Rates of cellular attachment to an established biofilm
by J Cahyono Gunawan
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Chemical Engineering
Montana State University
© Copyright by J Cahyono Gunawan (1991)
Abstract:
There is no predictive theory available for predicting the attachment rate of viable cells to an
established biofilm [11] . The need for a reliable prediction of attachment rate of viable cells to an
established biofilm is imperative to generate an accurate mathematical model of biofilm accumulation
on a surface.
An experimental method has been developed to use radiolabelled cells to measure the rate at which
cells attach to an existing biofilm. First, a C12 Pseudomonas aeruginosa biofilm was grown in a
rotating annular bioreactor (RotoTorque). After an established biofilm was obtained, C14 labelled P.
aeruginosa cells were introduced into the RotoTorque. The rate of cellular attachment to an established
biofilm and the rate of cellular detachment can be measured by counting the radioactive intensity on the
surface of the established biofilm using a liquid scintillation counter.
Gross attachment rates (cellular attachment rates in the absence of simultaneous detachment) ranged
from 103 to 105 CFU/(cm2 minute), while net attachment rates (cellular attachment rates measured
with simultaneous detachment) ranged from 102 to 104 CFU/ (cm2 minute). The difference between
the gross and net rate attachment is the rate of detachment.
Preliminary results indicate the attachment rate of viable cells to an established biofilm is a function of
temperature and bulk cell concentration. The effect of shear stress was indeterminate.
A model is proposed, coupling film theory and pseudosteady-state transport theory, describing the
attachment rate of viable cells to an established biofilm in -a RotoTorque system. 
RATES OF CELLULAR ATTACHMENT TO AN 
ESTABLISHED.BIOFILM
by
J .Cahyono Gunawan
A thesis submitted in partial fulfillment 
of the requirements for the degree
of
Master of Science 
in
Chemical Engineering
MONTANA STATE.UNIVERSITY 
Bozeman, Montana
AUGUST 1991
ii
APPROVAL
of a thesis submitted by
J.Cahyono Gunawan
This thesis has been read by each member of the thesis 
committee and has been found to be satisfactory regarding 
content, English usage, format, citations, bibliographic 
style, and consistency, and is ready for submission to the 
College of Graduate Studies.
June 11, 1991
Date Chairperson, Graduate Committee
Approved for the Major Department
June 12, 1991
Date H^ad, Major Department
Approved for the College of Graduate Studies
Date0 GraduatevDean
iii
STATEMENT OF PERMISSION TO USE
In presenting this thesis in partial fulfillment of the 
requirements for a master's degree at Montana State 
University, I agree that the Library shall make it available 
to borrowers under rules of the Library. Brief quotations from 
this thesis are allowable without special permission, provided 
that accurate acknowledgment of source is made.
Permission for extensive quotation from or reproduction 
of this thesis may be granted by my major professor, or in 
his/her absence, by the Dean of Libraries when, in the opinion 
of either, the proposed use of the material is for scholarly 
purposes. Any copying or use of the material in this thesis 
for financial gain shall not be allowed without my written 
permission.
Signature
Date
c-ftkjwio
-AtsW 5-> 1991
iv
ACKNOWLEDGEMENTS
I would like to thank the following people without whom 
this thesis would not be possible:
Dr. Ron W. Larsen for his love, encouragement, 
discipline, support, patience, and enthusiasm which paced me 
through my graduate work.
Dr. John Sears for his concern, encouragement, advice, 
and contributions to my graduate program. Dr. Robert Nickelson 
for serving on my thesis committee.
Dr. Warren Jones, Anne Camper, and Brent Peyton for their 
valuable time to clarify the problem in the experimental 
system and their valuable time to go through the draft.
Dr. Clifford Bond for letting me use the liquid 
scintillation counter. Lyman Fellows, Gordon Williamson and 
his crew members for technical assistance.
Jane Curtis and Margaret Jensen for their excellent 
"paper work" assistance and "doughnuts". All my friends at 
CIMPE and for their support and motivation.
Chemical Engineering Department/Montana State Engineering 
Experiment Station and National Science Foundation through 
C.I.M.P.E. for providing the financial support.
My parents, Mr and Mrs Huang, and my wife, Veronica, for
their patient and everlasting support;......... and my lovely
daughter, Cynthia Kartika for keeping me awake in the middle 
of the night so that I can go to school to type this thesis.
TABLE OF CONTENTS
INTROD U C T I O N.....................    I
LITERATURE R E V I E W ....................................... , 3
Biofilm ............................................ 3
Biofilm Processes .............................  3
Biofilm Properties .............    6
Pseudomonas aeruginosa ...................... 7
Nutrient Medium  ^ ........... 9
Previous Mathematical Models ...................... 12
Mathematical Model of Cells .................  12
Cell death and decay..................... 14
Model for the rate of spontaneous natural
d e a t h ...................................  14
Y i e l d ...................................  17
Mathematical model for cell growth . . .  18
Mathematical Model for Chemostats ........... 20
Mathematical Model for RotoTorque ........... 23
Fluid kinematics . ......................  23
Substrate balance........................  3 0
MODEL DEVELOPMENT.......................................   32
Attachment M o d e l ..........   32
Experimental Approach ............................  39
EXPERIMENTAL ............................................ 48
Reactors............................................... 51
Chemostat......................................  51
R o t o T o r q u e .......................................52
Preparation . . . .................................  52
General............  52
Nutrient Medium ..............................  55
Experimental System and Design .................... 56
Detachment Experiment ........................  63
Liquid Scintillation Counter . . .    64
Plate C o u n t ............................   65 .
Conversion from CPM to CFU . . .   65
R E S U L T S..................................................  67
Summary of Results................................. 73
Effect of Suspended Cells Concentration on
Attachment R a t e ..............................  74
Effect of Temperature ........................  76
Effect of Fluid Shear on The Rate of Cellular 
Detachment
V
77
TABLE OF CONTENTS - continued
Detachment.........................................  77
Independent Measurement of Detachment . . . .  77
Comparing the Rates of Total Cellular 
D e t a c h m e n t .......................................80
CONCLUSIONS..............................................  87
RECOMMENDATIONS .........................................  88
REFERENCES CITED .........................................  90
A P P E N D I C E S .................  94
APPENDIX A: RAW D A T A .................................. 95
PHASE I E X P E R I M E N T ............................. 96
PHASE 2 E X P E R I M E N T ............................. 98
Run I ....................................... 99
Run 2 ......................................101
Run 3 ......................................103
Run 4 ......................................105
Run 5 ......................................107
Run 6 ......................................109
Run 7 .............   Ill
Detachment Result ...................... 113
APPENDIX B : DATA A N A L Y S I S ..............   115
PHASE I .......................................... 116
PHASE 2 .......................................... 120
Run I ......................................120
Run 2 .............................   123
Run 3 ...................................12 6
Run 4 ......................................129
Run 5 ......................................132
Run 6 ......................................135
Run 7 ......................................138
APPENDIX C: FLUID SHEAR PREDICTION IN THE ROTOTORQUE . 156
vi
vii
LIST OF TABLES
1. General Characteristics of P. aeruginosa . . .  9
2. Dimensions of R e a c t o r s ..........................51
3. Experimental Conditions - General............... 59
4. Experimental Condition Stage I, Establish
Biofilm........................................... 60
5. Experimental Condition Stage 2, Condition
S y s t e m ........................................... 60
6. Experimental Condition Stage 3, Attachment . . 61
7. Influent Fresh Substrate Glucose
Concentration for Phase 2 Run 3 Experiment . .63
8. Summary of R e s u l t s .............................. 74
9. Net Rate of Total Cellular Attachment
per unit area as a function of Xb ............. 74
10. Net and Gross Rate of Cellular Attachment
per unit area vs. Temperature................... 76
11. Rate of Cellular Detachment per unit area
vs. Temperature.................................. 76
12. Rate of Cellular Detachment per unit area
vs. Fluid s h e a r .................................. 77
13. Rate of Total Cellular Detachment I
Table Page
80
viii
14. Phase I, Run I: Radioactivity L e v e l s ...........97
15. Phase I, Run I: Viable C o u n t s ................... 97
16. Phase 2, Run I: Radioactivity L e v e l s ...........99
17. Phase 2, Run I: Viable C o u n t s .................. 100
18. Phase 2, Run 2: Radioactivity Levels . . . .  101
19. Phase 2, Run 2: Viable C o u n t s............. 102
20. Phase 2, Run 3: Radioactivity Levels . . . .  103
21. Phase 2, Run 3: Viable C o u n t s ............. 104
22. Phase 2, Run 4: Radioactivity Levels . . . .  105
23. Phase 2, Run 4: Viable C o u n t s............. 106
24. Phase 2, Run 5: Radioactivity Levels . . . . 107
25. Phase 2, Run 5: Viable C o u n t s............. 108
26. Phase 2, Run 6: Radioactivity Levels . . . .  109
27. Phase 2, Run 6: Viable C o u n t s.................. H O
28. Phase 2, Run 7: Radioactivity Levels . . . .  Ill
29. Phase 2, Run 7: Viable C o u n t s...............   112
LIST OF TABLES - continued
Table Page
ix
30.
31.
32 .
33 .
34 .
35.
36.
37.
38.
39.
40.
41.
42.
- Table
LIST OF TABLES - continued
Page
Phase 2, Run 4: Viable Cell 
Concentration in the Bulk
Liquid in the RotoTorque vs. T i m e .............. 113
Phase 2, Run 6: Viable Cell 
Concentration in The Bulk
Liquid in the RotoTorque vs. Time .............. 114
Phase I, Run I: Result I ....................... 117
Phase 2, Run I: Result 2 .................... 12 0
Phase 2, Run 2: Result 3 ...........   123
Phase 2, Run 3: Result 4 ....................... 126
Phase 2, Run 4: Result 5 ....................... 129
Phase 2, Run 5: Result 6   132
Phase 2, Run 6: Result 7 . : .................. 135
Phase 2, Run 7: Result 8   138
Numerical Values of Coefficients for
Regression Equations ...............  152
dXs14/d[Tm] ......................................153
The Rate of Total Cellular Detachment II . . 154
Values for Saturation-Type Equation43. 155
XLIST OF FIGURES
Figure Page
I. Schematic of a C h e m o s t a t ......................2 0
2. Mass Transfer or Friction Factor vs. Reynolds 
N u m b e r ......................................... 2 5
3 . Flow Between Two Concentric Cylinders ......... 29
4. Idealized Film t h e o r y .......................... 33
5. Experimental System of Phase I, Run I .........49
6. Experimental System of Phase 2 Experiments . .50
7. RotoTorque Parts of Phase I Experiment . . . .53
8 . RotoTorque Parts of Phase 2 Experiments . . . .  54
9 . Attachment Experiment .................  . . . .  58
10. P 2 R I: C14 Viable Cells of the
Bulk L i q u i d ..................................... 69
11. P 2 R I: Accumulation of C14 Viable Cells . . .  70
12 . P 2 R I: Rate of C14 Cellular Detachment
vs. T i m e ....................................... 73
13 . Rftg vs. Xb ■........................ 75
14. Detachment: P 2 R 4 ............................ 78
15. Detachment: P 2 R 6 ............................ .79
16. P 2 R I: Rate of C14 Cellular Detachment
vs. T i m e ......................................... 81
17. P 2. R 3: Rate of C14 Cellular Detachment
vs. T i m e ......................................... 82
18. P 2 R 4: Rate of C14 Cellular Detachment
vs. T i m e ......................................... 83
19. P 2 R 5: Rate of C14 Cellular Detachment
vs. T i m e ......................................... 84
20. P 2 R 6: Rate of C14 Cellular Detachment
vs. T i m e ....................................... 85
21. P 2 R 7: Rate of C14 Cellular Detachment
vs. T i m e ....................................... 8 6
22. P I R I: Accumulation of C14 Viable Cells . . 118
23. P I R I: C14 Viable Cells of the
Bulk L i q u i d ......................................119
24. P 2 R I: Accumulation of C14 Viable Cells . . 121
25. P 2 R I: C14 Viable Cells of the
Bulk Liquid ................................. 12 2
26. P 2 R 2: Accumulation of C14 Viable Cells . . 124
27. P 2 R 2: C14 Viable Cells of the
Bulk L i q u i d ..................................   125
xi
LIST OF FIGURES - continued
Figure Page
Xll
Figure 
28.
29.
30.
31.
32
33 .
34.
35.
36.
37.
38.
39.
40.
P 2 R 3: Accumulation of C14 Viable Cells . . 127
P 2 R 3: C14 Viable Cells of the
Bulk L i q u i d ......................................128
P 2 R 4: Accumulation of C14 Viable Cells . . 13 0
P 2 R 4: C14 Viable Cells of the
Bulk L i q u i d ......................................131
P 2 R 5: Accumulation of C14 Viable Cells . . 133
P 2 R 5: C14 Viable Cells of the
Bulk L i q u i d ......................................134
P 2 R 6: Accumulation of C14 Viable Cells . . 136
P 2 R 6: C14 Viable Cells of the
Bulk L i q u i d ......................................137
P 2 R 7: Accumulation of C14 Viable Cells . . 139
LIST OF FIGURES - continued
Page
P 2 R 7: C14 Viable Cells of the
Bulk L i q u i d ......................................140
P I R I: Accumulation of C14 Viable Cells
vs. [Tm] .........................................143
P 2 R I: Accumulation of C14 Viable Cells
vs. [Tm] ......................................... 144
P 2 R 2: Accumulation of C14 Viable Cells
vs. [Tm] ......................................... 145
Xlll
41.
42.
43 .
44.
45.
46.
Figure
LIST OF FIGURES - continued
P 2 R 3: 
vs. [Tm]
P 2 R 4: 
vs. [Tm]
P 2 R 5: 
vs. [Tm]
P 2 R 6: 
vs. [Tm]
P 2 R 7:
Accumulation of C14 Viable Cells
Accumulation of C14 Viable Cells
Accumulation of C14 Viable Cells
Accumulation of C14 Viable Cells
Accumulation of C14 Viable Cells
vs. [Tm] .....................................
Fluid Sheaf on the Inner Surface of RotoTorque
146
147
148
149
150 
158
Page
xiv
ABSTRACT
There is no predictive theory available for predicting 
the attachment rate of viable cells to an established biofilm 
[11] . The need for a reliable prediction of attachment rate of 
viable cells to an established biofilm is imperative to 
generate an accurate mathematical model of biofilm 
accumulation on a surface.
An experimental method has been developed to use 
radiolabelled cells to measure the rate at which cells attach 
to an existing biofilm. First, a C12 Pseudomonas aeruginosa 
biofilm was grown in a rotating annular bioreactor 
(RotoTorque). After an established biofilm was obtained, C14 
labelled P. aeruginosa cells were introduced into the 
RotoTorque. The rate of cellular attachment to an established 
biofilm and the rate of cellular detachment can be measured by 
counting the radioactive intensity on the surface of the 
established biofilm using a liquid scintillation counter.
Gross attachment rates (cellular attachment rates in the 
absence of simultaneous detachment) ranged from IO3 to IO5 
CFU/(cm2 minute), while net attachment rates (cellular 
attachment rates measured with simultaneous detachment) ranged 
from IO2 to IO4 CFU / (cm2 minute). The difference between the 
gross and net rate attachment is the rate of detachment.
Preliminary results indicate the attachment rate of 
viable cells to an established biofilm is a function of 
temperature and bulk cell concentration. The effect of shear 
stress was indeterminate.
A model is proposed, coupling film theory and pseudo­
steady-state transport theory, describing the attachment rate 
of viable cells to an established biofilm in a RotoTorque 
system.
IINTRODUCTION
A biofilm, a surface accumulation of cells, organic and 
inorganic debris immobilized at a substratum and embedded in 
an organic polymer matrix of microbial origin, is not 
necessarily uniform in time and space; that is, it may be 
spatially non-homogeneous, and change with time. A substratum 
is a support surface which may be either a solid or a liquid. 
"Cells" in the biofilm may consist of living, non-viable, 
and/or decaying cells. Non-viable cells are incapable of 
growth temporarily, while decayed cells are no longer capable 
of life processes.
Accumulation of biofilm is encountered in many natural 
and man-made environments. Natural surface water quality, root 
surfaces, cooling tower fill, teeth and gums, are all affected 
by adsorbed microorganisms. Biofilms serve beneficial purposes 
in some natural and man-made environments but in certain cases 
biofilms are considered a nuisance [11].
Zobell (1943) is probably the research pioneer on the 
association between microorganisms and solid surfaces. This 
research continued in a spasmodic fashion until the last 
decade. Rapid progress in this field in recent times has made 
it possible to take a more fundamental approach to describe 
biofilm processes in a system.
Adherence of living and/or non-living particles from the 
fluid to the surface of biofilm, attachment, is one of the
2processes leading to biofilm accumulation. This work concerns 
with the rate of cellular attachment to an established 
biofilm, which is defined as the sorption rate of living cells 
from the bulk liquid to an established biofilm.
Although a kinetic expression of attachment is proposed 
in this work, the focus of this research is to develop a 
technique to measure cellular attachment rates from suspended 
pure culture to single population biofilms.
3LITERATURE REVIEW
Biofilm
Biofilm Processes
Biofilm accumulation is the result of chemical, physical 
and microbial processes occurring in the system. These 
processes are interrelated. The substrate composition, for 
example, can affect the growth rate and the ability of cells 
to attach [26]. Increasing calcium concentration has been 
shown to increase the cohesiveness of the biofilm as indicated 
by a lower detachment rate [33].
Viruses and most bacteria are so small that they behave 
as colloidal particles in aqueous systems. Perhaps they are 
better considered as "living colloids" [7]. Physicochemical 
principles, coupled with a model to describe growth and 
microbiological phenomena can be used to describe the biofilm 
accumulation in a system.
The surface upon which a biofilm will accumulate, the 
substratum, is first conditioned by adsorped organic 
macromolecules and nutrients from the liquid system. It does 
not usually take a long time (within minutes) to condition the 
substratum [11]. Concentrating nutrients on the substratum 
because of adsorption will enhance microbial growth on the 
substratum. On the other hand, adsorped molecules can inhibit
4microbial adsorption [11]. Characklis [11] concludes that the 
role of the conditioning film in microbial adsorption to a 
surface is not yet clear.
Microorganisms can be transported from the bulk liquid to 
the liquid-substratum interface by many means. Physical 
phenomena such as diffusion, gravity, thermophoresis, and 
radial fluctuation (convection) in a turbulent flow system 
and cell motility are important factors. System parameters 
such as temperature, pH, liquid viscosity, and flow pattern 
will decide which factors are most significant [7].
Microorganisms which have already been transported to the 
liquid-substratum interface may be adsorped by the substratum. 
Variables affecting this adsorption process are the character 
of microorganism, the character of substratum, and the 
character of the environment [28]. All these variables will 
determine how fast the microorganism will be adsorbed and 
whether the adsorption is going to be permanent or non­
permanent. Microorganisms leave the substratum surface by a 
process called desorption.
After an initial accumulation of microorganisms is 
established, a different phenomena begins to take place. 
Microorganisms are now attaching to the initial biofilm. The 
character of the substratum becomes less important for 
attachment of a microorganism to an established biofilm. The 
ability of microorganism to form extracellular polymeric 
substances (EPS) may be an important factor in determining
5whether or not a microorganism will adhere to the surface of 
biofilm [7].
As mentioned before, some of the microorganisms will not 
adsorb permanently, but will desorb from the substratum and 
return to the bulk liquid, a process that is called 
desorption. If either microorganisms or biomass are lost from 
an established biofilm, the process is called detachment. 
Desorption, the loss of cells adsorbed to the substratum, 
occurs from the moment of initial adsorption, while 
detachment, the loss of cells or biomass away from the 
substratum, happens only after the biofilm is established.
Characklis and Marshall [11] describe three types of 
detachment. The first is erosion, a continuous loss of small 
portions of biofilm, which is highly dependent on fluid 
dynamic conditions. Sloughing, the second type, is a rapid, 
massive loss of biofilm which generally occurs with thicker 
biofilms. The last type is abrasion, i.e., a loss of biofilm 
due to repeated collisions between suspended particles and the 
biofilm, or between multiple substratum particles as in a 
fluidized bed.
Once living microorganisms are adsorbed, they start 
using substrate on the surface for growth, replication, 
maintenance, and for the formation of extracellular products. 
The living microorganisms may use non-viable cells as nutrient
sources as well.
6The interaction among those processes: adsorption and 
desorption followed by attachment and detachment, growth and 
death, will determine the total accumulation of biofilm on a 
surface. The accumulation, however, is not necessarily uniform 
in time and space. For example, sloughing, which generally 
occurs with thicker biofilms can contribute significantly to 
the unsteady-state behaviour of biofilms accumulation on a 
substratum. However, it will usually take a few days before 
"thicker biofilms11 accumulate on a substratum. This means that 
although a steady-state condition is not necessarily 
accomplished, one or more processes can be forced to reach a 
nearly steady-state value for a certain period of time under 
certain conditions. Under such conditions a "pseudosteady- 
state" hypothesis may be used to describe the processes 
mathematically.
Biofilm Properties
Biofilm properties are related to properties of their 
main components, i.e., water and microorganisms with their 
EPS. The biological properties of the microorganisms: growth 
rate, substrate utilization, metabolic path, molecular 
structure of EPS produced, etc.; are dependent on the 
particular environment in which the microorganisms are 
growing.
Biofilm thickness (100 - 1000 jitm) and dry mass density 
(10 - 50 kg m'3 in fluid flow systems) [33] are highly
7dependent on fluid dynamics of the system, the type of 
microorganism, nutrient , substrate composition and 
concentration. The physical appearance of the biofilm depends 
partially on the type of microorganisms. Biofilms composed of 
pure culture Pseudomonas aeruginosa have a relatively "smooth" 
surface [11].
The chemical properties of a biofilm are highly dependent 
upon the type of microorganism and the nature of the 
substrate. Different microorganisms will have different 
byproducts and different metabolic pathways. The nature of the 
substrate will especially affect the metabolic path. Sucrose 
grown Streptococcus mutans produces more EPS than glucose 
grown S . mutans. Under electron micrography, sucrose grown S . 
mutans produces diffuse EPS while glucose grown S. mutans 
produces relatively highly organized EPS [3].
Pseudomonas aeruginosa
P. aeruginosa is a member of the family pseudomonadaceae. 
The name was created about seventy years ago [37]. As 
presently defined, the family of pseudomonadaceae are 
characterized by the absence of prostheceae, a metabolism 
typically respiratory, an absence of fermentation and 
photosynthesis, and a capacity for growth at the expense of a 
large variety of organic substrates with the exception of the 
1-carbon compounds [32].
8Pseudomonas is a genus within the family of the 
pseudomonadaceae. It is a motile, gram negative, oxidase 
positive rod. Only one species is frequently pathogenic in 
man; others affect plants, fishes and some animals. The 
oxidation-fermentation (0/F) reaction is oxidative, 
distinguishing the genus from aeromonas [27].
Phylogenetically, based on 16s-rRNA sequencing, the 
various genera of pseudomonads scatter within subdivisions 
alpha, beta, gamma purple bacteria. The delta group, however, 
does not have pseudomonads within its group. The 16S-rRNA 
sequences are used as a tool to classify the pseudomonads 
phylogenetically, showing an evolutionary relationship 
determined by differences and similarities 16s-rRNA of the 
bacteria.
Although pseudomonads are diverse groups. Pseudomonas 
aeruginosa is quite homogeneous physiologically. All isolates 
fit into a very narrow range of distribution characteristics 
[9]. .
P. aeruginosa produces green-blue pigment (pyocyanine) on 
cultures and wound pus. Yellow pigment (fluorescein) may also 
be apparent on agar plate. The species occurs as a pathogen in 
urine, burns, wounds etc., often with other bacteria. Growing 
pseudomonas produce an antibiotic substance (pyocyanase) 
inhibitory to some other bacteria [27].
P. aeruginosa is a polymer forming bacterium. The primary 
mode of growth is in polymer-enclosed microcolonies [31],
9attached to a wide variety of substrata. The polymer capsule 
may*act as a protecting layer. The layer is relatively diffuse 
and easily dispersed in the liquid phase. The polymer capsule, 
however, may have an important role in assisting the bacteria 
to attach on a surface [33].
Table I.
Shape 
Breadth (jum)
Length (/xm)
Motility 
Respiration 
Gram stain
Optimal Temperature (0C) 
Optimal pH
aeruginosa. [31]
Rod
0.5 - 0.8
1.5 - 4.0
Polar flagella
Obligate aerobe
Negative
35 - 37
6.8
General Characteristics of P.
Nutrient Medium
Nutrients or substrates are substances in the environment 
which are used by organisms for metabolism. Nutrients are 
usually divided into two classes: I) essential nutrients,
without which cell growth will be hindered; 2) non-essential 
nutrients which are not essential to cell growth, but which 
will be used by microorganisms if they are available.
Essential nutrients include: carbon, hydrogen, oxygen, 
nitrogen, phosphorous, sulfur, potassium, magnesium, calcium,
10
sodium, and iron. The required nutrients are divided into two 
groups by the amount required by the organism: macronutrients 
and micronutrients.
Those nutrients listed above are found in nature or 
provided in a man-made reactor as organic or inorganic 
compounds. The form in which these substances are available 
can affect the metabolic efficiency. If the carbon source, for 
example, were given in the form of CO2 instead of glucose, the 
efficiency of metabolism would be lower [1,8]. Cells will take 
carbon from the environment and change it into cell 
constituents. The oxidation state of carbon in cell 
constituents is zero. Some energy, then, is needed to reduce 
the oxidation state of carbon in CO2 to zero.
In a man-made reactor, the way a substrate solution is 
made also an important factor. Most substrate solution is 
sterilized before being delivered to the reactor. The common 
way to sterilize substrate is by autoclaving. At high 
temperature, glucose (a common carbon source) in the presence 
of phosphate will form substances which may be poisonous to 
some organisms [2] . Additionally, caramelization should be 
considered.
The amount of nutrient given will also affect the rate at 
which microorganisms grow. In general, the higher the nutrient 
concentration, the faster the microorganisms will grow. The 
growth rate, however, will be constant above a certain 
nutrient concentration. The nutrient concentration which gives
11
the maximum growth rate varies from one organism to another. 
Some organisms will reach their maximum growth rate at a low 
substrate concentration and a higher concentration of 
substrate may inhibit growth or even stop it. Cell lysis may 
occur because of the osmotic pressure difference between the 
inside and outside of the cell wall [8].
The important aspect to be noted, then, is that the 
substrate composition is an important factor which may alter 
kinetic parameters significantly. Any modelling effort should 
consider the changes in kinetic parameter values that might be 
induced because of substrate composition changes.
12
Previous Mathematical Models
Mathematical Model of Cells
Biological populations consisting of a single species 
more than likely differ physiologically, morphologically and 
possibly genetically too [11]. The individuals combine to form 
populations in which properties, such as size, age, biological 
activity, etc. follow different distribution patterns although 
the cells grow in the same environment. To incorporate all 
these factors will be impossible because of many restrictions 
such as time limitation and instrument capability. In order to 
come up with a manageable model, some simplifications will be 
used.
If the number of cells per unit volume in a particular 
system is large enough, average state properties can be used. 
A model which uses average state properties and neglects the 
distribution of state properties is called a deterministic 
model [30]. Such a model is used in this research.
In a multicellular microorganism or a complex system like 
a biofilm, life is segregated into structurally and 
functionally discrete units, i.e., cells. These cells may grow 
under different conditions because of spatial inhomogeneity in 
the system variables such as nutrient concentration, 
temperature, pH, etc. As a result, the number of cells is an 
important parameter to, at least partially, describe the 
system. A system consisting of "n" cells will have a different
13
biological characteristic than a system which has "2n" cells. 
If the, number of cells in the system is high enough (n -> °o) , 
n will be approaching 2n and segregation of cells in the 
system can be ignored. A model in which segregation is ignored 
is called a non-segregated or distributed model and assumes 
that there is a uniform cell mass distribution [30].
Two microorganisms which have the same biomass and 
environment may, however, have different properties and 
activities. It is a problem of state. The two organisms may 
have different states; one organism is younger than the other 
one with respect to the period of time elapsed since the two 
organisms were formed by fission of their parents. A model 
which does not recognize the existence of a distribution of 
states is called a non-structured model. A non-structured 
model is used in this research. Such a model assumes the 
biological structure and the state of the cells as determined 
by. previous history need not be taken into account. This 
assumption is valid if cell growth is balanced, i .e., if all 
extensive properties of the growth system are altered in the 
same way as a function of time. Balanced growth is difficult 
to achieve in a high growth rate system [30].
In the short term, cells may be considered as small 
living reactors which behave in the same manner under the same 
conditions.
14
Cell death and decay. It has long been recognized that 
only a portion of the biomass present in biochemical 
operations is actually alive and contributing to the activity. 
On the other hand, only recently has the spontaneous death of 
cells become known [18].
Viability is defined as the mass of living or viable 
cells present divided by total mass of cells.
£ l _
+
(i)
where
V. = viability
Xv = mass of viable cells [M]
Xd = mass of non-viable cells [M]
As currently defined, a viable cell is one that will form a 
colony on solid growth media, and a non-viable cell is one 
which has lost that ability.
Model for the rate of spontaneous natural death. McKinney 
[24] was one of the first engineers to try to model the 
generation of inactive (non-viable and decayed) cells in 
biochemical operations. His work was followed by B.L. Goodman 
and A.J Englande [17]; and also by D.R. Christensen and P.L. 
McCarty [13]. Nevertheless, none of them was trying to
15
correlate viable cells to the generation rate of non-viable 
cells.
The only model available today for bacterial death which 
has been verified against experimental data is that proposed 
by Sinclair and Topiwala [16] . Their model says that the death 
rate of viable cells, rDxv, is directly proportional to the 
concentration of viable cells in the medium [16].
rD x v = - Y x V (2 )
■Gxd - rDxv (3)
where
Y = death rate coefficient [T"1]
r Gxd = generation rate of non-viable cells [M T"1]
Cell decay is a term representing the loss of cell mass. 
If an exogenous substrate, substrate outside the cell which is 
available to be converted into energy that can be utilized by 
the cell, falls below the needs for maintenance, minimum 
energy necessary for keeping the cell functioning, then a 
portion of cell mass will be degraded to supply maintenance 
energy. In heterogenous culture predators may consume other 
cells, resulting in a loss of cell mass because the growth 
efficiency of predators using other cells is not 100%. As some
16
cells die, they begin to leak their internal contents into the 
medium, a process which is called cell lysis. Only the 
remaining cell wall is large enough to be measured. This also 
contributes to the loss of cell mass [16].
Thus it can be seen that decay is actually a composite 
term, incorporating the effects of many factors. For this 
reason a first-order model of cell decay is strictly 
empirical. The justification of the model described below is 
based on its usefulness and ability to predict the loss of 
cell mass.
The loss of viable cell mass by decay, rdxv, is modelled 
as a first-order function of viable cell concentration and the 
loss of non-viable cell mass, rdxd, as a first-order function 
of non-viable cell concentration [16].
^ d X V - - b V x V  < 4 >
r ~ - b X
where bv and bd are the specific decay constants for viable and 
non-viable cells, respectively.
Living cells may lose their cell mass by endogenous 
metabolism (metabolism which are utilized nutrient stored 
inside the cell when exogenous substrate is available 
abundantly), maintenance requirements, and predation, whereas
17
non-viable cells may lose their cell mass mainly by predation. 
Consequently, the coefficient by is more likely to be greater 
than bd [18]. However, because of lack of data, it is assumed 
that by and bd are equal:
bv -bd -b (6)
Yield. Yield is defined as the amount of biomass formed 
per unit amount of substrate removed, and is a measure of the 
relative efficiencies of energy conservation and utilization. 
The vague term "amount” is used to stress that there is more 
than one definition which leads to different numerical values 
of the yield.
There are at least four definitions of yield which have 
been used. Differences among them are in the way the amount of 
substrate consumed is defined. The "amount of cells" is 
defined as the dry mass, generally expressed in grams. The 
amount of substrate consumed is expressed as: I) the 
equivalent amount of ATP which could be formed from it [I]; 2) 
the equivalent amount of total energy removed from the medium 
[I]; 3) the number of electrons initially available in the 
substrate for transfer to the terminal electron acceptor or 
for incorporation into cell material [1] and; 4) the reduction 
in the amount of organic matter present, expressed as COD
18
[16]. In this research, the last definition of yield will be 
used.
Under conditions of unrestricted growth, rate of energy 
utilization for maintenance is negligible in comparison to the 
rate of energy utilization for cell synthesis. Accordingly, 
the "true yield", Yg, is defined as the amount of cell 
material formed per unit of substrate utilized in the absence 
of maintenance energy requirements. For a detailed treatment 
see reference I, pages 135 through 148.
Mathematical model for cell growth. The reaction rate for 
cell growth can be expressed as:
where JLt is the specific growth rate. The Monod equation 
[1,2,11] will be used to model the substrate dependence of the 
specific growth rate. If only one limiting substrate is 
considered, then the Monod equation can be written as:
Gxv ^ ^v (7)
(8)
where
maximum specific growth [T"1]
19
S = The concentration of growth limiting substrate 
[M L"3]
Ks = The half saturation constant [M L'3]
Although there is a similarity between the Monod equation 
and the Michaelis-Menten equation used to describe enzyme 
reaction rates [2], the Monod equation is not derived on the 
same theoretical grounds. While the Michaelis-Menten equation 
can be derived from a consideration of the rates of chemical 
reaction catalyzed by enzymes, the Monod equation is strictly 
empirical [2]. The justification of the Monod equation 
(equation (8) ) is based on its demonstrate ability to describe 
the specific growth rate as a function of substrate 
concentration [16]. The Monod equation is used in this 
research.
Using the definition of the true yield [16], Yg, and the 
Monod equation, the rate of substrate utilization, -rg, can be 
expressed as a function of viable cell concentration, Xv, as 
follows:
-rS (9)
20
Mathematical Model for Chemostats
A chemostat is a 
continuous-flow stirred 
tank reactor (CFSTR); 
i.e. , the bulk liquid 
concentration gradient can 
be neglected. The 
chemostat consists of a 
reaction vessel and a 
stirrer. The surface area 
per unit volume is considerably less than that of a 
RotoTorque, so that the biofilm which grows on the inside 
surface of the chemostat may be ignored.
Incorporating the model of cell growth described in the 
previous section (equation (7)) and, assuming that the only 
solids in the reactor are cells, suspended solid balance under 
steady-state conditions [16]:
Figure I. Schematic of a Chemostat
inlet - outlet + growth - death - decay = O
v - F  X v + rCxv v -  (-Idxv) v - (-Idxv) V =  O ( 1 0 )
where,
F = inlet and outlet volumetric flow rate [L3 T'1]
V = volume of the reactor [L3]
21
The first term of equation (10) , the input term is zero 
because the total mass of suspended solids, M0, is zero. M0 is 
the sum of inlet inert solids (Zj0), inlet biodegradable solids 
(Zb0) , and inlet cell concentration (X0) [16] .
M0 = X0 + Zio + (11)
using equations (2),(4),(5),(6), the Monod equation (equation 
(8) ) and equation (11),
I
T
+ y + b (12)
where
x = V
F
(13)
Using equations (8) and (12), substrate concentration in 
the reactor, S, can be expressed as a function of space time, 
T1 as follows:
K3 + Y + b)
Via - + Y + b)
S (14)
22
Equation (14) indicates that the substrate concentration in 
the chemostat, S, is controlled solely by T and S does not 
depend on inlet substrate concentration S0. C.P.L. Grady, Jr., 
et al. [16] have demonstrated this for a pure culture growing 
on a single substrate. For a mixed culture, Ks will be a 
function of S0 [16].
If T becomes large enough, 1/r will be close to zero and 
S will reach its minimum value. The minimum value of S, Smin, 
is given by;
S  ~ Ks ^  + ^  (15)
mln _ I*. -  (Y + W
Smin is the minimum substrate concentration that can be 
approached in a CFSTR.
The maximum rate at which a bacteria can grow upon a 
given substrate depends upon the influent substrate 
concentration, S0. The specific growth rate, ii', under this 
condition is given as follows:
/ (16)
The minimum space time is also known as the point of 
wash-out because at shorter space times, all cells are 
washed out of the reactor and no net growth will occur
23
(provided no cells have adsorbed on the inside surface of 
the reactor and no cell comes in with the inlet flow). 
Consequently, the minimum space time, Tmin, can be calculated 
by setting n in equation (7) equal to n' in equation (16) :
lmin S0 (\xm - y - b) - Ks (y + b)
(17)
If there are cells coming in with the influent; the same 
procedure yields modified expressions for, n, Xv, S, Xd, X, and 
V. which are recorded in reference [16].
Mathematical Model for RotoTorcrue
A RotoTorque is a continuous-flow stirred tank reactor. 
(CFSTR), i.e., the bulk liquid concentration gradient is 
negligible. The RotoTorque consists of two concentric 
cylinders, a stationary outer cylinder and a rotating inner 
cylinder. The RotoTorque provides a large surface area per 
unit volume of fluid. In this case, the biofilm which grows on 
the inner surface of the reactor cannot be ignored.
Fluid kinematics. There are four flow regions to be , 
considered in a RotoTorque: laminar streamline flow, laminar 
flow with Taylor vortices, turbulent flow, and turbulent flow 
with vortices [29]. For this study, it is enough to know that 
the transition between the laminar streamline flow to other
24
zones flow pattern can be correlated by the transition 
Reynolds number, Retrans, given by equation (18) [6] . For a
detailed treatment see reference 27, pages 525 through 531.
(18)
where
f2 = angular velocity of the inner cylinder [T"1 ]
K = the radius ratio of the inner cylinder to the
outer cylinder
R = radius of the outer cylinder [L] 
p = mass density [M L"3]
jit = viscosity [M L'1 T"1]
Some work on the fluid kinematics and mass transfer for 
laminar and turbulent flow in an annular geometry has been 
carried out. R.B. Bird and C.F. Curtiss [6] describe the 
tangential, Newtonian, laminar flow in annuli for unsteady 
flow conditions. Joseph Kaye and E.C. Elgar [20] describe the 
mode of fluid motion in an annulus with an inner, rotating 
cylinder. Using a long vertical annulus with the gap to inside 
diameter ratio of 0.18, they mentioned that the critical 
rotation rate at which vortexes appeared in the annulus for 
zero axial velocity is 28.6 rpm; the theoretical value 
predicted by Taylor's theory is 28.3 rpm [20]. R. Kappesser,
25
I. Cornet, and R. Greif [19] give a correlation for mass 
transfer near a rotating cylinder with turbulent flow in terms 
of the Sherwood number, and as a function of Reynolds number 
and Schmidt number. They also present a graph which correlates 
critical Reynolds number to roughness of the wall (Figure 2) . 
A.K. Wang and L.W. Gelhar (1971) give a prediction of the mean 
velocity profiles for turbulent couette flow. However, one 
parameter and one constant must be evaluated experimentally in 
order to apply their prediction to a turbulent annular flow.
8
o
CO
o.i
o.oi -
0.001
100 1000 10000 100000 1000000
Re
Figure 2. Mass transfer or friction factor vs. Re [19]
26
Although a lot of work has been done in an attempt to 
describe the fluid kinematics in an annular geometry, none can 
be applied directly to describe the fluid kinematics in the 
RotoTorque used in this experiment unless additional 
measurements are made. In order to use A.K. Wang and L.W. 
Gelhart1s result, the torque, mixing length, and the velocity 
at a certain point in the annuli have to be known. To use the 
mass transfer correlation above; the concentration of 
substrate at the wall and the roughness of the wall have to be 
known.
Nevertheless, if the wall surface is assumed very rough 
(d/e = 87, where e is roughness in cm), which is a reasonable 
assumption for many biofilm surfaces, then, the correlation 
for mass transfer and friction factor can be used (Figure 2); 
Nomenclature for Figure 2 is as follows:
Sh = (N d)/ (D AC)
Re = (w d2) / (2 v)
Sc = Schmidt number
N = mass flux at wall, g equiv/(cm2 sec) 
d = diameter of the rotor, cm 
D = diffusion coefficient, cm2/sec 
C = concentration, g equiv/cm3 
w = angular velocity, radians/sec 
v = kinematic viscosity, cm2/sec
Using Figure 2, the friction factor can be estimated if 
the Reynolds number is known.
27
To estimate the shear stress on the surface of 
RotoTorque, the circumferential time averaged velocity must be 
calculated first. Neglecting the curvature, the problem can be 
simplified into a problem of two parallel plates (couette 
flow). If the distance between those two parallel plates is 
2h, with the lower plate assumed stationery and the upper 
plate moving with a constant velocity of 2 Vw in the X 
direction (Cartesian coordinates are now used and the 
direction of flow is chosen as the X direction), then, A.K. 
Wang and L.W. Gelhar have solved the problem using Zagustin1s 
energy balance [34]. The velocity distribution is given as 
follows:
(19)
where
v* = (7-0/p)"-5
T 0 = shear stress on the wall, (dyne/cm2) 
p = fluid density (gram/cm3) 
k = Von Karman constant = 0.4
Vw = fluid velocity at the inner wall (cm/second)
The average velocity over the cross section (A) can be 
calculated using :
28
„ = U v d A  
T T d A
(20)
Using Figure 2 to get the friction factor and equations 
(30 and 31) , shear stress for a given rotor rotation speed can 
be calculated using the following equation (21):
xO (21)
Another method which may be used to calculate shear 
stress uses Figure 3 [29]. Using this approach, the
coefficient of friction is given as a function of Taylor 
number.
Coefficient of friction is defined as
0.5 n p V21 R 21 h
(22)
where
M. = moment induced by the rotor [H L2 T"2] 
p. = density of liquid [M L"3]
Vj = peripheral velocity of the rotor [L t'1] 
Rj = radius of the rotor [L]
h = height of the rotor [L]
= gap between two concentric cylinders [L]d
29
linear Iheary
nonlinear theory, Slusrt
Iarninsr-- ;!-- Isininsrwilh Taylor vortices— — IurDulent
wilhoul vortices 4/J x^. I
s a io 5 a in*
Figure 3. Flow between two concentric cylinders; torque 
coefficient for inner cylinder in terms of the Taylor number, 
Ta.[29]
Figure 3 was obtained originally using d/R. value of
0.028. However the data are reported using Taylor number which 
has taken the dimension of the system into consideration.
30
A good approximation of torque coefficient, then, can be 
obtained for different d/R, and Reynolds numbers. Figure 3 
also indicates that turbulence in the system occurs for Taylor 
numbers greater than 400, although vortices are apparent for 
Taylor numbers as low as 41.3.
Substrate balance. A biofilm reactor model can be based 
on total number of cells or total number of viable cells. From 
an experimental point of view the choice of variable of cells 
is determined. For example, if a plate count is utilized, the 
number of viable cells (actually Colony Forming Units or CFU) 
is determined. If an optical measurement (e.g. acridine orange 
analyzer) is used, total number of cells is determined.
A substrate balance on the bulk liquid in a RotoTorque 
can be written using the same approach as a chemostat, so long 
as the biofilm is accounted for at steady-state. Grady and Lim 
[16] have solved the problem as follows:
I  —  r +  * o  -I +  ________ H  o -^ s________________
T K s + Sb Y  {Ks + Sb) (S0 - Sb) V  (23)
2, -
Where,
qm = maximum substrate consumption [M L"2 T'1]
Sb = bulk substrate concentration [M L3]
As = Surface area of the biofilm [L2]
V = reactor volume [L3]
nn = overall effectiveness factor
31
The values of the overall effectiveness factor for many 
different conditions are given in reference 16, page 539. For 
a detailed treatment see reference 16, pages 52 3 through 540.
Biofilm accumulation on the inside surface of the reactor 
is the net result of attachment (ratt) and growth in the 
biofilm (rfg) minus detachment (rdet) .
dXf
~dt ~ Zatt + rfg "det
(24)
32
MODEL DEVELOPMENT
Attachment Model
An expression for the rate of cellular attachment will be 
developed using a pseudosteady-state hypothesis coupled with 
a film theory model. A pseudosteady-state hypothesis can be 
used for a system which changes slowly so that steady-state 
processes can be assumed.
The rate of cellular attachment to an established biofilm 
per unit area (Ra) can be described as a two step process. 
First, cells are transported from the bulk liquid to the 
liquid-biofilm interface. The rate of cell transport per unit 
area, Nx, will be developed using the film theory model. The 
Second is the rate of attachment of cells at the liquid- 
biofilm interface to the surface of biofilm per unit area, rg.
The rate of cellular attachment per unit area to an 
established biofilm, Ra, will be determined by equating the 
processes above. Assuming pseudosteady-state, the rate of cell 
transport from the bulk liquid to the liquid-biofilm interface 
per unit area, Nx, will be equal to the rate at which cells 
attach (at the liquid-biofilm interface) to the biofilm 
surface per unit area, rg.
The film theory model assumes the resistance to mass 
transport occurs entirely in a thin film adjacent to the 
surface. Since the flow in the film is primarily laminar,
33
STAGNANT
F I L M  L I Q U I D
BU LK  L I Q U I D
D I STANCE
Figure 4. Idealized Film Theory
the suspended cell concentration gradient changes rapidly 
within the film until the turbulent region is reached. The 
film theory is usually derived for a flat surface [15].
By hypothesizing a stagnant liquid film of thickness Lh, 
the cell concentration gradient in the liquid phase is 
restricted to the stagnant liquid film. The cell concentration 
throughout the remaining region of liquid, the bulk liquid in 
Figure 4, is assumed constant. Lh is not the thickness of the
34
laminar sublayer of fluid flow region but a fictitious film 
thickness which would be required to account for the entire 
resistance to transfer of cells from the bulk liquid to the 
surface if only molecular transport was involved.
Under the idealized model above, the flux of cells from 
the bulk liquid to the surface is given as follows:
Nx = kx (Xb - X w) (25)
where
Nx = the rate of cell transport per unit area [CFU L"2 T'1] 
kx = proportionality constant [L T'1]
Xb = cell concentration in the bulk liquid region 
[CFU L"3]
Xw = cell concentration on the surface [CFU L"3]
The proportionality constant kx has dimensions of 
LT'1, and is a parameter associated with diffusive and 
convective cell transport. Its value is a function of the 
properties of the fluid, the diffusion coefficient of cells in 
the liquid, and Reynolds number [15]. Fortunately, kx can be 
obtained by a simple equation derived theoretically for a flat 
surface as follows [5,15]:
35
(26)
where
Dxb = diffusion coefficient for cells in the liquid 
[L2 T"1]
Lh = liquid film thickness [L]
The values for liquid film thickness, Lh, must be found 
experimentally. This value is independent of the rate of cell 
transport [15].
Different microorganisms will have quite different values 
for Dxb, as it depends strongly on whether or not the 
microorganism is motile. Ignoring the motility of cells could 
underestimate the transport by a factor as much as 20 to 50 
times. Dxb for motile cells can be predicted using a 
correlation as follows [11] :
Dxb 3 (I
Vr dr
cosa)
(27)
where
Vf = velocity of motility [L T'1] 
dr = free length of random run [L] 
a = angle of turn
36
The next step in developing the attachment model is 
obtaining an expression for the attachment of cells on the 
liquid-biofilm interface to the established biofilm. Many 
factors, such as ability to form EPS (which is part of the 
biomass), molecular and physical structure of the biofilm, and 
others which are not yet fully understood may affect the 
attachment rate.
The attachment rate of cells from the liquid-biofilm 
interface to an established biofilm per unit area, rg, can be 
modelled as a function of cell concentration at the liquid- 
biofilm interface as follows:
r a = (28)
The attachment of cells, then, is modelled as a two-step 
process, i.e., transport of cells from the bulk liquid to the 
surface and the attachment of cells at the liquid-biofilm 
interface to the established biofilm. An effort to model the 
rate of attachment has to incorporate these two mechanisms. 
Mathematically, it is difficult to solve unless a steady-state 
condition can be assumed.
As mentioned before, biofilm accumulation is not 
necessarily a steady-state process. In fact, in most cases, it 
is not a steady-state process. However, if the system 
conditions such as temperature, pH, substrate concentration, 
and fluid shear are maintained constant, then, for short
37
periods of time (at least in the order of the replication time 
of the cells), the system can be forced to approach steady- 
state. This argument leads us to use the pseudosteady-state 
hypothesis to incorporate Nx and ra into an attachment rate per 
unit area expression (Rft) .
Using the pseudosteady-state hypothesis, then, Nx will be 
equal to ra, and Rft will be equal to rg.
Ra = kx (Xb - X w) = k a X% (29)
or.
k a X£ + kx X w - k x X b = 0 (30)
and.
Ra = k m2g (31)
The problem in obtaining an expression for Rft as a 
function of bulk cell concentration is, now, to express as 
a fuction of ka, kx, and Xb. Then, the expression for Xw can be 
subtituted into equation (31) to obtain an expression for Rft.
A numerical value of the power "n" from equation (28) or 
(31) will be determined by experimental data on the rate of 
cellular attachment per unit area to an established biofilm, 
Rft vs. viable cell concentration in the bulk liquid of the
38
RotoTorque, Xb. If n equals zero, then the rate of cells 
transport per unit area from the bulk liquid to biofilm-liquid 
interface, Nx, is the controlling mechanism.
The rate of cellular attachment per unit area to an 
established biofilm, Ra, in equation (31) is a net rate of 
attachment per unit area. The net rate of cellular attachment 
per unit area to an established biofilm can be described with 
an example. Suppose at a certain period of time, there are 
10,000 cells per unit area per unit time attaching to the 
surface of the biofilm. This is termed a gross rate of 
cellular attachment per unit area, Rftg. Some of those cells 
will detach and return to the. bulk liquid. Assume that 9,000 
cells per unit area per unit time detach, then the net rate of 
cellular attachment per unit area to an established biofilm, 
Ra, during that particular period of time will be 
(1,000 = 10,000 - 9,000) cells per unit area per unit time. 
The rate of cellular detachment is usually modelled as a 
function of cell concentration on the surface of the biofilm. 
This research is concentrated on the rate of cellular 
attachment so that the rate of cellular detachment will not be 
explored further.
Hereafter, the term "rate of cellular attachment per unit 
area" should be understood to refer to the gross rate of
cellular attachment per unit area, R Ag- The net rate of
cellular attachment per unit area, R An' will be clearly
indicated by the subsript "n" when used.
39
Experimental Approach
Consider a RotoTorque which is being operated with inputs 
from two sources: I) a steady input of fresh substrate, e.g., 
glucose and 2) the effluent of a chemostat operating at 
steady-state. At time t = 0, the fresh substrate input to the 
RotoTorque is switched off. The liquid volume inside the 
RotoTorque is kept constant by maintaining the effluent flow 
rate equal to the influent flow rate. The condition of the 
RotoTorque and chemostat at t = 0' is known. A turbulent flow 
regime is induced only by the speed of the rotor.
Three balances are required to model the rate of 
attachment in a RotoTorque. The first is a cell balance on the 
bulk liquid, and the second is cell balance on the surface. 
The third is a substrate balance. Ignoring death and decay 
terms because of their considerably smaller magnitudes 
compared to the other terms in the balances, the cell balance 
in the bulk liquid for the unsteady-state condition can be 
written as follows:
Accumulation of cells in the bulk liquid =  input - output 
- attachment +  detachment +  growth (bulk liquid)
Cell balance on the surface (biofilm):
40
Accumulation of cells on the surface =  attachment 
-detachment +  growth (surface)
Substrate balance over the RotoTorque:
Accumulation of glucose in the bulk liquid =  input - output 
- substrate uptake (bulk liquid +  biofilm)
The Monod equation (equation (8)) is usually used to 
model growth in the bulk liquid. The same equation can be used 
to model growth in the biofilm, but mass transfer resistance 
from the bulk liquid to the biofilm and diffusion of substrate 
through the biofilm must be taken into account. For a thin 
biofilm, diffusion within the film is negligible compared to 
mass transfer resistance in the fluid adjacent to the film 
[16]. Mass transfer rates for non-living particles are given 
by reference 2.
A substrate balance is needed because the specific growth 
rate is a strong function of substrate concentration as given 
by equation (8).
Accumulation of cells in the bulk liquid, concentration 
of cells on the surface, and substrate accumulation can be 
measured experimentally.
41
The attachment and detachment rate coefficients can then 
be calculated by simultaneously solving the three equations 
described above.
Even using first order kinetic model, the procedure to 
determine attachment and detachment rate coefficients is quite 
complex.
If the attachment rate coefficient could be obtained 
independently under steady-state conditions, the effort 
required to obtain parameters for the system would be 
simplified. One way to solve the problem is to use 
radiolabelled cells. This is the approach taken in this work.
First, a biofilm is grown using C12 glucose under steady- 
state conditions (i.e., constant temperature, fluid shear, 
inlet substrate concentration, and residence time). While a 
biofilm is being established , the RotoTorque influent is 
switched to the effluent from a first chemostat which is fed 
steadily with C12 glucose. After a certain period of time (> 
3t) when fluctuations in the RotoTorque are diminished, 
radiolabelled cells are introduced. At time t = 0, the 
RotoTorque influent is switched to the effluent from a second 
chemostat which has been operating exactly the same as the 
first, except for operation on C14 glucose.
At time t = O+, the RotoTorque with a C12 cell biofilm and 
C12 cells in the bulk liquid is receiving an effluent of a 
chemostat operating on C14. Both the chemostat and the 
RotoTorque are operating at steady-state with respect to the
42
total cell concentration (C12 and C14 cells) in the bulk 
liquid. The fraction of C14 cells in the RotoTorque will 
increase from zero at t = O to nearly one, at t > tL. The 
concentration of the C14 cells in the RotoTorque is not 
constant over time. The accumulation of radiolabelled cells 
can be determined by writing a C14 cell balance on the 
RotoTorque (assuming pure CFSTR behavior) . The result is as 
follows:
^  f  (44 - * 14) (32)
where
F = inlet and outlet flow rate of the RotoTorque 
[L3 T'1]
V = the liquid volume in the RotoTorque [L3]
Xi14 = inlet C14 cell concentration [CFU L"3]
X14 = bulk C14 cell concentration [CFU L'3]
t = time [T]
The inlet C14 cell concentration, X.14, the volume, V, and 
the inlet and oulet flow rates, F, are constants. Equation 
(32) can be integrated easily to give:
where r is the space time as given by equation (13).
The total number of cells in the RotoTorque, Xtotal, 
assuming pure CSFTR behavior, will be equal to the inlet C14 
cell concentration, X1-14. The assumption is justified since the 
RotoTorque receives only the effluent from the chemostat, the 
glucose concentration of the bulk liquid in the RotoTorque is 
low, and the residence time of the RotoTorque was set 
considerably lower than the residence time of the chemostat, 
thus growth is minimized.
The rate of cellular attachment and detachment per unit 
area are both negligible compared to other terms in equation 
(32) . This will be demonstrated below in the results section.
The ratio of the C14 cell concentration to total cell 
concentration in the RotoTorque, then, can be given as 
follows:
jf-total
(34)
Assuming that the C14 cells are behaving the same as the 
C12 cells, the ratio of the gross rate of C14 cellular 
attachment per unit area to an established biofilm, Rftg14, to
44
the gross rate of total cellular (C12 cells + C14 cells) 
attachment per unit area to an established biofilm, will be:
Rlg - (I - e-t/x) Rlgtal t^O 05)
Equation (35) holds for any time greater than or equal to 
zero as indicated above. On the other hand, the ratio of the 
net rate of C14 cellular attachment per unit area to an 
established biofilm to the net rate of total cellular 
attachment per unit area to an established biofilm, which will 
be given below, holds only for a large time as determined by 
the experiment. This is caused by the fact that ,the C14 cells 
which just attached to the surface will not detach as fast as 
the C12 cells which have been attached for a longer time and 
initially cover a larger portion of the surface. Eventually, 
at time t > tL, as indicated by a steady-state rate of C14 
cellular detachment per unit area, both C14 cells and C12 cells 
will behave identical with regard to attachment and 
detachment, and the ratio of the rate of cellular attachment 
per unit area of the C14 cells to the rate of total cellular 
attachment per unit area will be:
t ztLR H  = (I - e~t/x) Rlltal (36)
45
Ideally, the time tL is chosen as the time at which the 
rate of C14 cellular detachment per unit area reaches its 
steady-state, however, for practical purposes the time tL 
could be chosen as the rate of C14 cellular detachment per unit 
area reaches 90% of its steady-state value. Appendix B 
describes how the time tL is chosen for this work.
We know that;
R1A-Rll-Rf (3?)
Using equation (35) to substitute for RAg14.
rA  - (I - e"t/T) Rlgtal - Rl4 (38)
The rate of C14 cellular detachment per unit area in 
equation (37) is zero at time t = 0. Let us assume for a 
moment that the rate of C14 cellular detachment per unit area 
is zero at any time greater than zero. Integrating equation 
(38) over time will give the accumulation of C14 cells per unit 
area of biofilm surface, the experimentally measured quantity.
acc. of C14 = J R ^ d t  = f (I - efc/T) R ^ tal dt (39)
The (gross) rate of total cellular attachment per unit 
area to an established biofilm, Rftg, is constant because the
46
number of total cells (C12 + Cu cells) in the bulk fluid of 
the RotoTorque is constant, as are the System parameters such 
as RPM, temperature, pH, etc. Integrating equation (38) will 
give:
accumulation of C14 p e r  unit area - R ^ tal {Tm\ (40)
where
[Tm\ = t - T (I - S-t^ ) (41)
t = time [T]
[Tm] = modified time, defined by equation (41) [T]
T = residence time, F/V [T]
F = inlet and outlet volumetric rate [L3 T'1]
V = liquid volume of the RotoTorque [L3]
However, equation (40) is strictly true only for time t 
= 0 because that is the only time it can be strictly known 
that the rate of C14 cellular detachment per unit area is zero 
at time t = O as assumed during the derivation of equation 
(39).
For time t > tL, equation (36) can be integrated to give:
accumulation of C14 p e r  unit area = R ^ tal [Tm] (42)
47
In conclusion, the method described above can 
theoretically be used to measure the net and gross rates of 
cellular attachment to an established biofilm, and by 
difference the rate of cellular detachment for a particular 
experimental condition. To obtain a model of the rate of 
attachment as a function of bulk cell concentration many runs 
with different bulk cell concentrations must be 
performed.
48
EXPERIMENTAL
The experiments were carried out under aerobic conditions 
with a monopopulation system. In order to avoid contamination, 
substrate and all equipment which was in direct contact with 
the inside surface of reactors was autoclaved prior to each 
experiment. Sterile air filters were used to avoid 
contamination from the surroundings. If one of the reactors 
had to be opened, direct contact with the inner surface was 
always avoided and the opening was performed near a bunsen 
burner to minimize contamination from airborne microorganisms.
Two phases of experiments were performed. First a system 
which consisted of six small RotoTorgues and two chemostats 
was used. The first chemostat was used to grow C12 cells and 
the other chemostat was used to grow C14 cells. At any time, 
there was only one chemostat connected to the RotoTorgues as 
shown in Figure 5. The attachment data were collected from the 
rotor surface of each RotoTorgue.
The system for the second phase of the experiments 
consisted of one standard RotoTorgue and two chemostats. As 
above, one RotoTorgue was used to grow C12 cells while the 
other one was used to grow C14 cells. At any time, there was 
only one chemostat connected to the RotoTorgue (see Figure 6) . 
The attachment data were collected from twelve slides attached 
to the stationary inside surface of the RotoTorgue.
49
Figure 5. Experimental System of Phase I, Run I. Fci -
fresh substrate to the chemostat, Fri - fresh substrate to 
each RotoTorque, Fro - the effluent of the RotoTorques, 
see Table 3a, 3b, and 3c for numerical value of each flow.
50
fresh
FRi substratefresh
substrate
V m I
A sqcm
Chemostat RotoTorque
Figure 6. Experimental System of Phase 2 Experiments.
Fci - fresh substrate to the chemostat, Fri - fresh 
substrate to the RotoTorque, Fco - outlet flow of the 
chemostat, Fro - effluent flow of the RotoTorque, see 
Table 3a, 3b, and 3c for numerical value of each flow.
51
Reactors
Chemostat
The characteristics of the chemostats are listed in Table
2.
Table 2. Dimensions of Reactors.
Phase I Phase 2
Chemostat
Volume 4000 ml Volume 3840 ml
Fci 12 ml/min Fr,- ■ 7.11 ml/min
RotoTorque
Volume 180 ml volume 640 ml
D I 5 cm D I 10 cm
D 2 6.75 cm D 2 11.6 cm
L I 7 cm SW 1.8 cm
L 2 adjusted SL 19 cm
A i
F ro
258.5 cm2 A2 1289.31 cm2
2 ml/min F ro 7.11 ml/min
where,
D l =  diameter of the inner cylinder of the RotoTorque 
D 2 =.diameter of the outer cylinder of the RotoTorque 
L I =  height of the inner cylinder of the RotoTorque 
L 2 = liquid height in the phase I RotoTorque 
SW = slide width
SL = liquid height in the phase 2 RotoTorque 
A = surface area for attachment, subscript refers to 
the experimental phase 
Fci = inlet flow rate into the chemostat 
Fpo = inlet flow rate into the RotoTorque
52
RotoTorque
A RotoTorque is an annular reactor consisting of two 
concentric cylinders, a stationary outer cylinder and a 
rotating inner cylinder. Draft tubes (two for small 
RotoTorques (Figure 7) and four for a standard RotoTorque 
(Figure 8)) were bored at angles in the inner cylinder. The 
draft tubes cause mixing of the liquid phase in the reactor, 
by virtue of the rotating cylinder. The inner cylinder is 
driven by a magnetic stirrer for the small RotoTprque and 
direct coupling to a motor for the standard version.
The inside wall of the reactor and the peripheral area of 
the rotor are considered as the only area for attachment. This 
will give a total area of 258.49 cm2 (A1) and 1289.31 cm2 (A2) 
for the small and the standard RotoTorques respectively.
Preparation
General
In preparation for each experiment, all equipment was 
cleaned. Hydrogen peroxide solution was, then, used to wash 
all reactor components, followed by rinsing with flowing 
distilled water for half an hour to wash out all hydrogen 
peroxide and C14 glucose residue. This was followed by drying 
before the reactors were set up.
D2 Dl
Figure 7. RotoTorque Parts of Phase I E x p e r i m e n t .
Ul
W
Sv/
V-T^
III
• I !  II I /
L J  I. I ii \ I
/ /, <
/ » /
/ / '
< / /
XlH'X I >/ '
\ I I /
Dl
/
Z
TOP VIEW REACTOR CASING ROTOR
Ul
Figure 8. RotoTorque Parts of Phase 2 Experiments.
SL
55
To minimize contamination during an experiment, any leak 
on the system was avoided. Before all equipment was 
autoclaved, the system was operated with water at a flow rate 
twice as high as the anticipated experimental condition for 24 
hours. Any leak found during this period was easily eliminated 
and contamination during the actual experiment was minimized.
All equipment was autoclaved for fifteen minutes at 
1210C prior to use, except for any apparati which were not in 
direct contact with the growth media. All tube ends were 
sealed before autoclaving except the air filter inlet.
Nutrient Medium
The composition of the 
solution was as follows: 
K2HPO4 
KH2PO4 
(NH4)2SO4 
MgSO4
supplied nutrients per liter of
2800 mg.
1200 mg.
640 mg.
400 mg.
The mineral solution (this term will be used throughout this 
thesis) was autoclaved first, then, after cooling, the glucose 
was introduced by filter sterilization. Thirty milligrams of 
glucose as a carbon source were added and acted as the 
limiting nutrient.
When an experiment required a different glucose 
concentration, the concentration of mineral solution was
56
adjusted accordingly. If 10 mg/1 glucose, for example, were 
used, then, the concentration of mineral solution would be 
adjusted to one third the original concentration given above. 
In this way the C/N and N/P ratios were maintained at the same 
level in all experiments.
Experimental System and Design
The system for the phase one experiment consisted of two 
chemostats and six small RotoTorques. The chemostat provided 
a steady supply of planktonic P . aeruginosa along with a low 
substrate concentration. Biofilms were grown in all six 
RotoTorques under the same experimental conditions, i.e., the 
same shear stress (induced by the rotational speed of rotors), 
identical substrate feeds,' and identical dilution rates. 
Theoretically, the same biofilm in terms of thickness, and 
physical and morphological properties should be obtained. 
However, some uncertainties such as human errors, fluctuation 
of the room temperature, etc. might induce variations in 
properties of the biofilms obtained from each RotoTorque. Care 
was taken to minimize these variables.
The same procedure was also followed with the second 
experimental system, except that, in this system, there was 
only one standard-sized RotoTorque equipped with slides (there 
are 12 slices in a RotoTorque), and two chemostats. > 
All experimental conditions are listed in Tables 3, 4, 5, 6.
57
Original cultures of P. aeruginosa were obtained from 
Anne Camper, Staff Microbiologist, Engineering Research Center 
for Interfacial Microbial Process Engineering, Montana State 
University, Bozeman, Montana.
Each experiment started by growing a pure culture of P. 
aerucrinosa in the chemostat under aerobic conditions. To grow 
pure culture in the chemostat, the chemostat was inoculated 
with I ml solution of pure stock culture. The outlet of the 
chemostat went to the RotoTorque(s) (phase one) which were 
also maintained under aerobic conditions. To maintain aerobic 
conditions, the chemostat and RotoTorques were purged with 
filtered air. The rotational speed of each rotor (phase one) 
was set to the same speed. This speed was changed as a 
variable in every experiment.
At the beginning of an experiment, fresh substrate was 
added to each RdtoTorque at the rate of 2 ml/min while fresh 
substrate at the rate of I ml/min was fed to the chemostat. 
During this period, the residence time of the chemostat was 
4000 minutes. The system was operated under these conditions 
for seven days (See Figure 9) . The same procedure was followed 
with the second phase experiment system.
The purpose of the procedure described above was to obtain an 
established biofilm in each RotoTdrque.
Establish Biofilm 
7 days
Stage I
Stage 2
Condition System 
2 days
Stage 3
Attachment Exp.
Chemostat
Chemostat Chemostat
Collected
Chemostat
illected
Figure 9. Attachment Experiment.
59
Table 3. Experimental Conditions - General.
Phasel Phase 2
Rotor
RPM 600 run I 289
' run 2 20
run 3 289
run 4 289
run 5 289
run 6 289
run 7 289
Room Temperature (0C)
run I 22 run I 22
run 2 22
run 3 22
run 4 22
run 5 22
run 6 22
run 7 22
PH
Fresh Substrate 7.2 7.2
RotoTorque Eff. 6.9 6.9
Concentration of the C12 Fresh Substrate glucose (mg/1)
run I 30 run I 30 
run 2 30 
run 3 ** 
run 4 30 
run 5 30 
run 6 30 
run 7 30
Concentration of the C14 Fresh Substrate Glucose (jLtCi/1)
run I 1.5 run I 1.5
run 2 - 7  2.5
**) See Table 4
60
Table 4. Experimental Stage I, Establish Biofilm.
Phase I Phase 2
Duration (days)
run I 7 run 1 - 6  7
run 7 I
Chemostat (ml/min)
FO1
FC0
I 7
I 7
RotoTorgue (ml/min)
Fr.
F r o
2 7.1
2.2 14.2
Note: The flow rate of each stream listed in Tables 4, 5, 6 as
defined in Figure 5, and Figure 6 are given below. The units
are ml/min.
Table 5. Experimental Condition Stage 2, Condition System.
Phase I Phase 2
Duration
run I 2 run 2 - 7  2
Chemostat (ml/min)
Fci
F c o
12 7
12 7
RotoTorque (ml/min)
H1
H1
O 
—• 0 O
2.2 7.1
61
Table 6. Experimental Condition Stage 3, Attachment 
Experiment.
Phase I Phase 2
Chemostat (ml/min)
Fci
Fc0
12 7
12 7
RotoTorque (ml/min)
Fr1-
Fr,
O O
2.2 7.1
After seven days, the flow of fresh substrate to each 
RotoTorque was stopped. At the same time, the flow rate of 
fresh substrate to the chemostat was changed to 12 ml/min. The 
effluent of the chemostat went to the RotoTorques so that each 
RotoTorque received 2 ml/min of fluid from the chemostat. This 
condition was maintained for 2 days. This procedure 
conditioned each RotoTorque for the attachment experiment.
Meanwhile, the second chemostat was operated under the 
same conditions as the first chemostat, except that C14 glucose 
was used instead of C12 glucose. In this way, every parameter 
in both systems was the same except the second chemostat had 
C14 cells and small amounts of C14 glucose in the bulk liquid. 
The specific activity of C14 glucose used was 8.1 millicurie 
per millimole.
The attachment experiment was performed by introducing 
the second chemostat effluent (with C14 cells) to the 
RotoTorque in place of the first chemostat effluent. All
62
experimental variables were maintained constant except now, C14 
cells were entering the RotoTorque system instead of C12 cells. 
The chemostat was still receiving fresh C14 substrate. The Same 
procedure was followed for the second, single RotoTorque 
system.
Data were taken at predetermined intervals. The exact 
times of data collection were recorded.
In phase 2, run 3 experiment, a lower bulk cell 
concentration than the bulk cell concentration in the phase 2, 
run I experiment in the RotoTorque was desired. For this 
experiment, the fresh glucose substrate concentration 
introduced to the system was changed gradually from 3 0 mg/I at 
day I to 3 mg/1 at day 10 as listed in Table 7. The purpose of 
the gradual decrease in substrate concentration was to obtain 
a substantial biofilm growth on the inside surface of the 
RotoTorque and at the same time to prevent shock in the 
system.
Phase 2 run 6 (P 2 R 6) was the duplicate experiment of 
P 2 R I. P 2 R 7 had the same experiment conditions as P 2 R 
I except the C12 biofilm was grown for only I day instead of 
7 days ( i.e.,stage I was only one day long).
All liquid contaminated with C14 glucose was collected and 
submitted to the radiological safety officer for proper 
disposal.
63
Table 7. Influent Fresh Substrate Glucose 
Concentration for Phase 2, Run 3 Experiment.
Day Glucose Concentration
I O mg/1
2 30 mg/1
3 15 mg/1
4 15 mg/1
5 10 mg/1
6 10 mg/1
7 5 mg/1
8 3 mg/1
9 3 mg/1
10 3 mg/1
Detachment Experiment
The rate of total cellular detachment per unit area was 
measured independently for two sets of experimental 
conditions, i.e., phase 2 run 4 (P 2 R 4), and phase 2 run 6 
(P 2 R 6). For the detachment experiment, the RotoTorque with 
an established biofilm was flushed with a high flow rate of 
mineral solution (with a glucose concentration of 2.1 mg/1) so 
that the RotoTorque would have a shorter residence time than 
its minimum residence time (the point of washout).
64
then
First, a biofilm was grown in the RotoTorque. The 
experimental condition at this time was the same as the 
experimental condition at P 2 R 4, and P 2 R 6 (see Table 3) .
After one week, the fresh substrate flow rate was 
increased to 94 ml/min for P 2 R 4, and 67 ml/min for P 2 R 6.' 
The fresh substrate glucose concentration used to flush the 
RotoTorque was 2.1 mg/1 which was the concentration of glucose 
in the bulk liquid of RotoTorque while the biofilm was being 
established. One milliliter volumes of bulk liquid RotoTorque 
effluent were taken at a prescribed times. Plate counts were 
used to enumerate the viable cells for each sample taken.
Liquid Scintillation Counter
A liquid scintillation counter was used to measure the 
radioactivity level obtained from biofilm samples. The units 
of the measured results were counts per minute (CPM).
The following procedure was used to prepare samples for 
counting. First, each sample was obtained by scraping the 
surface of a rotor (phase I) or slide (phase 2). The biofilm 
thus obtained was dissolved in 15 ml cocktail solution 
(Aquasol, Dupont, Massachusetts). Now the sample was ready to 
be counted in the liquid scintillation machine.
65
Plate Count
R2A agar was used to make the agar plates. Approximately 
20 ml of the agar solution was used for each plate. Two types 
of samples were taken for plate count. First, samples were 
taken from the bulk liquid of the RotoTorque. Second, samples 
were taken from the bulk liquid of the chemostats.
The same plate count procedures were used for both types 
of liquid samples. One milliliter of sample liquid was 
transferred to a reaction tube containing 9 ml of mineral 
solution (the first dilution). The second dilution was 
performed by transferring I ml of solution from the first 
dilution to a reaction tube containing 9 ml of the solution. 
Seven serial dilutions were made for each sample.
One-tenth milliliter of each dilution, then, was spread 
over the surface of an agar plate. A sterile glass spreader 
was used to spread the solution over the agar surface. After 
three days of incubation (to minimize contamination) at room 
temperature, colonies were ready to be counted.
Conversion from CPM to CFU
The number of C14 viable cells of experimental run in the 
bulk liquid of each of chemostat was determined by the plate 
count method. The unit of the viable cell count was CFU/ml. 
The intensity of radioactivity level of the bulk liquid, 
consisted of C14 cells and negligible amount of C14 glucose, of
66
the chemostat was measured by a liquid scintillation counter. 
The unit was CPM/ml.
A correlation was established between the number of 
viable cells determined by plate count method (the units are 
CFU) in the chemostat and the CPM of the bulk liquid in the 
chemostat. This standard was performed for each experiment and 
was used to convert CPM to CFU for each particular experiment.
67
RESULTS
Some terms used in this work will be explained again 
here to avoid confusion. The term "total" means the total 
number of C14 and C12 cells. The term "gross", as in the net 
rate of total cellular attachment per unit area to an 
established biofilm means the number of cells attaching to the 
surface per unit area per unit time, i.e. as, if no cells are 
detaching from the surface. The term "net", as in the net rate 
of total cellular attachment per unit area to an established 
biofilm, means the "gross" rate of total cellular attachment 
per unit area to an established biofilm minus the rate of 
total cellular detachment per unit area.
The rate of total cellular detachment per unit area, and 
the gross and net rate of total cellular attachment per unit 
area to an established biofilm can be determined by measuring 
slopes of the graph of C14 cell concentration on the surface 
of the biofilm, Xs14, versus [Tm], the modified time defined by 
equation (51).
As expected, it was observed that the net rate of 
cellular attachment was very small compared to the number of 
cells flowing into or out of the RotoTorque. From P 2 R 7 
experimental run, the number of cells flowing into the 
RotoTorque (48 IO6 CFU/ml) x (7.1 ml/minute) = 3.4 IO8 
CFU/minute, while the net rate of cellular attachment was 
(1400 CFU/cm2 minute) x (1289 cm2) = 1.8 IO6 CFU/minute (it was
68
only .5% of the number of cells flowing into the RotoTorque). 
The profile of bulk C14 cell concentration over time could not 
be used to measure the rates of cellular attachment or 
detachment. Instead, measurement of the accumulation of the C14 
cells on the surface over time were used to determine the 
gross, and net rates of Cellular attachment and, by 
difference, the rate of cellular detachment. Details of this 
procedure are described in the model development section.
The solid line in Figure 10 is a theoretical prediction 
of the C14 cells concentration profile over time based on the 
assumption that the RotoTorque is behaving as a CFSTR. The 
presence of a film is ignored in this calculation. The squares 
are the actual experimental measurement of the C14 cells 
concentration as a function of time. The difference between 
these two should be the net rate of attachment per unit area. 
However, the accuracy of the plate count method limits the 
ability to determine the rate of cellular attachment and 
detachment from the Xb14 vs. time curve.
Direct measurement of the C14 cell accumulation on the 
surface can be used to determine both the gross and net rates 
of cellular attachment per unit area, as well as the rate of 
detachment per unit area. Provided with the graph of Xs14, C14 
cells on the surface per unit area (CFU/cm2) , vs. [Tm] , the 
modified time (see Figure 11), the slope (slope I) of the 
graph at the modified time [Tm) = O will give the value of the 
gross rate of total cellular attachment per unit area while
C
F
U
/m
l
69
the slope (slope II) of the same graph at time t > tL, where 
tL is chosen as large as the data allowed, will give the value 
of the net of Cu cellular attachment to an established 
biofilm.
Theoretical prediction based on
a CSFTR behavior o f the RotoTorqiie
Experimenld data
0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00
Time minutes
Figure 10. P 2 R I: Cu Viable Cells of The Bulk Liquid in 
The RotoTorque vs. Time. Inlet flow rate = outlet flow 
rate = 7.11 ml/min, liquid volume in the RotoTorque = 640 
ml.
70
50.00 100.00 150.00 200.00 250.00 300.00 350.00
[Tm] minutes
Figure 11. P 2 R I: Accumulation of C14 Viable Cells on The 
Surface of an Established Biofilm vs. Modified Time [Tm].
Regular RotoTorque, RPM = 289, fluid shear = 20 dyne/cnr, 
substrate glucose concentration chemostat influent = 30 
mg/1, temperature = 22°C.
The net rate of total cellular attachment per unit area to an 
established biofilm, RAntotal, is correlated to RAn14, the net 
rate of C14 cellular attachment per unit area by equation (36) .
71
The modified time, [Tm], is correlated to time, t, as given by- 
equation (41).
= (I - e"t/x) t *t£ (36)
[Tm] - t - x {1 - e_fc/T) (41)
By using equation (36) to calculate RAnt0tal' is said 
that the value of R Antotal is estimated based on the R An14 
calculated from an experimental data set when the C12 and C14 
cells on the surface of biofilm are behaving identically. That 
is, the C14 detachment rate has stabilized and now assumed 
steady. Based on this procedure, R Agtotal of 16,000 CFU/ (cm2 
minute) and R Antotal of 1,800 CFU/ (cm2 minute) for P 2 R I are 
obtained.
The rate of total cellular detachment per unit area can 
be computed as the difference between the gross rate of total 
cellular attachment per unit area, RAgtotal, and the net rate of 
total cellular attachment per unit area, R Antotal• This method 
to calculate the rate of total cellular detachment per unit 
area will be called the first method of calculating Rdtotal. 
Rdtotal of 14,000 CFU/(cm2 minute) is obtained using the first 
method.
The net rate of C14 cellular attachment per unit area to 
an established biofilm, RAn14, is the slope (dXs14/dt) of the
72
graph of C14-Gell accumulation vs. time. Rftn14 is a function of 
time.
The gross rate of C14 cellular attachment area, RAg14, 
equals the gross rate of total cellular attachment per unit 
area, RAgtotal/ multiplied by (I - e"t/T) as shown by equation 
(35) .
Rlg = (I - e~t/z) R^gtal t*0 (35)
The rate of C14 cellular detachment per unit area, Rd14, 
which is a function of time, is the difference between the 
gross rate of C14 cellular attachment per unit area to an 
established biofilm, RAg14, and the net rate of C14 cellular 
attachment per unit area, RAn14.
A saturation-type equation can be used to fit the rate of 
Rd14 as a function of time. The maximum rate of C14 cellular 
detachment per unit area, Rdmax14, should be the same as the 
rate of total cellular detachment per unit area, Rdtotal. This 
provides a second method for computing RdtotaU Rdmax14 obtained 
(see Figure 12) is 16,000 CFU/ (cm2 minute). Rdtotal obtained 
using the first method is 14,000. See summary of results below 
for the results of the other experimental conditions.
\
73
0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00
Time minutes
Figure 12. P 2 R I: Rate of Cu Cellular Detachment vs. 
Time. Regular RotoTorque, RPM = 289, fluid shear = 2 0 
dyne/cm2, temperature = 22°C, substrate glucose 
concentration chemostat influent = 3 0  mg/1.
Summary of Results
Based on the experimental procedures and the theoretical 
background described in this work, it is possible to measure 
the rate of total cellular detachment per unit area, and the 
gross and net rates of total cellular attachment per unit area 
to an established biofilm.
74
Table 8. Summary of Results. Xb = the cell concentration of 
the bulk liquid in the RotoTorque (CFU/ml), T = temperature in 
0C, FS = fluid shear (dyne/cnr) , the units of Ragtotal/ RAnt0tal' 
and Rdtotal are CFU/(cm2 minute) (computed by the first method) .
t - x" x“l as
CFU/ml 0C dyne/cm2 CFU/(cm2 minute)
P I R I 4.5 22 20 0.16 — —
P 2 R I 45 22 20 1.6 0.18 1.4
P 2 R 2 51 22 0.2 - - -
P 2 R 3 12 22 20 0.18 0.018 0.16
P 2 R 4 58 28 20 11 0.89 10.1
P 2 R 5 55 28 2 5.1 2.6 2.5
P 2 R 6 52.5 22 20 - 0.12 -
P 2 R 7 43.3 22 20 2.1 0.14 I; 5
Effect of Suspended Cell Concentration on Attachment Rate
Both gross and net rates of total cellular attachment per 
unit area, R Agtotal and R Antotal/ are functions of the cell 
concentration in the bulk liquid of the RotoTorque as shown by 
the results of P I R I, P 2 R I and P 2 R 3 (see Figure 13 and 
Table 9).
P I R I, P 2 R I, and P 2 R 3 have the same experimental 
conditions except for the cell concentration in the bulk 
liquid of the RotoTorques7 Xb. The P l R l  run was performed 
using the small RotoTorques.
Table 9. Net Rate of Total Cellular Attachment per Unit Area 
as a function of bulk suspended cell concentration, Xb.
EXPERIMENT Xb R ftn
CFU/ml CFU/(cm2 minute)
P 2 R 3 12. IO6 180
P 2 R I 45. IO6 1800
75
O 10 20 30 40 50
Xb C F U /m l 
(M illions)
Figure 13. Ra v s . Xb. RAg = the gross rate of total 
cellular attachment to an established biofilm, Xb = cell 
concentration in the bulk liquid of the RotoTorques.
At this point, however, no correlation can be made
between the rate (both gross and net) of total cellular
attachment pee unit area and the cell concentration in the
bulk liquid RotoTorque, Xb. More experimental data are needed.
76
Effect of Temperature
Both gross and net rates of total cellular attachment per 
unit area seem also to increase with temperature as shown by 
the result of P 2 R I, and P 2 R 4 (see Table 10).
Table 10. Net and Gross Rates of Cellular Attachment per unit 
area as a Function of Temperature, T.
EXPERIMENT T - Rftn Ra
0C CFU/(cm2 minute) CFU/(cm2 minute)
P 2 R I 22 1,800 16,000
P 2 R 4 28 8,900 110,000
The rate of total cellular detachment per unit area also
appears to increase with temperature. Table 8 was obtained
\
using data from P 2 R I, and P 2 R 4. The P 2 R 4 run was 
performed at a temperature of 28°C. The net accumulation of Cu 
cells is higher in P 2 R 4 than the net accumulation of C14 
cells in P 2 R I (see Figures B.18 and B .21) . It seems likely 
that the higher accumulation of C14 cells in P 2 R 4 causes a 
higher rate of detachment.
Table 11. Rate of Cellular Detachment per Unit Area (first 
method) as a function of Temperature, T.
EXPERIMENT T Rd
0C CFU/(cm2 minute)
P 2 R I 22 14,000
P 2 R 4 28 101,000
77
Effect of Fluid Shear on The Rate of Cellular Detachment
In agreement with Characklis [11], increasing the fluid 
shear increases the rate of total cellular detachment per unit 
area (see Table 12). Table 12 is obtained from P 2 R 4, and P 
2 R 5.
Table 12. Rate of Cellular Detachment per Unit Area (first 
method) as a Function of Fluid Shear, FS.
EXPERIMENT ES Rd
dyne/cm2 CFU/(cm2 minute)
P 2 R 5 20 101,000
P 2 R 4 2 25,000
Detachment
Independent Measurement of Detachment
The rate of total cellular detachment per unit area can 
be calculated using equation (43) and the graph of the 
concentration of viable cells in the bulk liquid RotoTorque 
vs. time during flushing with mineral solution. Refer to 
Figures 14 and 15 for Xb vs. time graphs.
□  total 
K dexp
X^tF1 (43)
where,
78
dexp
t o ta l
X stb
F
A rot
the rate of total cellular detachment per 
unit area, CFU/(min cm2). 
steady-state value of the viable cells 
in effluent during flushing, (CFU/ml). 
flow rate of mineral solution into the 
RotoTorque, (ml/min).
Surface area for detachment, (cm2) .
OmmiHed
Time minutes
Figure 14. Detachment: P 2 R 4. Plot of the cell 
concentration in the bulk liquid of RotoTorque, Xb (CFU/ml) 
vs. time (minutes), inlet and outlet volumetric rate of 
fresh substrate to the RotoTorque = 94 ml/min, no cells 
flow in, the line is a curve fit (Xb = 8080938 + 2.0 IO8 t' 
1, r2 = 0.82, t = time).
79
X o
Time minutes
Figure 15. Detachment: P 2 R 6. Plot of the cell 
concentration in the bulk liquid of RotoTorque, Xb (CFU/ml) 
vs. time (minutes), inlet/outlet volumetric rate of fresh 
substrate to the RotoTorque = 67 ml/min, no cells flow in, 
the line is a curve fit (Xb = 198891 + 24645686 t"1, r2 = 
0.94, t = time).
80
Comparing The Rates of Total Cellular 
Detachment Computed by First and Second Method
By fitting the rate of C14 cellular detachment per unit 
area data with equation (44), the maximum value of the curve 
of equation (44) , Rdmax14, (see Figures 16 - 21) should be the 
same as the rate of total cellular detachment per unit area.
□  jl_
d 14 _  -“ -dmax & (44)
Table 13. Rate of Total Cellular Detachment I. Rdtotal is the 
rate of total cellular detachment per unit area using the 
first method (CFU/cm2 minute) , Rdmax14 is the maximum rate of C14 
cellular detachment per unit area (CFU/cm2 minute) , Rdex total is 
the rate of total cellular detachment per unit area measured 
independently.
•p t o ta l
(!O'*)
R 14 
<10“ )
P  to ta l
^ i T 1)
Units CFU/(cm2 minute)
P 2 R I 1.4 1 . 6 _ _
P 2 R 3 0.16 0.23 —
P 2 R 4 1 0 . 1 1 1 . 6 45
P 2 R 5 2.5 5.6 -
P 2 R 6 - 1.9 1.7
P 2 R 7 1.95 2 . 1 —
The results of these calculations are compared in Table 
13 with the rate of total cellular detachment per unit area, 
RdtotalZ calculated by substracting the net rate of total 
cellular detachment per unit area to an established biofilm, 
RAntotal, from the gross fate of total cellular attachment per
81
unit area to an established biofilm, RAgtotal. Rdtotal has been
called the first method used to calculate the rate of total
cellular detachment per unit area.
S
0.00 50.00 100.00 150.00 200.00 250.00 500.00 350.00 400.00 450.00
Time minutes
Figure 16. P 2 R I: Rate of C14 Cellular Detachment per 
Unit Area vs. Time. Regular RotoTorque, RPM = 289, fluid 
shear = 20 dyne/cm2, temperature = 22°C, substrate glucose 
concentration chemostat influent = 30 mg/1.
82
ii
3
S
u
S
-1000
-1500
0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00
Time minutes
Figure 17. P 2 R 3: Rate of C14 Cellular Detachment per
Unit Area vs. Time. Regular RotoTorque, RPM = 289, fluid
shear = 2 0  dyne/cm2, temperature = 22°C, substrate glucose
concentration chemostat influent = 3 mg/1.
83
+J
I
S
z— S
W
X5
C
O
O
3
O
X
S
0 .00  2 0 .0 0  40 .00  6 0 .0 0  80 .00  100 .00  120 .00  140 .00  160 .00  180 .00
Time minutes
Figure 18. P 2 R 4: Rate of C14 Cellular Detachment per
Unit Area vs. Time. Regular RotoTorque, RPM = 289, fluid
shear = 2 0  dyne/cm2, temperature = 28°C, substrate glucose
concentration chemostat influent = 30 mg/1.
84
S
15
10
5
OW-
0.00 50 .0 0  100 .00  150 .00
Hme minutes
200.00 250 .0 0
Figure 19. P 2 R 5: Rate of Cu Cellular Detachment per
Unit Area vs. Time. Regular RotoTorque, RPM =7 0, fluid
shear = 2 dyne/cm2, temperature = 28°C, substrate glucose
concentration chemostat influent = 3 0  mg/1.
85
U ^
Time minutes
Figure 20. P 2 R 6: Rate of C14 Cellular Detachment per
Unit Area vs. Time. Regular RotoTorque, RPM = 289, fluid
shear = 20 dyne/cm2, temperature = 22°C, substrate glucose
concentration chemostat influent = 30 mg/1.
86
S
I
E
U
§
200.00 250.00
Time minutes
Figure 21. P 2 R 7: Rate of Cu Cellular Detachment per 
Unit Area vs. Time. Regular RotoTorque, RPM = 289, fluid 
shear = 2 0  dyne/cm2, temperature = 22°C, substrate glucose 
concentration chemostat influent = 30 mg/1, one day C12 
biofilm.
CONCLUSIONS
The following conclusions are valid within the range of 
experimental conditions tested, which include a low glucose 
environment in which P. aeruginosa grown on simple substrate 
was used for all experiments.
The experimental procedure and method used in this 
research can be utilized to determine the net or gross rate of 
celullar attachment per unit area to an established biofilm, 
while the difference between the gross and net rate attachment 
per unit area will give the rate of cellular detachment per 
unit area.
Results obtained by the experimental procedure developed 
in this work indicate that the rate of cellular attachment per 
unit area to ah established biofilm appears to be a positive 
function of temperature. The rate of cellular attachment per 
unit area to an established biofilm also appears to be a 
positive function of bulk cell concentration. The effect of 
shear stress upon the rate of cellular attachment per unit 
area, however, is indeterminate. Reproducibility has been 
demonstrated at one set of conditions. The rate of cellular 
detachment per unit area measured by flushing the RotoTorque 
with mineral solution showed a comparable agreement with the 
rate of cellular detachment per unit area measured by 
difference of R. total and R. total.Ag An
87
88
RECOMMENDATIONS
To develop a kinetic expression for a cellular attachment 
to an established biofilm as a function of bulk cell 
concentration, more experiments at various bulk cell 
concentrations are needed.
Although during the attachment experiment (stage 3) , 
good control of experimental temperature was obtained, minimal 
temperature control throughout all stages of the experiments 
was available with the current set up. A controlled 
experimental temperature throughout all stages is required so 
that more uncertainties in the experimental procedure will be 
minimized. A water bath with heating and cooling elements and 
thermostats could be used.
More experiments at various fluid shear are needed to 
develop a kinetic expression for the rate of cellular 
attachment as a function of fluid shear.
One of the general conditions of the experiments was an 
oligothropic (low nutrient) environment. Bacteria would be 
expected to behave differently in copiotrophic (rich nutrient) 
environment. By changing the concentration of the glucose in 
the environment where the bacteria are living, a different 
behaviour of the rate of cellular attachment may be observed. 
More experiments in copiothrie environment are needed to 
develop a kinetic expression for the rate of cellular 
attachment as a function of nutrient concentration.
REFERENCES CITED
90
REFERENCES CITED
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3. Berkeley, R.C.W., et al. , eds., Microbial Adhesion to 
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4. Beyer, William H., C R C  Standard Mathematical Tables. 
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6. Bird, R. B., and C. F. Curtiss, "Tangential Newtonian 
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9. Bryers, J. D., and W. G. Characklis, "Kinetics of 
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System," Fouling of Heat Transfer Equipment, 
Washington, D.C.: Hemisphere Publishing Corp., 1981:
349 - 368.
91
10. Characklis, W. G., R. Bakke, and M. H. Turakhia,
Theoretical and Experimental Analysis of a Pseudomonas
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1988.
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14. Goggle, J. E., Biological Effects of Radiation.
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Taylor & Francis, Inc., 1983.
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16. Grady, C. P. Leslie, Jr., and Henry C. Lim, Biological 
Waste Water Treatment. New York: Marcel Dekker, 1980.
17. Goodman, B.L., and A. J. Englande, Jr., "A Unified 
Model of the Activated Sludge Process," Journal of the 
Water Pollution Control Federation, 46 (1974): 312-
332.
18. Hugo, William Barry, and Society of Chemical Industry, 
Inhibition and Destruction of the Microbial Cell, ed. 
R.C.W. Berkeley, New York: E. Norwood for the Society of 
Chemical Industry, London, 1980.
19. Kappesser, R., I. Cornet, and R. Greif, "Mass Transfer 
to a Rough Rotating Cylinder," J. Electrochem. Soc. . 
118 (December 1971): 1957 - 1959.
92
20. Kaye, Joseph, and E. C. Elgar, "Modes of Adiabatic and 
Diabatic Fluid Flow in an Annulus with an Inner 
Rotating Cylinder," Transactions of the ASME (April 
1958): 753 - 765.
21. Kim, Yeoung-Chul, "Diffusion Coefficients for
Klebsiella Pneumoniae and Pseudomonas Aeruginosa," 
Master's thesis, Montana State University, 1989.
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Understanding Radioactive Waste, ed. Judith A. Powell, 
Columbus: Batelle Press, 1989.
23. McCabe, W. L., J. C* Smith, and P. Harriot, Unit
Operations of Chemical Engineering, 4th ed., New York: 
McGraw-Hill, Inc.,1985.
24. McKinney, R. E., "Mathematics of Complete Mixing 
Activated Sludge," Journal of the Sanitary Engineering 
Division. ASCE, 88 (1962): 87-113. Quoted in C. P.
Leslie Grady, Jr., and Henry C. Lim, Biological Waste 
Water Treatment. New York: Marcel Dekker, 1980.
25. Matson, J. V., and W. G. Characklis, "Diffusion into 
Microbial Aggregates," Water Research, 10 (1976):
877 - 885.
26 Mueller, R.F., "Characterization of Initial Events of
Bacterial Colonization at Solid-Water Interfaces Using 
Image Analysis," Master's thesis, Montana State 
University, 1990.
27. Samson, Philip, Glossary of Bacteriological Terms, 
London: Butterworth, 1975.
28. Savage, C. Dwayne, and Madilyn Fletcher, Bacterial 
Adhesion. New York: Academic Press, 1971.
29. Schlichting, Hermann, Boundary Laver Theory, 7th ed. , 
trans. J. Kestin, New York: McGraw-Hill, 1979.
93
30. Schugerl, Karl, Bioreaction Engineering, trans. Valerie 
Cottrell, Chichester (West Sussex); New York: Wiley,
1987.
31. Siebel, Maarten Alexander, "Binary Population 
Biofilms,11 Ph.D. diss., Montana State University, 
1987.
32. Starr, Mortimer P. et al., eds., The Prokaryotes. 
vol. I, Introduction to the Family Pseudomonadaceae, by 
Norberto J . Palleroni. Heidelberg: Springer-Verlag, 1981.
33. Turakhia, M., and W. G. Characklis, "Influence of a
Calcium-Specific Chelant on Biofilm Removal," Applied and 
Environmental Microbiology. 46 (1983): 1236-1238.
34. Wang, A. K., and L. W. Gelhar, "Turbulent Couette 
Flow," J. of Fluids Engineering. (December 1974).
35. Wanner, O., Personal Communication, 1990.
36. Warwood, Brian, Personal Communication, 1991.
37. Winslow, C . E. A. et al., "The Families and genera of The 
Bacteria," Preliminary report of the Society of American 
Bacteriologist on Characterization and Classification of 
Bacterial Types ," Journal of Bacteriology, 2 (1917):
505-566. Quoted in Mortimer P. Starr et al., eds., The 
Prokaryotes. vol. I, 655. Heidelberg: Springer-Verlag, 
1981.
94
APPENDICES
95
APPENDIX A 
RAW DATA
96
APPENDIX A
PHASE I EXPERIMENT
RotoToraue (smaII)
Surface area for attachment = 258.4 cm2 
Rotor peripheral area = 109.96 cm2
Inside wall surface area of one RotoTorque =148.44 cm2 
Liquid volume = 180 ml 
RPM = 600
Number of RotoTorques = 6 
Units of measurement
Liquid Scintillation (L.S.) = counts per minute (CPM) 
plate count = colony forming units (CFU)/ml 
Time of measurement of each L.S. sample = I minute 
Fresh substrate = 1.5 jLtCi/1 as glucose 
Bulk liquid of chemostat = 2190 CPM
97
Table 14. Phase I, Run Is Radioactivity Levels. Experimental 
data on radioactivity levels in the bulk liquid in the 
RotoTorque (CPM/ml), biofilm on the rotor surface (CPM), and 
the outer cylinder (CPM).
TIME BULK LIQUID ROTOR WALL
(min) CPM/ml CPM CPM
10 404.0 269.0 99.0
20 603.0 555.0 257.0
30 999.0 711.0 237.0
40 494.0 974.0 214.0
50 1023.0 397.0 451.0
60 1437.0 906.0 152.0
Table 15. Phase I, Run I: Viable Counts. Experimental data on 
number of cells (CFU/ml) of the bulk liquid in the chemostat.
TIME CHEMOSTAT
(min) CFU x 10"5/ml
10
20
30
40
50
60
42
40
48
44
48
33
98
PHASE 2 EXPERIMENT
RotoToraue fstandard)
Surface area for attachment = 1289.31 cnf
Rotor peripheral area = 596.90 cm2
Number of slides = 12 
Area of one slide = 34.2 cm2.
Time of measurement of each sample = I minute
Inside wall surface area = 692.41 sqcm
Liquid volume = 640 ml
Number of RotoTorque(s) = I
Temperature = 22°C
Unit of measurement
Liquid scintillation = count per minute (CPM) 
plate count = colony forming units (CFU)/ml
99
Run I
Fresh substrate = 1.5 /zCi/1
Bulk liquid of chemostat = 1591.33 CPM/ml
Temperature = 22 0C
RPM = 289
Table 16. Phase 2, Run I: Radioactivity Levels. Experimental 
data on radioactivity levels in the bulk liquid in the 
RotoTorque (CPM/ml), and biofilm on the slide surface (CPM).
TIME BULK LIQUID SLIDE
(min) (CPM/ml) (CPM)
10 105 96 97 54 59 53
20 - - - 53 85 56
27 226 233 249 - - -
32 293 286 298 119 129 103
42 334 338 392 125 115 146
52 426 431 431 152 164 156
62 482 502 463 123 116 133
122 743 819 798 618 618 616
182 890 950 913 328 343 340
242 953 928 906 467 444 459
302 986 1003 1083 663 715 647
362 979 1032 1011 556 560 580
402 1235 1214 1204 906 945 887
100
Table 17. Phase 2, Run I: Viable Counts. Experimental data on 
number of cells (CFU/ml) in the bulk liquid in the RotoTorque.
TIME BULK LIQUID R0T0T0RQUE
(min) (CPU x 10'6/ml)
10 49 52
20 40 39
32 42 42
42 31 37
52 54 50
62 48 49
122 45 45
COH 46 42
242
r
51 50
302 42 44
x
101
RUN 2
RPM = 2 0
Fresh substrate = 2.5 juCi/1 as glucose
Bulk liquid of chemostat = 2942 CPM/ml
Temperature = 22 0C
Table 18. Phase 2, Run 2: Radioactivity Levels. Experimental 
data on radioactivity levels in the bulk liquid in the 
RotoTorque (CPM/ml), and biofilm on the slide surface (CPM).
TIME BULK LIQUID SLIDE
(min) (CPM/ml) (CPM)
10 638 549 574 89 85 89
20 715 718 676 132 161 129
30 1001 921 1004 168 182 155
40 1129 1132 1111 432 450 390
50 1164 1140 1156 113 134 128
60 1201 1263 1228 378 3 63 337
75 1513 1519 1498 204 212 242
90 1545 1568 1546 1049 1021 954
120 1903 1929 1884 253 236 211
225 2369 2417 2380 1123 1058 1075
315 2688 2569 2572 996 987 986
405 2762 2715 2760 778 739 748
102
Table 19. Phase 2, Run 2: Viable Counts. Experimental data on
number of cells (CFU/ml) in the bulk liquid in the RotoTorque
and in the chemostat.
TIME BULK LIQUID ROTOTORQUE
(min) (CFU x 10"6/ml)
10 62 64
20 51 59
30 40 38
40 45 45
50 440 420
60 390 410
75 400 420
BULK LIQUID CHEMOSTAT
(CFU x 10'6/ml)
34 50
103
RUN 3
Table 20. Phase 2, Run 3s Radioactivity Levels. Experimental 
data on radioactivity levels in the bulk liquid in the 
RotoTorque (CPM/ml), and biofilm on the slide surface (CPM).
TIME BULK LIQUID SLIDE
RPM = 289
Fresh substrate = 2.5 /zCi/1 as glucose
Bulk liquid of chemostat = 2278.00 CPM/ml
Temperature = 22 0C
(min) (CPM/ml) (CPM)
10 259 293 296 78 78 66
20 426 471 515 108 104 107
30 649 612 607 150 150 143
40 715 714 688 175 207 202
50 874 831 884 233 226 231
60 917 929 953 231 222 216
75 1100 984 1051 287 304 3 65
95 1192 1227 1254 431 460 418
120 1406 1379 1306 500 491 496
150 - 1417 1423 1443 - - -
180 1526 1443 1477 611 614 694
104
Table 21. Phase 2, Run 3: Viable Counts. Experimental data on
number of cells (CFU/ml) in the bulk liquid in the RotoTorque
and in the chemostat (CFU/ml).
TIME BULK LIQUID R0T0T0RQUE
(min) (CFU x 10"6/ml)
10 8.3 9
20 5 5.6
30 39 41
40 96 98
50 3.7 4.2
60 3.7 4.0
75 3.4 3.6
95 104 91
120 3 3.6
150 11.2 14
180 11.6 11
BULK LIQUID CHEMOSTAT
(cfu X 10"6/ml)
I
5.1 5.0
105
RUN 4
RPM = 289
Fresh substrate = 2.5 jitCi/l as glucose
Bulk liquid chemostat = 2897 CPM/ml
Temperature = 28 0C
Table 22. Phase 2, Run 4s Radioactivity Levels. Experimental 
data on radioactivity levels in the bulk liquid in the 
RotoTorque (CPM/ml), and biofilm on the slide surface (CPM).
TIME BULK LIQUID SLIDE
(min) (CPM/ml) (CPM)
10 307 308 301 475 504 469
20 430 438 3 95 606 590 611
30 551 494 520 1147 1183 1151
40 599 637 619 1000 1029 1000
50 756 692 734 1265 1310 1182
60 774 793 740 1705 1663 1735
75 924 896 868 1743 2032 1910
90 957 964 936 1998 1877 1912
120 1064 1088 1033 3109 3067 3047
150 1461 1519 1425 3538 3633 3711
164 1377 1417 1331 _ -
106
Table 23. Phase 2, Run 4: Viable Counts. Experimental data on
number of cells in the bulk liquid in the RotoTorque (CFU/ml)
and in the bulk liquid chemostat (CFU/ml).
TIME BULK LIQUID ROTOTORQUE
(min) (CFU X IO'6)
10 47 51
20 54 51
30 98 93
40 56 59
50 65 66
60 59 58
75 60 59
90 62 58
120 40 41
150 41 43
BULK LIQUID CHEMOSTAT
(CFU X 10"6/ml)
31 33
107
RUN 5
RPM = 7 5
Fresh substrate = 2.5 jLtCi/1 as glucose
Bulk liquid of chemostat = 2897 /zCi/ml
Temperature = 28°C
Table 24. Phase 2, Run 5: Radioactivity levels. Experimental 
data on radioactivity levels in the bulk liquid in the 
RotoTorque (CPM/ml), and biofilm on the slide surface (CPM).
TIME
(min)
BULK LIQUID 
(CPM/ml.)
SLIDE
(CPM)
10 317 311 306 341 364 353
20 495 505 438 574 587 575
30 614 595 576 947 978 925
40 779 790 798 1223 1234 1173
50 1880 1942 1905 1601 1619 1538
60 - - - 1928 1911 1929
75 1180 1173 1189 2266 2254 2301
90 1289 1295 1317 , 2749 2718 2793
120 1455 1455 1405 4392 4522 4435 ,
150 1553 1636 1639 4164 4160 4168
180 1871 1801 . 1789 5796 5599 56.92
210 1873 1955 1913 7483 7464 7660
108
Table 25. Phase 2, Run 5: Viable Counts. Experimental data on
number of cells (CFU/ml) in the bulk liquid in the RotoTorque
and in the chemostat (CFU/ml).
TIME BULK LIQUID ROTOTORQUE
(min) (CFU x IO'6)
10 38 41
20 - -
30 49 47
40 104 102
50 91 87
60 40 40
75 - -
90 60 62
120 53 53
150 49 48
BULK LIQUID CHEMOSTAT
(CFU x 10"6/ml)
32 3 3
\
109
RUN 6
RPM = 289
Fresh substrate = 2.5 jtiCi/1 as glucose
Bulk liquid of Chemostat = 1973 CPM/ml
Temperature = 22 0C
Table 26. Phase 2, Run 6s Radioactivity Levels. Experimental 
data on radioactivity levels in the bulk liquid in the 
RotoTorque (CPM/ml), and biofilm on the slide surface (CPM).
TIME
(min)
BULK LIQUID 
(CPM/ml)
SLIDE
(CPM)
30 552 552 559 262 226 230
60 827 864 851 265 298 318
90 975 977 1043 332 308 295
120 1113 1086 1152 288 314 323
150 1226 1220 1227 335 373 333
180 1335 1369 1344 476 474 435
210 1392 1374 1371 474 494 490
240 1433 1428 1364 489 502 502
270 1457 1418 1451 537 518 537
300 1505 1479 1505 556 558 571
330 1497 1517 1505 568 613 585
360 1517 1548 1553 595 573 592
H O
Table 27. Phase 2 Run 6: Viable Counts. Experimental data on
number of cells (CFU/ml) in the bulk liquid in the RotoTorque
and in the chemostat (CFU/ml)
TIME
(min)
BULK LIQUID ROTOTORQUE 
(CFU x 10"6/ml)
30 49 49
60 62 60
90 43 40
120 27 32
150 50 54
180 42 47
210 51 50
240 44 42
270 48 49
300 82 60
330 31 37
BULK LIQUID CHEMOSTAT
(CFU x 10'6/ml)
81 90
Ill
RUN 7
RPM = 289
Fresh substrate = 2.5 /zCi/l as glucose
Bulk liquid of chemostat = 2897 CPM/ml
Temperature = 22°C
Table 28. Phase 2, Run 7: Radioactivity Levels. Experimental 
data on radioactivity levels in the bulk liquid in the 
RotoTorque (CPM/ml), and biofilm on the slide surface (CPM).
TIME
(min)
BULK LIQUID 
(CPM/ml)
SLIDE
(CPM)
2 58 56 57 31 33 31
4 114 118 119 32 30 34
6 169 169 162 87 87 90
8 221 223 233 90 96 94
10 275 277 270 97 106 96
20 522 528 528 96 153 101
30 744 756 748 216 210 216
60 1280 1284 1272 225 216 242
120 1930 1976 1945 .465 465 570
150 2126 2125 2125 590 600 590
210 2433 2432 2428 740 738 738
240 2483 2484 2680 860 879 , 860
112
Table 29. Phase 2, Run 7s Viable Counts. Experimental data on
number of cells (CFU/ml) in the bulk liquid in the RotoTorque
arid in the chemostat (CFU/ml) .
TIME BULK LIQUID ROTOTORQUE
(min) (CFU x :10"6/ml)
10 39 38
20 38 41
30 49 47
60 40 40
120 32 34
150 60 62
210 54 49
240 38 32
BULK LIQUID CHEMOSTAT
(CFU X 10-6/ml)
46 50
113
Detachment Result
Table 30. Phase 2 Run 4: Viable Cell Concentration in the Bulk 
Liquid in the RotoTorque vs. Time during flushing. Flow rate 
of mineral solution into the RotoTorque = 94 ml/min, no cells 
flow in.
TIME
(min.)
Xb
CFU x 10'5/ml
xb
CFU x 10"6/ml»■
5 > 400 45
10 > 400 82
15 313 29
20 . 237 20
25 130 16
30 141 13
40 176 14
50 57 4
60 67 3
70 94 6
114
Table 31. Phase 2 Run 6: Viable Cell Concentration in the Bulk 
Liquid in the RotoTorque vs. Time during flushing. Flow rate 
of mineral solution into the RotoTorque = 67 ml/rnin, no cells 
flow in.
Time Xb Xb
(min.) (CFU x I(TzVml) (CFU x 10'5/ml)
10 245 24
20 182 18
30 122 16
60 43 4
12 0 21 2
150 - 31 3
210 32 3
240 35 2
115
APPENDIX B 
DATA ANALYSIS
116
APPENDIX B
Units of results presented in this section are CPM/ml 
(count per minute per milliliter) and CFU/ml (colony forming 
units per milliliter) for liquid samples. For samples taken 
from a surface, results are reported on a square centimeter 
basis.
If more than one measurement was made, the average value 
will be reported in this section. Individual values are 
reported in appendix A.
There is one run in the phase one experiment and seven 
runs in the phase two experiment.
Phase I
At time zero the RotoTorque influent was switched to the 
chemostat effluent with C14 labelled cells. Intensity of 
radioactivity at time zero in the RotoTorque was set at zero, 
it was not obtained experimentallly.
The intensity of radioactivity on the surface of biofilm 
is obtained by dividing rotor CPM (Table 14) by 109.96 cm2 
which is the rotor peripheral area in square centimeters (not 
including the top and bottom part of the rotor) since the 
biofilm accumulated on the rotor peripheral area only were 
scrapped off.
117
RUN I
RPM = 600
Fluid shear = 2 0  dyne/cm2
Table 32. Phase I, Run I? Result I. Radioactivity levels of 
the bulk liquid in the RotoTorque (CPM/ntl) , and biofilm on the 
rotor surface (CPM/cm2) as a function of time.
TIME
(min)
BULK LIQUID 
(CPM/ml)
ROTOR
(CPM/cm2)
0 0 0
10 404.00 2.45
20 603.00 5.05
30 999.00 6.47
40 494.00 8.87
50 1023.00 3.61
60 1437.00 8.24
118
I
/-N
CO
TJ
C
O
CO
3
O
T
t—
<_/•
4
2
O
0.00 10 .00  2 0 .0 0  3 0 .0 0  4 0 .0 0
Time minutes
50 .0 0 6 0 .0 0
Figure 22. P I R I: Accumulation of C14 Viable Cells on the 
Surface of the Established Biofilm. Small RotoTorque, RPM 
= 600, fluid shear = 20 dyne/cm2, substrate glucose 
concentration chemostat influent = 30 mg/1, temperature = 
22°C.
C
F
rL
T/
m
l
 
(M
il
li
on
s)
119
Time minutes
Figure 23. P I R I: C14 Viable Cells in the Bulk Liquid in
the RotoTorque vs. Time. At the time of data gathering,
inlet flow rate = outlet flow rate = 2 ml/min, inlet
concentration of viable C14 cells = 42.5 x IO5 CFU/ml,
liquid volume in the RotoTorque = 180 ml.
12 0
Phase 2
Slide results.are obtained by dividing slide CPM by 34.2 
cm2, which is the area of one slide.
Run I
RPM = 289
Fluid shear = 2 0  dyne/sqcm.
Table 33. Phase 2, Run I: Result 2. Radioactivity levels in 
the bulk liquid in the RotoTorque (CPM/ml), biofilm on the 
slide surface (CPM/cm2) , and the viable count in the bulk 
liquid in the RotoTorque as a function of time.
TIME BULK LIQUID SLIDE BULK LIQUID
ROTOTORQUE ROTOTORQUE
(min) (CPM/ml) (CPM/cm2) (CPU x 10"6/ml)
O 0 0 -
10 99.33 1.62 50.5
20 - 1.89 39.5
27 236 -
32 292.33 3.42 42
42 354.67 3.76 34
52 429.33 4.6 52
62 482.33 3.63 48.5
122 786.67 18.05 45
182 917.67 9.85 44
242 929 13.35 50.5
302 1024 19.74 43
362 1007.33 16.53 -
402 1217.67 . 26.69 -
121
800
700
BOO
9"w
500
M
\
J
*
J
"0 
C
« 400
o
.£
^500
200
100
0 .00  5 0 .00  100 .00  150 .00  2 0 0 .0 0  2 5 0 .0 0  3 0 0 .0 0  3 5 0 .0 0  400 .0 0  450 .0 0
Time minutes
Figure 24. P 2 R I: Accumulation of Cu Viable Cells on the 
Surface of the Established Biofilm. Regular RotoTorque, 
RPM = 289, fluid shear = 2 0 dyne/cm2, substrate glucose 
concentration chemostat influent = 30 mg/1, temperature = 
2 2 0C.
122
I
8
0 .00  5 0 .0 0  100 .00  150 .00  2 0 0 .0 0  2 5 0 .0 0  3 0 0 .0 0  3 5 0 .0 0  4 0 0 .0 0  4 5 0 .0 0
Time minutes
Figure 25. P 2 R I: C14 Viable Cells in the Bulk Liquid in
the RotoTorque vs. Time. At the time of data gathering,
inlet flow rate = outlet flow rate = 7.1 ml/min, inlet
concentration of viable C14 cells = 42 x IO6 CFU/ml, liquid
volume in the RotoTorque = 640 ml.
123
RPM = 2 0
Fluid shear = 0.2 dyne/cm2
Table 34. Phase 2, Run 2: Result 3. Radioactivity levels in 
the bulk liquid in the RotoTorque (CPM/ml), biofilm on the 
slide surface (CPM/cm2) and, viable count of the bulk liquid 
in the RotoTorque (CFU/ml).
Run 2
TIME
(min)
BULK LIQUID 
R0T0T0RQUE 
(CPM/ml)
SLIDE
(CPM/cm2)
BULK LIQUID 
ROTOTORQUE 
(CFU x 10"6/ml)
O 0 0 —
10 587 7.69 63
20 703 4.11 54.5
30 975.33 4.92 39
40 1124 12.40 45
50 1153.33 3.65 430
60 1230.67 10.51 400
75 1510 6.41 410
90 1553 29.47 -
120 1905.33 6.82 -
225 2388.67 31.73 -
315 2609.67 28.94 -
405 2745.67 22.08
124
I
450
400
350
500
3^00
Tl
C
W 250  
o
.C
t-200
150
100
50
0
0 .00  50 .00 100 .00  150 .00  200 .00  250 .00  300 .00  3 5 0 .0 0  400 .0 0  450 .00  
Time minutes
Figure 2 6. P 2 R 2: Accumulation of C14 Viable Cells on the 
Surface of the Established Biofilm. Regular RotoTorque, 
RPM = 20, fluid shear = .2 dyne/cm2, substrate glucose 
concentration chemostat influent = 3 0  mg/1, temperature = 
2 2 0C.
125
0 .00  5 0 .0 0  100 .00  150 .00  2 0 0 .0 0  2 5 0 .0 0  3 0 0 .0 0  3 5 0 .0 0  4 0 0 .0 0  4 5 0 .0 0
Time minutes
Figure 27. P 2 R 2: Cu Viable Cells in the Bulk Liquid in
the RotoTorque vs. Time. At the time of data gathering,
inlet flow rate = outlet flow rate = 7.1 ml/min, inlet
concentration of viable Cu cells = 42 x IO6 CFU/ml, liquid
volume in the RotoTorque = 640 ml.
12 6
Run 3
RPM = 289
Fluid shear = 2 0  dyne/cm2
Glucose concentration chemostat influent = 3 mg/1
Table 35. Phase 2, Run 3: Result 4. Radioactivity levels in 
the bulk liquid in the RotoTorque (CPM/ml), biofilm on the 
slide surface (CPM/cm2) , and viable count of the bulk liquid 
in the RotoTorque (CFU/ml).
TIME
(min)
BULK LIQUID 
ROTOTORQUE 
(CPM/ml)
SLIDE
(CPM/cm2)
BULK LIQUID 
ROTOTORQUE 
(CPU X 10'6/ml)
10 282.67 2.16 8.65
20 470.67 3.1 5.3
30 622.67 4.3 40
40 705.67 5.7 97
50 863 6.7 3.95
60 933 6.5 3.85
75 1045 9.3 3.5
95 1224.33 12.8 97.5
120 1363.67 14.5 3.3
150 1427.67 - 12.6
180 1482 18.7 11.3
0 .00  2 0 .0 0  4 0 .00  6 0 .00  8 0 .00  100 .0 0  120 .00  140 .00  160 .00  180 .00
Time minutes
Figure 28. P 2 R 3: Accumulation of C14 Viable Cells on the 
Surface of the Established Biofilm. Regular RotoTorque, 
RPM = 289, fluid shear = 2 0 dyne/cm2, substrate glucose 
concentration chemostat influent = 3 mg/1, temperature = 
22°C.
C
F
U
/
m
l
(M
il
li
on
s)
128
0 .00  2 0 .0 0  4 0 .0 0  60 .00  8 0 .0 0  100 .00  120 .00  140 .00  160 .00  180 .00
Time minutes
Figure 29. P 2 R 3: C14 Viable Cells in the Bulk Liquid in
the RotoTorque vs. Time. At the time of data gathering,
inlet flow rate = outlet flow rate = 7.1 ml/min, inlet
concentration of viable C14 cells = 5.05 x IO6 CFU/ml,
liquid volume in the RotoTorque = 640 ml.
129
Run 4
RPM = 289
Fluid shear = 2 0  dyne/cm2 
Temperature = 28 0C
Table 36. Phase 2, Run 4: Result 5. Radioactivity levels in 
the bulk liquid in the RotoTorque (CPM/ml), biofilm on the 
slide surface (CPM/cm2) , and viable count of the bulk liquid 
in the RotoTorque (CFU/ml).
TIME
(min)
BULK LIQUID 
ROTOTORQUE 
(CPM/ml)
SLIDE
(CPM/cm2)
BULKLIQUID 
ROTOTORQUE 
(CFU x 10"6/ml)
10 305.33 14.7 49
20 421 17.6 52.5
30 461.33 33.9 95.5
40 618.33 29.5 57.5
50 727.33 36.7 58.5
60 769 49.7 59.5
75 896 55.4 60
90 952.33 56.4 40.5
120 1061.67 89.89 42
150 1468.33 106.06 42
164 1375 - ■ —
C
F
U
/
 s
q
c
n
a
 
(M
il
li
on
s)
130
0 .00  2 0 .0 0  4 0 .0 0  6 0 .00  8 0 .0 0  100 .00  120 .00  140 .00  160 .00  180 .00
Time minutes
Figure 30. P 2 R 4: Accumulation of C14 Viable Cells on the 
Surface of the Established Biofilm. Regular RotoTorque, 
RPM = 289, fluid shear = 20 dyne/cm2, substrate glucose 
concentration chemostat influent = 30 mg/1, temperature = 
28°C.
131
I
3
0 .00  2 0 .0 0  4 0 .0 0  6 0 .0 0  8 0 .0 0  100 .0 0  1 2 0 .0 0  140 .0 0  160 .00
Time minutes
Figure 31. P 2 R 4: C14 Viable Cells in the Bulk Liquid in
the RotoTorque vs. Time. At the time of data gathering,
inlet flow rate = outlet flow rate = 7.1 ml/min, inlet
concentration of viable C14 cells = 32 x IO6 CFU/ml, liquid
volume in the RotoTorque = 640 ml.
132
Run 5
RPM = 75
Fluid shear = 2 dyne/cm2 
Temperature = 28 0F
Table 37. Phase 2, Run 5: Result 6. Radioactivity levels of 
the bulk liquid in the RotoTorque (CPM/ml), biofilm on the 
slide surface (CPM/cm2) , and viable count of the bulk liquid 
RotoTorque (CFU/ml).
TIME BULK LIQUID SLIDE BULK LIQUID
R0T0T0RQUE ROTOTORQUE
(min) (CPM/ml) (CPM/cm2) (CFU x 10'6/ml)
10 311.33 10.3 39.5
20 479.33 16.9 -
30 595 27.8 48
40 789 35.4 103
50 1909 46.4 89
60 - 56.2 40
75 1180.67 66.5 40
95 1300.33 80.5 61
120 1438.33 130.1 53
150 1609.33 121.8 48.5
180 1820.33 166.5 -
210 1913.67 20.3 -
C
 F
U
zZ
s
q
c
m
 
(M
il
li
on
s)
133
100.00 150 .00 200.00 2 5 0 .0 0
Time minutes
Figure 32. P 2 R 5: Accumulation of Cu Viable Cells on the 
Surface of the Established Biofilm. Regular RotoTorque, 
RPM = 70, fluid shear = 2 dyne/cm2, substrate glucose 
concentration chemostat influent = 30 mg/1, temperature = 
2 S0C .
134
100.00 150 .00 200.00 250 .0 0
Time minutes
w
Figure 33. P 2 R 5: C14 Viable Cells in the Bulk Liquid in
the RotoTorque vs. Time. At the time of data gathering,
inlet flow rate = outlet flow rate = 7.1 ml/min, inlet
concentration of viable Cu cells = 32.5 x IO6 CFU/ml,
liquid volume in the RotoTorque = 640 ml.
135
Run 6
RPM = 289
Fluid shear = 2 0  dyne/cm2
Temperature = 22 0C
Duplicate experiment of P 2 R I.
Table 38. Phase 2, Run 6: Result 7. Radioactivity levels in 
the bulk liquid in the RotoTorque (CPM/ml), biofilm on the 
slide surface (CPM/cm2) , and viable count of the bulk liquid 
RotoTorque (CFU/ml).
TIME BULK LIQUID SLIDE BULK LIQUID
R0T0T0RQUE R0T0T0RQUE
(min) (CPM/ml) (CPM/cm2) (CPU x 10"6/ml)
30 554.33 7 49
60 847.3 8.6 61
90 998.3 9.1 41.5
120 1117 9.0 29.5
150 1224.3 10.2 52
180 1349.3 13.5 44.5
210 1379 14.2 50.5
240 1408 14.6 43
270 1442 15.5 48.5
300 1496 16.4 72
330 1506 17.21 34
360 1539 17.2
136
800
700
600
500Eo
l i
Z  % 400
u ^
r
H
M
X
300
200
100
o#-
100 150  2 0 0  2 50
Time minutes
3 0 0  3 50  400
Figure 34. P 2 R 6: Accumulation of Cu Viable Cells on the 
Surface of the Established Biofilm. Regular RotoTorque, 
RPM = 289, fluid shear = 20 dyne/cm2, substrate glucose 
concentration chemostat influent = 30 mg/1, temperature = 
22°C.
137
Time minutes
Figure 35. P 2 R 6: C14 viable Cells in the Bulk Liquid in
The RotoTorque vs. Time. At the time of data gathering,
inlet flow rate = outlet flow rate = 7.1 ml/min, inlet
concentration of C14 viable cells = 85.5 x IO6 CFU/ml,
liquid volume in the RotoTorque = 640 ml.
138
Run 7
RPM = 289
Fluid shear = 2 0  dyne/cm2 
Temperature = 22 0C
Experimental condition is the same as P 2 R 6 except, the 
C12 biofilm was grown for only 24 hours instead of 7 days.
Table 39. Phase 2, Run 7: Result 8. Radioactivity levels of 
the bulk liquid in the RotoTorque (CPM/ml), biofilm on the 
slide surface (CPM/ml), and viable count of the bulk liquid 
RotoTorque (CFU/ml).
TIME BUlK LIQUID SLIDE BULK LIQUID
ROTOTORQUE ROTOTORQUE
(min) (CPM/ml) (CPM/cm2) (CPU x 10'6/ml)
2 57 0.9 —
4 117 0.9 -
6 166.7 2.6 -
8 225.7 2.7
10 274 2.9 38.5
20 526 3.4 39.5
30 749.3 6.3 48
60 1278.7 6.7 40
120 1950.3 14.6 33
150 2125.3 17.3 61
210 2431 21.6 51.5
240 2549 25.3 35
139
100.00 200.00 250.00
Time minutes
Figure 36. P 2 R 7: Accumulation of C14 Viable Cells on the 
Surface of the Established Biofilm. Regular RotoTorque, 
RPM = 289, fluid shear = 20 dyne/cm2, substrate glucose 
concentration chemostat influent = 3 0  mg/1, temperature = 
2 2 0C.
140
100.00 150.00 200.00 250.00
Time minutes
Figure 37. P 2 R 7! Cu Viable Cells in the Bulk Liquid in
the RotoTorque vs. Time. At the time of data gathering,
inlet flow rate = outlet flow rate = 7.1 ml/min, inlet
concentration of C14 viable cells = 48 x IO6 CFU/ml, liquid
volume in the RotoTorque = 640 ml.
141
At large times, the net rate of C14 cellular attachment 
per unit area to an established biofilm is correlated to the 
net rate of total cell attachment per unit area to an 
established biofilm as given by equation (36).
•^ An - (I ~ e-t/T) R ^ tal (47)
The net rate of total cellular attachment per unit area 
to an established biofilm, RAntotal r is constant throughout each 
experimental run. It also means that RAntotal is constant for a 
fixed bulk cell concentration (within a specific experimental
run) . At time t ---> oo, Rftn14 will equal to RAntotal for the same
specific condition. This means that each experimental run will 
give one value of RAn14.
The method described in the Model Development section 
and the experimental data enable us to calculate the gross 
rate of total cellular attachment per unit area, RAgtotal, the 
net rate of total cellular attachment per unit area, R Antotal, 
the rate of total cellular detachment per unit area, Rdtotal, 
and the rate of C14 cellular detachment per unit area, R d14.
Equations (35), (40), (41), and (42) as derived 
previously in the Model Development section will be used to 
calculate R Antotal / and RAgtotal.
142
R% - (I - e~t/x) Rlltal C k O  (35)
accumulation of C14 per unit area = R H tal [r] (42)
which is true for time t > tL.
accumulation of C14 per unit area - Rlltal [r] (40)
which is true for time t = 0.
[T] = t - T ( l -  e"t/T) (41)
The graphs of the accumulation C14 per unit area, Xs14, as 
a function of modified time, [Tm], are given on the following
pages.
143
0 .0 0  2 .0 0  4 .00 6 .0 0  8 .0 0  10 .00  12 .00  14 .00  16 .00  18 .00
fTm] minutes
Figure 38. P I R I: Accumulation of C14 Viable Cells on the 
Surface of an Established Biofilm vs. Modified Time, [Tm].
Small RotoTorque, RPM = 600, fluid shear = 2 0 dyne/cm, 
substrate glucose concentration chemostat influent = 30 
mg/1, temperature = 22°C, ■ experimental data, - curve fit 
( x s14 = 261.63 + 6089.97 [Tm] r2 = 0.99, the last point 
was omitted).
144
0 .0 0  5 0 .0 0  100 .00  150 .00  2 0 0 .0 0  2 5 0 .0 0  3 0 0 .0 0  3 5 0 .0 0
[Tm] minutes
Figure 39. P 2 R I: Accumulation of Cu Viable Cells on the 
Surface of an Established Biofilm vs. Modified Time, [Tm].
Regular RotoTorque, RPM = 289, fluid shear = 2 0  dyne/cm , 
substrate glucose concentration chemostat influent = 30 
mg/1, temperature = 22°C, I experimental data, - curve fit 
(Xs14 = 153.97 + 38.13 [Tm] \  r2 = 0.99, the two most 
divergent points were omitted).
145
s* ^ 300
0 .0 0  5 0 .00  100 .00  150 .00  2 0 0 .0 0  2 5 0 .0 0  3 0 0 .0 0  3 5 0 .0 0
[Tm] minutes
Figure 40. P 2 R 2: Accumulation of C14 Viable Cells on the 
Surface of an Established Biofilm vs. Modified Time, [Tm].
Regular RotoTorque, RPM = 20, fluid shear = 0.2 dyne/cirr, 
substrate glucose concentration chemostat influent = 30 
mg/1, temperature = 22°C, I experimental data.
146
100.00 120.00
[Tm] minutes
Figure 41. P 2 R 3: Accumulation of C14 Viable Cells on the 
Surface of an Established Biofilm vs. Modified Time, [Tm].
Regular RotoTorque, RPM = 289, fluid shear = 2 0  dyne/cnr, 
substrate glucose concentration chemostat influent = 3 
mg/1, temperature = 22°C, I experimental data, - curve fit 
(Xs14 = 772.4 + 4179.1 [Tm]"5, r2 = 0.99).
147
[Tm] minutes
Figure 42. P 2 R 4: Accumulation of C14 Viable Cells on the 
Surface of an Established Biofilm vs. Modified Time, [Tm].
Regular RotoTorque, RPM = 289, fluid shear = 2 0  dyne/cnr, 
substrate glucose concentration chemostat influent = 30 
mg/1, temperature = 28°C, I experimental data, - curve fit 
(Xs14 = 89209.7 + 187194.4 [Tm]"5, r2 = 0.94).
148
2 .5
0 .0 0  2 0 .0 0  4 0 .00  6 0 .0 0  8 0 .00  100 .00  120 .00  140 .00
[Tm] minutes
Figure 43. P 2 R 5: Accumulation of C14 Viable Cells on the 
Surface of an Established Biofilm vs. Modified Time, [Tm].
Regular RotoTorque, RPM = 70, fluid shear = 2 dyne/cm , 
substrate glucose concentration chemostat influent = 30 
mg/1, temperature = 28°C, I experimental data, - curve fit 
(Xs14 = 328.3 + 155.2 [Tm]-5, r2 = 0.97) .
149
[Tm] minutes
Figure 44. P 2 R 6: Accumulation of C14 Viable Cells on the 
Surface of an Established Biofilm vs. Modified Time, Time 
[Tm]. Regular RotoTorque, RPM = 289, fluid shear = 20 
dyne/cm2, substrate glucose concentration chemostat 
influent = 30 mg/1, temperature = 22°C, I experimental 
data, - curve fit (Xs14 = 137043.6 + 39478.5 [T] "5, r2 = 
0.93)
150
)  8 0 .0 0  Il
[Tm] minutes
120 .00  140 .00 160.00
Figure 45. P 2 R 7!Accumulation of C14 Viable Cells on the 
Surface of an Established Biofilm vs. Modified Time, [Tm].
Regular RotoTorque, RPM = 289, fluid shear = 2 0  dyne/cnr, 
substrate glucose concentration chemostat influent = 30 
mg/1 temperature = 22°C, one day C12 biofilm, I experimental 
data, - curve fit (Xs14 = -664.6 +32542.2 [T] "5, r2 = 0.97).
The slope of each graph at time t = 0, and at time t > tL 
yields the values of Rftg14, and RAn14 respectively for each
151
experimental run (Figures 3 8  through 4 5 )  . Given RAg14, and RAn14; 
RAgtotalf and RAntotal are then calculated using equations ( 3 5 )  and 
equation ( 3 6 ) . Ideally, tL would be chosen where the rate of 
C14 cellular detachment per unit area is reaching steady-state 
at tL — > oo„ in this work, however, tL was chosen as large the 
data allowed.
Equation ( 3  6 )  was used to correlate RAntotal to RAn14 by ( I  - 
e"t/T) as given in equation ( 3  6 )  at times t > tL. Basically, by 
using equation ( 3 6 ) ,  it is said that RAntotal will be estimated 
based on the Rftn14 calculated from an experimental data set 
when the C14 labelled cells on the surface of biofilm are 
behaving as the C12 cells on the surface of biofilm.
The solid line on each graph is a curve fit. The slope of 
each graph at tL was calculated using one of the curve fit 
equations given in Table 4 0 .  However, because of the inability 
of the equations to predict the slope at time t = 0, the slope 
of each graph at time t = 0 was determined by calculating the 
slope of another curve fit to the lower portion of each data 
set (the first 5 points).
152
Table 40. Numerical Values of Coefficients for Regression 
Equations.
Equation Form
X14s = A + B [Tm] -5 i
= (A + B [Tm] -5)2 ii
X14s = (A - B e" [Tm]/T)2 iii
X", = A + B [Tm] iv
Run
All Data Points First 5 Points
Form A B r2 Form A B r2
P l R I i 261. 6 6090 0.99 iii 123 116.1 0.94
P 2 R I ii 154* 38.1* 0.98 iii314.3 286.2 0.82
P 2 R 3 i 772. 4 4179.1 0.99 iii 110.3 101.3 0.83
P 2 R 4 i 89209. 7 187194.4 0.94 iii773.0 701 0.86
P 2 R 5 ii 328. 3* 155.2* 0.97 iii820.8 788.4 0.77
P 2 R 6 i 137043. 6 39478.5 0.93 - - -
P 2 R 7
1
— 664 .6 32542.2 0.97 iv 0 20549.9 0.98
Calculated slopes from each graph are listed in Table 41. 
Slope I is the slope at time t = 0. Slope II is the slope as 
time approaches tL. "Time" is the time at which the slope II 
is calculated
153
Table 41. dXs14/d[Tml. dXs14/dTm is the slope of the 
accumulation curve, c'4 labelled cell concentration on the 
surface of an established biofilm, Xg14, vs. modified time, 
[Tm], slope I is the slope at time t = 0, slope II is the 
slope as time approaches tL.
Run
Slope I Slope II tL RAntotal
CFU/(cm2 minute) (min) (CFU/cm2 min)
P I R I 1.6 IO3 - - -
P 2 R I 1.6 IO4 1.8 IO3 402 1.76 10
P 2 R 3 1.8 IO3 2.1 IO2 180 1.8 IO2
P 2 R 4 1.1 IO5 1.1
OH
150 8.9 IO3
P 2 R 5 5.1 IO4 2.9 IO4 210 2.6 IO4
P 2 R 6 - 1.2 IO3 360 1.22 10'
P 2 R 7 2.1 IO4 1.4 IO3 240 1.5 IO3
The rate of total cellular detachment per unit area is 
the difference between the gross rate of total cellular 
attachment per unit area, RAgtotal/ and the net rate of total 
cellular attachment per unit area, RAntotal• This method to 
calculate the rate of total cellular detachment per unit area 
has been called the first method to calculate Rdtotal.
-,-,total ^  J-, total _ jj total 
-ttCi - -ttAg- -ttAn (B.4)
The net rate of C14 cellular attachment per unit area to 
an established biofilm, RAn14, is the slope (dXg14/dt) of the
154
graph of net C14 cellular accumulation vs. time. It is a 
function of time.
The rate of C14 cellular detachment per unit area, Rd14 
which is a function of time, is the difference between the 
gross rate of C14 cellular attachment per unit area to an 
established biofilm, Rftg14, and the net rate of C14 cellular 
attachment per unit area, RAn14.
Table 42. The Rate of Total Cellular Detachment II. R1 
calculated using the first method.
to t a l
Run Fluid Shear
(dyne/cm2)
Temperature t o t a l
(0C) (CFU/cm*2 min)
22 14240
22 1620
28 101100
28 25000
22 19500
P 2 R I 
P 2 R 3* *)
P 2 R 4 
P 2 R 5 
P 2 R 7*
20
20
20
2
20
*) Low glucose substrate concentration in chemostat feed 
therefore low bulk cell concentration in the RotoTorque.
**) One day C12 biofilm.
A saturation-type equation (B.5) can be used to fit the 
rate of C14 cellular detachment per unit area, Rd14, as a 
function of time.
R 14 _ d  -
^dmax £
k d + t
(B.5)
155
The maximum rate of C14 cellular detachment per unit area, 
Rdmax14/ is supposed to be the same as the rate of total 
cellular detachment per unit area, Rdtotal. The values of kd and 
R14max in equation (B.5) for each experimental run are given in 
Table 43.
Table 43. Values for Saturation-Type Equation. The units of 
Rdmgx14 is (CFU of C14 labelled cells/ cm2 minute) , while kd has 
units of minutes.
Run R 14
(CFU/cm* min)
, k,
(min)
r2
P 2 R I 16117 70 0.99
P 2 R 3 2328.55 56.1 0.95
P 2 R 4 116307. 33.61 0.98
P 2 R 5 56270. 19.94 0.96
P 2 R 6 18920 70 0.99
P 2 R 7 21376 70 0.99
APPENDIX C
FLUID SHEAR PREDICTION IN THE ROTOTORQUE
157
APPENDIX C
Fluid shear on the surface of the biofilm, induced by the 
rotational speed of the rotor, can be predicted using Figure 
46. Two methods of predicted the fluid shear as a function of 
RPM of the inner rotating cylinder are shown in the graph.
The lower line, marked "predicted", was calculated using 
Figure 3. Details of the computational procedure are given in 
the Model Development Section. The upper line, marked 
"measured", weas obtained by measuring the torque 
experimentally using a torque monitor (Torque Monitor TDS-DN- 
TMl, General Thermodynamics . Corporation, Plymouth, 
Massachusetts). The fluid inside the RotoTorque during the 
torque measurement was water. No biofilm was present on the 
inside surface of the RotoTorque. No significant torque 
difference can be measured using this equipment with a 
RotoTorque with or without biofilm [36].
In this work, fluid shear was reported using the 
"predicted" line (the lower line on Figure 46)
Sh
ea
r 
St
re
ss
 
d
y
n
e
/
sq
c
158
Measured
Predicted
Figure 46. Fluid Shear on The Inner Surface of RotoTorgue
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