more realistic models. However, validation of such models require determination o f many parameters which would make it necessary to use some kind of curve fitting procedure. While this procedure is an accepted method in. practice, making the parameters easily adjustable invalidates to some extent their fundamental generality. The critical problem is to determine which microbial population, suspended, attached or both play the dominant function in substrate assimilation and its kinetics. This may not be possible, admittedly, in 36 every situation. Once the kinetic expression is determined, it may be utilized in the stream model. THEORETICAL CONSIDERATIONS This section deals with all the theoretical considerations and formulations involved in the subsequent chapters qti mathematical modeling o f streams.. Mathematical Models Any natural system can be looked upon as a mathematical system with complex I interacting subsystems. Natural background water quality is determined by a number of external inputs to the system such as rainfall and solar radiation. In addition, the system may also be subjected to various man-made stresses caused by, for example, wastewater discharges. The response o f such a system can be evaluated by studying the spatial and temporal distribution o f the concentration o f various substances affecting the water quality. In this study, the system is a river and the substance is organic carbon. Conceptual Description The system deflnitiqn and the processes involved in a substrate-biomass model can best be illustrated in a diagrametic form as shown in Fig. I . The importance and relevance of these processes have already been discussed in detail under the previous section on the review of literature. Specification o f Interactiqps . i • The mechanisms involved in affecting the model parameters have to be specified in the construction of the model. The lack of knowledge and understanding of a significant mechanism will affect the realistic modeling of some of the water quality parameters. On 38 SUSPENDED BIOMASS AND SOLIDS ^ - DETACHMENT * • B IO FILM COBBLY STREAM BED SUBSTRATESETTLEMENT ADVECTION AND D ISPER SIO N Fig. I . Schematic Diagram of the Model Frame Work. the other hand, the inclusion of all possible interactions will substantially complicate the model. Therefore in a complex system, it is only realistic to consider the pre-dominant mechanisms and elements. The processes involved in the substrate biomass model are: Transfer Processes (1) Advection or bulk fluid flow (2) Dispersion Transformation Processes (1) Substrate—Uptake by Biofilm and Suspended Biomass (2) Suspended Biomass-Growth, Settlement and Decay (3) Biofilm—Attachment, Growth, Decay and Detachment. 39 In a small stream or river, the mixing characteristics are such that the dispersion of the mass of material may be very small and it may be neglected in comparison to the flow. The computational complexity can be reduced significantly by such an assumption. Fundamental to the analysis of the model to be described subsequently is the point form o f continuity equation which describes the relationship between the flux and the sources and sinks of mass. In general, 98: —— = - v *j + r: (15) 9 t J in which, Sj = concentration of a water quality variable t = time j = flux = 9 S/9 Z - U.S = transfer processes for a one dimensional system V = Del.operator U = mean stream velocity Z = distance = Longitudinal Dispersion Coefficient rj = sources and sinks of Sj given by the transformation processes. The transformation processes may be described by several reactions in natural waters with different kinetic order. However, the limiting step may be represented by a simple first or second order kinetic expression. 40 Assumptions and Conditions In the analysis that follows, several assumptions are made which are given below: (I) The substrate removal by suspended biomass is negligible in shallow streams com­ pared to that of the pre-dominantly heterotrophic biofilm. . (2) Organic carbon |s the rate limiting substrate for the heterotrophs lumped together. (3) The spatial system parameters for the river flow such as mean velocity and depth are assumed constant. (4) Major Dissolved Oxygen limitations are not present in the film. (5) Temporal steady state values for all system parameters and inputs are assumed. The consequences o f these assumptions are considered under the section on discussion. Based on the last assumption, the steady state model will not be able to describe diurnal variations in water quality. However, the applicability of a predictive model in many problem situations is important under critical short term conditions. The investigator may use the steady state model and input the maximum daily waste load for the worst con­ ditions, recognizing that the water quality response will improve at the lower steady state daily waste load levels. Unsteady state models involve complex, solutions and require extensive data for validation and hence a simpler steady state model is a reasonable com­ promise between complexity and practicality. 41 Modeling Organic Carbon in Streams Formulation of Models The main variables identified in the model framework are substrate S, suspended biomass X and heterotrophic fraction o f attached biomass, M^. Using the general continu­ ity Equation (15) the. following material balance expressions can be written based on assumptions 2, 3 ,4 and (5): 9S a2s as Rs r b (16)D t -------- U ■ - .. .....- - at L a Z2 az Ys Ya H ax ax r D (17)- u — + Re + -7 7 - at az s H 3Ma _ a f r B " r D (18) where Djj = longitudina