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This is to certify that the

thesis entitled

The Development of a Biochemical
Engineering Teaching Laboratory

presented by

Andrew Burkett Kinney

has been accepted towards fulfillment
of the requirements for

 

 

M.S. degree in Chem. Engr.

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Nov. 20! 1992

 

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THE DEVELOPMENT OF A BIOCHEMICAL
ENGINEERING TEACHING LABORATORY

By

Andrew Burkett Kinney

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Chemical Engineering

1992

ABSTRACT

THE DEVELOPMENT OF A BIOCHEMICAL
ENGINEERING TEACHING LABORATORY

By
Andrew Burkett Kinney

Biotechnology is an expanding field with great economic potential for engineers
able to apply chemical engineering fundamentals to problems in microbiology and
biochemistry. There is a shortage of engineers trained in the life sciences for
monitoring, designing and scaling-up biotechnology processes. To meet the educational
needs of the growing biotechnology industry, a undergraduate biotechnology laboratory
was developed. The experiments for the laboratory were designed to minimize operating
costs, waste disposal problems, and demonstrate applications of chemical engineering
principles in biotechnology. This thesis incorporates six experiments: batch ethanol
fermentation, enzyme kinetics, fermentation mass transfer, fermentation power transfer,
immobilized biocatalysts and membrane filtration. Each experiment is a chapter of the
thesis with its own abstract, introduction, background, theoretical analysis, results,
conclusions, recommendations, and an appendix containing specific experimental

protocols.

”October knew, of course that the action of turning a page, of ending a chapter
or of shutting a book, did not end a tale.

Having admitted that, he would also avow that happy endings were never difficult
to find: ’It is simply a matter,’ he explained to April,’of finding a sunny place in the
garden, where the light is golden and the grass is soft; somewhere to rest, to stop reading
and be content.’ "

-Neil Gaiman, The Season of Mists

ACKNOWLEDGMENTS

Mark Worden
Vicki Thompson
Ramkumar Subramanian
Tim Geiger
Rob Selden
Daina Briedis
Charles H. Byers
Tracy Mallory
Ray York
Bill TerBurgh
Francine Pelletier
Tracy Baker
Brook Thomas
Jonathan Grow
Graig Wierenga
Beth Curtis
Faith Peterson
Julie Caywood
Brad Kach
Eric Grulke

ii

TABLE OF CONTENTS

LIST OF TABLES ...................................... v
LIST OF FIGURES ...................................... vi
INTRODUCTION ....................................... 1
References ....................................... 3
Batch Ethanol Fermentation ................................. 4
Summary ........................................ 4
Introduction ...................................... 4
Background ...................................... 6
Theoretical Analysis ................................. 7
Experimental Equipment and Procedure ..................... 11
Results and Discussion ............................... 14
Conclusions and Recommendations ........................ 21
Symbols ........................................ 26
References ....................................... 26
Appendix ........................................ 27
Enzyme Kinetics ........................................ 41
Summary ........................................ 41
Introduction ...................................... 41
Background ...................................... 42
Theoretical Analysis ................................. 44
Experimental Equipment and Procedure ..................... 48
Experimental Results and Discussion ....................... 50
Conclusions and Recommendations ........................ 59
Symbols ........................................ 60
References ....................................... 61
Appendix ........................................ 62
Fermentation Mass Transfer ................................. 67
Summary ........................................ 67
Introduction ...................................... 67
Background ...................................... 67
Theoretical Analysis ................................. 69
Experimental Equipment and Procedure ..................... 72
Experimental Results and Discussion ....................... 75
Conclusions and Recommendations ........................ 75
Symbols ........................................ 78
References ....................................... 78
Appendix ........................................ 80

iii

Fermentation Power Transfer ................................ 85

Summary ........................................ 85
Introduction ...................................... 85
Theoretical Analysis ................................. 87
Experimental Equipment and Procedure ..................... 90
Results and Discussion ............................... 92
Conclusions and Recommendations ........................ 96
Symbols ........................................ 96
Bibliography ...................................... 97
Appendix ........................................ 98
Immobilized Cell Biocatalysts ............................... 104
Summary ....................................... 104
Introduction ..................................... 104
Theoretical Analysis ................................ 106
Experimental Equipment and Procedure .................... 110
Results and Discussion .............................. 112
Conclusions and Recommendations ....................... 118
Symbols ....................................... 120
References ...................................... 121
Appendix 1. Experimental Equipment and Procedure ............ 122
Appendix II. Difftr5: Program for Evaluation of D and a ......... 129
Membrane Filtration . .- .................................. 137
Summary ....................................... 137
Introduction ..................................... 137
Theoretical Analysis ................................ 141
Experimental Equipment and Procedure .................... 151
Results and Discussion .............................. 154
Conclusions and Recommendations ....................... 161
Constants ....................................... 161
References ...................................... 162
Appendix ....................................... 164

iv

LIST OF TABLES

Batch Ethanol Fermentation ................................. 4
Table 1. Available Electrons in Fermentation Products ............ 10
Enzyme Kinetics ........................................ 41

Table 1. Values of mele." and l/me for Different Types of
Enzyme Inhibition .............................. 48

Table 2. Kinetic Constants for Fumarase Determined by Different Plotting
Techniques .................................. 53

Table 3. Inhibition Constants for the effect of Citrate on Fumarase
Activity .................................... 58

Table 4. Inhibition Constants for the effect of Phosphate on Fumarase
Activity .................................... 58
Table 4. Dilution Schedule for the Fumarate Solutions ............ 62

LIST OF FIGURES

Batch Ethanol Fermentation ................................. 4
Figure 1. Setup for Autoclaving and Aseptic Transfer of Yeast Extract
Fraction .................................... 12
Figure 2. Simplified View of Fermentor Setup for Autoclaving ....... 13
Figure 3. Cell Growth Curves using Dry Weight and Optical Density . . . 16
Figure 4. Cell Dry Weight versus O.D. ..................... 17
Figure 5 . Fermentation Concentration Profiles versus Time ......... 18
Figure 6. Comparison of Experimental and Calculated Glucose
Concentrations ................................ 19
Figure 7. Electron Equivalents Present versus Time .............. 20
Figure 8_. Determination of the Experimental Ethanol Yield ......... 22
Figure 9. Determination of the Experimental Cell Yield ........... 23
Figure 10. Determination of Yields based on the Calculated Glucose
Concentration ................................. 24
Figure 11. Determination of Specific Ethanol Uptake Rate
for Z. mobilis ................................. 25
Enzyme Kinetics ........................................ 41
Figure 1. Reaction Catalyzed by the Enzyme Fumarase ........... 44
Figure 2. Calibration Curve for Fumarate Absorbance at 330 nm ..... 51
Figure 3. Lineweaver-Burk Plot for Determination of Kinetic
Constants ................................... 52
Figure 4. Hanes-Woolf Plot for Determination of Kinetic Constants . . . . 54
Figure 5 . Reaction Velocity versus Substrate Concentration for
Fumarate ................................... 55
Figure 6. Reaction Velocity versus Substrate Concentration for Fumarate
with 22.4 mM Citrate Present ....................... 56
Figure 7. Reaction Velocity versus Substrate Concentration for Fumarate
with 66.4 mM Phosphate Present ..................... 57
Fermentation Mass Transfer ................................. 67
Figure 1. Experimental Setup for Mass Transfer Experiment ........ 74
Figure 2. Dynamic Gassing Out Method of Determining k,a ......... 76
Figure 3. k,a versus RPM .............................. 77
Fermentation Power Transfer ................................ 85
Figure 1. Tank and Impeller Geometry ..................... 89
Figure 2. Experimental Setup for Mixing Power Equipment ......... 91
Figure 3. Power versus RPM ........................... 93
Figure 4. Power Number versus Reynolds Number .............. 94

Immobilized Cell Biocatalysts ............................... 104

Figure 1. Apparatus for Forming Gel Beads ................. 111
Figure 2. Experimental Setup for Determination of Effective Diffusion
Coefficients ................................. l 13
Figure 3. Calibration Curve for Conductance Measurements of Calcium
Chloride at 30°C .............................. 114
Figure 4. Disappearance of CaCl, from Solution versus Time ....... 115
Figure 5. Disappearance of CaCl2 from Solution versus Time ....... 116
Figure 6. Disappearance of CaC12 from Solution versus Time ........ 117
Figure 7. Effect of Shaker Speed on Diffusion Data at 30°C ........ 119
Membrane Filtration .................................... 137

Figure 1. Schematic Comparison of Dead End and Crossflow Filtration . 139
Figure 2. Schematic of Concentration Polarization and Boundary

Layer .................................... 144
Figure 3. Diagram of Spiral Cartridge Apparatus .............. 152
Figure 4. Diagram of Hollow Fiber Apparatus ................ 153
Figure 5. Cell Dry Weight versus Absorbance at 710 nm ......... 155
Figure 6. Calibration Curve for Blue Dextran Concentration versus

Absorbance ................................. 156
Figure 7. Concentration and Yield versus VCR for Z. mobilis ...... 157
Figure 8. Concentration and Yield versus VCR for Blue Dextran ..... 158
Figure 9. Hollow Fiber Flux Determination for Z. mobilis ......... 159
Figure 10. Spiral Cartridge Flux Determination for Blue Dextran . . . . 160

vii

INTRODUCTION

Biotechnology is a rapidly growing field with great economic potential for
engineers who can integrate chemical engineering fundamentals into the context of
microbiology and biochemistry. Engineers must respond to opportunities in
biotechnology by applying analytical approaches like unit operations and transport
phenomena (Wei, 1988). Many studies have indicted a shortage of "well-trained
bioprocess engineers” for monitoring, designing and scaling-up biotechnology processes.
The development of biotechnology requires individuals who are trained to operate in an
interdisciplinary environment of biology, biochemistry and engineering (Commercial,
1984). To produce engineers to accomplish this task, the curriculum taught in
universities must be revised to teach new concepts (Wei, 1988). Most existing
universities’ bioprocess engineering programs focus primarily on graduate level education
(Commercial, 1984). Recently universities have anticipated the nwds of a mature
biotechnology industry and have designed curricula at the B. S. level which focus on
recombinant DNA techniques and bioengineering (Carter, 1987).

Commercializing biotechnology requires innovative chemical engineers with
strong life- science and process-engineering backgrounds to achieve large-scale
implementation of biotechnology. The new university curricula must be developed to
coordinate academic programs in engineering with the life sciences to facilitate
interdisciplinary collaborations. Chemical engineers are nwded to work in
interdisciplinary groups to transform the results of health and biotechnology research into

practical products and applications. Some of the areas identified for research and

2

modeling are: biological interactions, biologieal surfaces and interfaces, bioprocessing,
separations, and engineering analysis of complex biological systems. In addition,
facilities for education and research in biotechnology must be financed and constructed
(Frontiers, 1988).

To meet the educational needs of the growing biotechnology industry, Michigan
State University expanded its undergraduate biotechnology course offerings. A
substantial investment was made to develop an undergraduate biochemical engineering
laboratory, which is now one of the best equipped laboratories of its type in the country.
The general course content of the laboratory was developed based on the needs of the
biotechnology industry and the biotechnology curricula that existed in other departments.
The experimental topics of the laboratory were formulated as nine summaries that briefly
described the tepics and goals of each experiment. Based on those abstracts, the
laboratory experiments were developed over a two-year period by a graduate student as
a Master’s thesis project. The project entailed selecting, purchasing, installing,
operating, and designing equipment for the laboratory as well as utilizing equipment
previously purchased for the laboratory. Each experiment described in the abstract was
developed through literature and experimental research, and designed to minimize
operating costs and waste disposal problems, while demonstrating applications of
chemical engineering principles in biotechnology. Ultimately, the list was expanded to
ten laboratory topics: aseptic techniques, batch ethanol fermentation, continuous and
annular chromatography, continuous sterilization, enzyme kinetics, fermentation mass and

power transfer, immobilized biocatalysts, membrane filtration, and plasmid stability.

3

The biotechnology laboratory also emphasizes modernization of the curricula, in that four
of the experiments utilize computerized data acquisition and control, and other
experiments use microprocessor controlled ferrnentors and motors. The laboratory also
focuses on scale-up techniques for mass and power transfer using a 100 gallon pilot-scale
fermentor for large-scale experiments.

This thesis consists of six chapters, each of which contains one of the following
experiments: batch ethanol fermentation, enzyme kinetics, fermentation mass transfer,
fermentation power transfer, immobilized biocatalysts and membrane filtration. Time
limitations prevented the complete design and optimization of all of the experiments so
only the six that were fully completed are included in the thesis. The experiments are
presented in a format similar to the laboratory reports required for the class but include

specific experimental protocols in the appendix of each chapter.

References
Carter, Thelma, ”Undergraduate Education in Biotechnology” , Biotechnology, vol. 5 ,
1987, pp. 347 - 349.

Commercial Biotechnology: An International Analysis, Washington, D.C.: U.S.
Congress, Office of Technology Assessment, OTA-BA-218, January 1984.

Frontiers in Chemical Engineering: Research Needs and Opportunities, National
Academy Press, Washington, DC, 1988, pp. 17 - 35.

Paul, Edward L. , and Carlos B. Rosas, ”Challenges for Chemical Engineers in the
Pharmaceutical Industry", Chemical Engineering Progress, December 1990, pp. 17 - 25.

Wei, James, "Future Directions in Chemical Engineering Education” , Chemical
Engineering Education, Winter 1988, pp. 12 - 16.

Batch Ethanol Fermentation

Summary
Glucose was converted to ethanol by the microorganism Zyrnomonas mobilis in

a microprocessor controlled fermentor. The fermentor was steam-sterilized, inoculated,
and maintained at a pH 6.5, 30°C, and agitated at 150 rpm. The concentrations of
glucose, cell mass, and ethanol were monitored for a several-hour period of the
fermentation. The specific growth rate, the specific ethanol-production rate, and the cell
and ethanol yield coefficients were calculated. The results calculated from the
experimental data varied significantly from the literature values in some cases. The
experimental results indicated that the method of determining glucose concentration was

in error.

Introduction

Fermentations use microorganisms to catalyze chemical reactions that produce
substances such as pharmaceuticals, organic acids, and alcohols. Fermentations can be
used to produce a large variety of products, but their commercial applications are limited
by their economic competitiveness with alternative processes. Advances in recombinant
DNA technology allow fermentations to produce complex biomolecules such as human
, insulin that cannot be synthesized by other means.

The most widely known fermentation process is the production of ethanol. Batch
yeast fermentations have been used for hundreds of years to produce alcoholic beverages

such as her and wine. Ethanol can be produced from a wide variety of plant-derived

4

5
starting materials as is evidenced by the large selection of alcoholic beverages for human

consumption. Ethanol can also be produced from agricultural wastes such as the chaff
from wheat or the remnants of sugar cane after the sugar has been removed.

Ethanol has many advantages for use as an alternative to non-renewable fossil
fuels. It is a liquid and easily transported, has a heating value 2/3 that of gasoline, and
can be blended with gasoline for use as an additive to increase the octane rating of the
fuel. Ethanol was used as a primary fuel before and during World War II, but was
replaced by cheaper petroleum and petrochemical products. Acetone and butanol
production by fermentation were also displaced by petroleum distillates (Bailey and Ollis,
1986). The unstable global economic forces that control petrochemical prices make
ethanol fuel production by fermentation a high economic risk since a drop in oil prices
could bankrupt an ethanol-fuel producer. However, the need for renewable energy
resources may spur an increase in the production of ethanol from agricultural products
by fermentation for use as a fuel.

Innovative processing strategies are required to make ethanol production
economically competitive with petrochemical products. New developments such as
continuous fermentations with a cell recycle and vacuum operation allow a twelve-fold
increase in productivity over conventional processes (Bailey and Ollis, 1986). Tower
fermentors are used to retain flocculent yeast, minimizing process costs by eliminating
theneedforauxiliaryseparau'ondevicesandacellrecycletomaintainhighcell
concentrations (Bailey and Ollis, 1986). Yeasts are sometimes replaced by bacteria that

reproduce faster and give higher yields of ethanol (Worden, 1982).

Background

Fermentations that are used to produce a specific product must be carried out in
a pure culture to assure that only the desired product is produced. Contamination of a
fermentation by unwanted microorganisms can result in inconsistencies in the product or
failure to produce the products. Contamination is minimized in the initial phases of the
fermentation by sterilizing the reactants and any components of the fermentor that will
come in contact with the fermentation. The procedures that prevent contamination of the
fermentation by foreign organisms after sterilization are known as aseptic techniques.

Typically the fermentor is sterilized to kill any organisms present and then it is
inoculated by aseptically adding a small quantity of the microorganisms selected for the
fermentation. After inoculation, a batch fermentation goes through four phases: the lag
phase, the exponential growth phase, the stationary phase, and the death phase. The lag
phase is the time period of adjustment by the cells to their new environment before they
begin growth after inoculation. The cell concentration increases exponentially in
exponential or logarithmic growth phase until the substrates are used up or high product
concentrations inhibit the reaction. Cell growth ceases in the stationary phase, and cells
begintodieinthedeathphase.

A fermentation is monitored by measuring the substrate, product, and cell
concentrations during the fermentation. Common methods for determining glucose and
ethanol concentrations use spectrophotometric measurements of enzymatic reaction
products. Unknown samples are combined with enzymatic reagents, and the optical

density of the mixture is measured and compared to a calibration curve constructed using

7
known standards. Cell concentrations are usually measured by either the optical density

of the fermentation broth or the cell dry weight. The optical density (O.D.) of a sample
of fermentation broth is often referred to as the turbidity or the absorbance. Absorbance
measurements are quicker and more precise than dry weight determinations but must be
converted to cell concentration units using a calibration curve. Cell dry weights provide
a direct measurement of cell mass, which is needed for carbon and electron balances.
The dry cell weight is determined by removing a known volume of fermentation broth,
centrifuging and rinsing the cells to remove nonvolatile salts and substrates, and then
drying and weighing the cells. The cell dry weight is the weight of the dried cells
divided by the volume of the original sample of fermentation broth. Dry-weight
measurements are time consuming and imprecise at low concentrations. However they
become more accurate at the high cell concentrations present in the late exponential phase

where they can be used to create a calibration curve for CD. versus cell concentration.

Theoretical Analysis

A rod shaped, anaerobic, gram negative, bacterium known as Zymomonas mobilis
(ATCC 10988) is often used to produce ethanol instead of yeasts because it grows and
produces ethanol faster than yeasts (Worden, 1982). Z. mobilis grows well at high
temperatures and is often used to brew alcoholic beverages in tropical climates. The

general reaction catalyzed by the cells is shown below:

cells (1)
ammonia + glucose .. ethanol 4» cells + carbon dioxide

8
Zymomonas mobilis grows well between pH 5.5 and 8 in solutions containing up

to 20% glucose and 1% yeast extract, a powdered nutrient obtained from yeast. The
carbon dioxide produced by the fermentation acidifies the medium, inhibiting the
fermentation, unless the pH is maintained by adding base or buffering the fermentation
broth (Worden, 1982).

Batch fermentations are autocatalytic in nature because as the reaction proceeds
the concentration of the reaction catalyst, cells, increases exponentially with time. The

rate equation for cell growth is:

(2)
= In

a-lfi:

where x is the cell concentration and t is time. The specific growth rate, a, is a function
of temperature, pH, and the substrate and product concentrations. The specific growth
rate is constant early in the fermentation until the substrate is consumed and inhibitory
products accumulate to a significant level. When u is constant, Equation (2) can be

integrated to yield:

3
ln(x)=ut+c H

where c is an integration constant. Equation (3) indicates that a plot of ln(x) versus t
should be linear with a slope equal to the specific growth rate. Excellent linear fits for
u are not uncommon for the growth of Z. mobilis over a several-hour period (Worden,
1982).

The mass of product per unit mass of substrate is given by the yield coefficient,

9

Y,,,. The slope of a plot of the product concentration versus the substrate concentration
gives the yield coefficient Y,,,. Alternatively, Y,,, may be determined using substrate and
product concentrations from any two times during the fermentation. When using this
method, the changes in the substrate and product concentrations should be as large as
possible to minimize the error due to imprecisions in the concentration data.

An electron balance can be used to evaluate the relative chemical-energy contents
of the fermentation products and substrates to determine the reaction efficiency. The
electron balance entails comparing the total number of available electron equivalents
contained in the substrate consumed to that in the products formed. The balance can be
performed using initial and final concentration data. The electron balance is a
combination of elemental mass balances because it is based upon reaction stoichiometry.
Electron balances use the reductance degrees of the substrates and products relative to
their combustion products. The reductance degree, 7, of a compound is defined as the
number of equivalents of electrons available for transfer to molecular oxygen during
combustion on a C-mole basis. One C-mole is the mass of substance containing 1 mole
(12 g) of carbon. Reductance degrees are calculated using values of 4, l, -2, and -3 for
the number of available electrons from carbon, hydrogen, oxygen, and nitrogen atoms,
respectively. For example, the reductance degree of the glucose (OJ-1,20.) is calculated
below. ‘

cc 4r + 12!! 15+ so -2e']Cerzos= 4e"

amino, 0 C‘Huo‘ H C‘Huo‘ o 6 Cmol Cmol

 

 

 

r=l

where e’ = electron equivalent

10
The chemical formula of Z. mobilis cells can be assumed to be CH,,.OO_,NM, indicating

that l C-mole of Z. mobilis cells is 24.6 grams. Table 1 shows a sample calculation for
a typical set of experimental data. The cell and ethanol yields are expressed in g product
produced per g glucose consumed. Ammonia and carbon dioxide are not considered in
this balance, because their reductance degrees are zero. Yeast extract is ignored in the
balance, because 2. mobilis does not metabolize carbon sources within the yeast extract
to a significant degree. Since 1 gram of glucose contains 0.133 electron equivalents, the
electron balance for this example would be within 2% of converting all of the glucose
to ethanol and cells. 1

Table 1. Available Electrons in Fermentation Products

 

Product Yield 7 Electron

Yield Equivalents
Ethanol 0.480 0.0209 6 0. 125
Cells 0.032 0.0013 4.2 0.005
Total Electron Equivalents 0.130

'l‘heelectronbalancecanalsobeinterpretedasatypeofenergy balancebecause
heats of combustion are directly proportional to reductance degrees by a factor of 27.5
kcal/e' for a wide range of organic materials, such as alcohols, sugars, alkanes and
biomass. The energy-recovery efficiency of the fermentation can be evaluated using the
enthalpy of the reactants and products. In the example above, 94 % of the available

electrons were recovered in the ethanol, and only 4 % in the biomass.

11

Experimental Equipment and Procedure

The fermentation broth for the experiment consisted of 2 wt % glucose and 1 wt
% yeast extract in a 0.01 M succinate buffer at pH 7. The glucose was autoclaved
separately from the yeast extract and the succinate buffer to prevent darkening of the
solution. The yeast extract and succinate were autoclaved in a 1000 ml flask equipped
with an aseptic transfer apparatus shown in Figure 1. The fermentation vessel was
autoclaved as shown in Figure 2, containing 500 ml of 4% glucose dissolved in the
succinate buffer. Four 250 ml flasks, two of which contained 50 ml and two containing
150 ml of 10% glucose and 2% yeast extract, were also autoclaved with cotton stoppers.
Two Pasteur pipettes with cotton plugs near the top were autoclaved wrapped in paper
towels to preserve sterility for aseptic transfer.

A culture of Z. mobilis (ATCC 10988) was revived from freezed dried storage
by aseptically transferring the cell pellet and resuspending the cells in 5 ml of sterile 5%
glucose and 1% yeast extract solution. The 5 ml sample was incubated at 35"C for three
days until a significant increase in bubbling and turbidity was observed. Portions of the
5 ml revived culture were transferred to two 250 Erlenmeyer flasks containing 25 ml of
sterile medium containing 5% glucose and 1% yeast extract. One of the flasks was used
as a storage culture and the other was used as a working culture. The working culture
was used to inoculate a flask containing 100 m1 of fermentation broth which was used
as the inoculum culture for the fermentor.

The fermentor used was a microprocessor controlled, New Brunswick

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Figure 2. Simplified View of Fermentor Setup for Autoclaving

14
BioFloIIC_, which is capable of maintaining a set pH, temperature, and agitation rate.

The pH was measured by a steam-sterilimble pH probe. The temperature was
maintained at 35 °C and was controlled by a heat exchanger unit contained in the bottom
of the fermentation vessel. The two equally-spaced Rushton, 6-bladed turbines were used
agitate the fermentor at 150 rpm. The cell, ethanol, and glucose concentrations were
measured and recorded at various times during the fermentation. The cell concentration
was assayed using both optical density and dry weight measurements. The ethanol
concentrations were determined using a YSI autoanalyzer which was calibrated against
known standards. The glucose was assayed using the YSI autoanalyzer, which was also
calibrated against known standards.

Results and Discussion

The results of the experiment varied from the literature values significantly in
most cases. Figure 3 shows the cell growth curves for both dry weight and optical
density. The specific growth rate was determined by linear regression from the slope of
a plot of ln(O.D.) versus time. The specific growth rate determined was 0.33 1; 0.01
hr‘ at 35°C. The literature value for the specific growth rate of Z. mobilis is 0.526 hr‘
at 36°C (Worden, 1982). The optical density data taken throughout the experiment were
correlated with the dry weight measurements as shown in Figure 4 to estimate cell mass
concentrations for the electron balance. The line was forced through zero for the linear
regression, since the Lambert-Beer law indicates that absorbance should be directly

proportional to concentration (Boyer, 1986).

15
Figure 5 illustrates the concentration profiles of glucose, cells and ethanol during

the course of the fermentation as well as a glucose concentration profile calculated using
the electron balance and the experimental ethanol and cell concentrations. Figure 6
demonstrates the scatter of the glucose data and the difference between the experimental
glucose concentration and the glucose concentration calculated from the electron balance.
The total number of electron equivalents calculated from the experimental data was not
constant over time, conflicting with the definition of a closed batch system. Figure 7
shows the relative contribution of each component of the fermentation to the total number
of electron equivalents present during the course of the fermentation. Figure 7 clearly
demonstrates that the experimental glucose concentration contributes most of the
fluctuation in the total number of electron equivalents until the last two hours of the
fermentation. The most likely explanation is that the glucose membrane for the YSI
autoanalyzer was not allowed sufficient time to equilibrate before the glucose assays were
performed. The fluctuation in the ethanol concentration was attributed to the slow
degeneration of the membrane due to operation above the specified temperature for the
membrane. The equipment lacked the temperature control component designed to lower
the operating temperature of the unit to increase the operating life of the ethanol
membrane.

The ethanol yield coefficient, Yum.“ (Y I,,,), was estimated from the
experimental data to be 0.735 :|: 0.134 g ethanol produced per g glucose consumed and
the fit to the data is shown in Figure 8. Similarly, Figure 9 shows the experimental cell
yield to be 0.181 :1; 0.019g cells produced per g glucose consumed. The literature data

16

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21
for the ethanol and cell yields for Z. mobilis at 34°C are 0.48 and 0.031 respectively in

units of g product per g glucose consumed (Lee, 1981). Estimates of the yield
coefficients were obtained using the glucose concentrations calculated from the electron
balance and the experimental ethanol and cell concentration data. Figure 10 shows less
data scatter and results in ethanol and cell yields of 0.49 and 0.099 respectively. The
specific ethanol production rate was calculated to be 1.49 g ethanol/g cells hr and is
shown in Figure 11. The literature value for the specific ethanol production rate is 8.0
g ethanol per g cells hr at 36°C (Worden, 1982).

The yields calculated for ethanol and cells using the glucose concentration
determined from the electron balance are much closer to the literature values than the
experimental data. This indicates that most of the experimental error was in the glucose
assay. This conclusion is also supported by Figure 7 which demonstrates the large
contribution of the glucose concentration to the failure of the electron balance. The
difference between the literature and experimental values of the specific growth rate and
the cell yield calculated from the electron balance indicates some potential experimental
error in the measurement of the biomass concentration. Fluctuations in the ethanol
concentration also produced error but were not significant until late in the fermentation

(see Figure 7).

Conclusions and Recommendations
The experiment has the potential to produce results with a good correlation to the

literature values as is indicated by the closeness of the estimated yields to the literature

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26
values. The glucose and ethanol assays can be effective using the YSI autoanalyzer but
the manufacturer’s protocols must be followed carefully. Both YSI assays are more
economical, quicker, and easier than their reagent based counterparts but it is still
advisable to retain samples for verifying the YSI method using reagent kits.

Use of the YSI autoanalyzer is recommended for convenience and economy and
may prove to be a useful analytical tool. The instructions as related to membrane life
and reagent expiration dates should be followed closely. The ethanol membrane
temperature adapter should also be installed whenever ethanol assays are performed as
well.

Symbols

1 - reductance degree

n a specific growth rate
c = integration constant
e‘ = electron equivalent
t = time

x = cell concentration

Yam,” = ethanol yield coefficient
Y,“ = general product yield coefficient

References

Bailey, LE. and Ollis, D.F., Biochemical Engineering Fundamentals, pp. 100-130,
McGraw-Hill Book Co., New York, pp. 757-758, 1986.

Boyer, Rodney F.(1986) Modern Experimental Biochemistrymp. 277-278, Addison
Wesley Pub. Co. , New York.

Lee, K. 1., M. L. Skotnicki, D. E. Tribe, and P.L. Rodgers, "The Effect of
Temperature on the Kinetics of Ethanol Production by Strains of Zymomonas mobilis“ ,
Biotechnology Letters, vol 3, No. 6, pp. 291-296 (1981).

Worden, R. M., ”A Kinetic Study of Ethanol Production by Zymomonas mobilis," M.S.
thesis, University of Tennessee, Knoxville (1982).

Appendix

27

Experimental Procedure

1. Day one

A. Preparation of Growth Media

1.

The yeast extract concentration in solution should be about 1 %
(10 g/l) and 10g shouldbeadded toSOO mlofwater since halfthe
volume of the media will be added as the yeast extract solution and
the other half will be added as the glucose solution. Prepare the
yeast extract in a 1000 mL erlenmeyer flask stoppered with the
apparatus shown in figure 1.

Make 500 ml 0.02 M succinate buffer by adding succinic acid
(succinate) to 300 - 400 ml of reverse osmosis water. Make a 1
N N aOH solution and add the base solution to the succinate
solution while checking the pH with a pH meter until it is 7.0.

The glucose concentration will be 2% (20 g/l) to keep the
fermentation short. The glucose solution should also be prepared
at 40 g/l ( i.e. add 20 g to 500 ml of succinate buffer). The
glucose concentration for the inoculum culture should be higher
(e. g. , 50 g/l) to provide a higher initial cell concentration. The
glucose and yeast extract solutions are prepared separately because
when they autoclaved together the medium darkens considerably.

Remove the top of the fermentor by gently sliding out the pH
probe and then loosening the three head plate knobs and earefully
lift off the top. Note that the pH probe enters the vessel in the
area where there are no baffle supports to prevent any obstruction
from damaging the glass probe. Clean up the fermentor and add
the glucose and buffer solution.

Replace the top carefully seating the top against the seal. Make
sure that the pH probe port is in the over the part of the vessel
with no obstructions. Lightly coat the pH probe with glycerol and
gently slide the probe into place.

Similarly, autoclave the inoculum medium in two 50 mL portions
in separate 250 mL Erlenmeyer flasks stoppered with wads of
cotton. Do not combine the glucose and yeast extract fractions
until it is time to use them. The soluu'ons will remain sterile
indefinitely until one of the vessels is opened and then they may

28
be contaminated by airborne microbes.

B. Calibration of pH Probe

1.

2.

Connect electrode to probe cable.
Turn agitation switch to OFF.

Make sure that water is flowing and the pressure is less than 30
psi. Turn on POWER switch.

Check the level of the electrolyte. It should be about 1 cm below
the level of the filling orifice. Remove the rubber plugs and set
them aside where they will not get lost.

Set the selector switch to pH and set the MODE switch to zero.

Immerse the pH probe into an external pH 7.0 buffer solution. Set
the display to read the pH value of the buffer with the INC/DEC
switch.

Immerse the pH probe in a basic standard pH solution. Set the
MODE switch to SPAN. Set the display to read the value of the
second buffer solution with the IN CIDEC switch.

C. Preparation for Autoclaving

1.

Remove the motor drive from the top of the vessel and place it on
the motor mount on top of the cabinet while placing the stainless
steel autoclaving cap where the motor rested over the bearings.

Calibrate the pH probe as per calibration instructions above. The
pH probe should be autoclaved in place (without the eable), with
the refill plug taped closed, and the red cap in place.

Disconnect all probes and remove all eables from the fermentor.
Make sure the anti-foam probe cable is disconnected at the top of
the probe and that it is pushed all the way down into the
fermentor.

Disconnect the air line on the vessel side of the filter and clamp
off the tubing.

Disconnect the jacket and exhaust condenser water lines.

10.

11.

29

Remove the sampler bulb and insert cotton into the port for the
bulb. Close the valve on the sampler bulb.

Any openings through which microbes could enter should also be
covered with cotton and then wrapped tightly in aluminum foil.
Masking tape can be used to hold the aluminum foil. Make sure
the feed tube of the fermentor is clamped and stoppered with
cotton and wrapped in aluminum foil beeause it will be used later
in the aseptic transfer of the yeast extract fraction into the
fermentor.

Tubes whose ends are submerged in the liquid medium should be
sealed, silicon tubing ean be clamped to prevent loss of liquid
during autoclaving. Use a small piece of silicon tubing to connect
the acid and base ports as shown in Figure 2.

Note that silicon tubing ean withstand the heat of autoclaving,
while Tygon tubing will melt.

Check the autoclaving setup against those in figures 1 and 2.

If in doubt, show the reactor to the instructor prior to autoclaving.

D. Sterilization

l.

The following items need to be autoclaved swled with glass wool:

a. Fermentor vessel containing 500 mL of glucose solution
and succinate buffer as in figure 2.

b. l L Erlenmeyer flask containing 500 mL of yeast-extract
solution with aseptic transfer setup attached as shown in
Figure l.

c. 250 m1. Erlenmeyer flask containing 50 mL of glucose
solution

(I. 250 mL Erlenmeyer flask containing 50 mL of
yeast-extract solution

e. Several glass sample bottles with screw-top lids (lids should
be screwed on loosely to allow pressure equilibration).

Openthe'upperaccessdoortothesterilizermakesurethatthe
chamberpressureisatornearOpsi(gauge). Makesurethe
manual control knob is turned to 'off' . Place aluminum foil

30

beneath the rack on the bottom of the autoclave this will aid in
cleanup if anything should spill or boil over. Talk with other
groupsandcoordinatesothatalltheitemsthatneedtobe
autoclaved can be sterilized in one batch.

Slide down the door beneath the silver "warning" plate on the left
front of the autoclave. Set the POWER and CONTROL switches
to ON. The control panel will then light up to demonstrate that all
the lights are functioning. The printer records the date and that
the power is turned on.

Checkthatthecorrecttimeanddateislistedbypressingthe
'time" or 'date' button. To change either the time or date press
the forward or reverse button until the correct time or date is
displayed.

Checktomakesurethereispaperandthatthepenisrecording
well.

Set the STERILIZE timer thumbwheels to 15 minutes. The set
time will be displayed on the primary control panel. Once the
cycle has been started the time eannot be changed using the
thumbwheels and the process must be restarted.

Check to make sure that the thumbwheel above the printer is set
to 121 for 121°C. If not, turn the thumbwheels to 121. If the
temperature is outside the allowable range a buzzer will be
sounded until an allowable temperature is selected. Once the cycle
has started the temperature cannot be changed using the
thumbwheels and the cycle must be stopped and restarted to
change the set temperature.

Check to make sure that the chamber pressure is sufficiently low
by opening the upper access door and reading the gauge labeled
chamber. Open the chamber door and load the sterilizer. The
printerwillrecordthatthedoorwasopened. Ifthedoorwillnot
unlock, turn the door wheel slightly clockwise and press the center
black button on the wheel. Since the door will not open if the
pressureistoohighitisimportanttocheckthechamberpressure
before attempting to open the door. Turn the handwheel counter
clockwise and open the door.

Checktomake surethatallcontainers withinthesterilizerareable
to equalize pressure through cotton and are not completely sealed.

10.

ll.

12.

13.

14.

15.

31

Close the door and press on the left hand side of the door to insure
a good seal. Then turn the door wheel clockwise to lock the door.
The DOOR UNLOCKED light on the panel should shut off at this
time. Once the chamber is pressurized, an integral pressure lock
will prevent the door from being opened. Turn on the steam and
water valves. Turn the III-LO knob to L0.

Touch the liquids cycle selector on the lighted panel. It should
increase in brightness. The CONDITION and WARNING HOT
LIQUIDS lights should come on. If you press the wrong cycle
selector simply press the white reset button and re-depress the
liquids button.

Afier the CONDITION phase is completed, the STERILIZE light
lights for the duration of the sterilization phase. The STERILIZE
TIME readout begins to countdown once the temperature and
pressure has been reached. The printed record will show when the
sterilize time began.

When the sterilization time runs out the Exhaust light comes on
and the chamber slowly begins to cool and depressurize. The
printed record will show the time, temperature and pressure the
exhaust phase begins.

Upon completion of the exhaust phase the buzzer will sound and
the COMPLETE light will come on. Crack open the door about
1/2" and leave it cracked for about 10 minutes. W

W

When the door is opened the buzzer will stop and the WARNING
HOT LIQUIDS light will begin to flash. At the end of ten
minutes the buzzer will sound again and the WARNING HUI“
LIQUIDS will stop flashing but remain lit. press the reset button
to silence the buzzer.

Open the chamber door and earefully remove the load from the
sterilizer. Press the reset button to shut off the warning hot liquids
light and tear off the paper form the printer. Shut off the power
and control switches for the sterilizer and shut off the steam and
water.

11. Day two: this should be performed the afternoon before your second laboratory period

A. Preparation of Inoculum Culture

IlI.Daythree

32

Aseptically combine your two flasks containing the yeast extract
and glucose solutions and then redivide them into two 50 ml
portions.

Aseptically transfer 5 mL of refrigerated Z. mobilis ”working“
culture to one of the flask using a 10 mL, disposable, sterile,
plastic pipette. Prepare two inoculum cultures, one receiving 5
mL of storage culture and the other receiving 0.5 mL. The second
culture will reach maturity several hours later than the first. This
precaution will help ensure that one of the flasks will have a
culture at the proper stage of development when it is time to
inoculate the reactor. The area where the culture is transferred
should have as little air flow as possible to minimize
contamination. The pipette should not be removed from the
wrapping until absolutely necessary and the tip of the pipette
should not be touched by anything but the media being transferred.
To help maintain sterility, whenever the cotton is removed or
replaced on a flask, the opening of the flask should be “flamed“
with a Bunsen burner. The instructor ean demonstrate this
technique.

Incubate the inoculum culture at 30°C in the incubator shaker until
the reactor is inoculated. Do not shake the flask.

The inoculum culture is sufficiently mature when it is highly turbid
and bubbles form when the flask is swirled. Culture maturity
should occur from 10 to 24 hours after addition to growth medium
at the proper temperature, depending on the condition of the
refrigerated culture.

A. Operating the Fermentor

1.

Aseptically combine the glucose and yeast extract fractions into the
fermentor and turn on the agitation to mix. This ean be
accomplished either by using filtered air to force the yeast extract
into the fermentor vessel or by using a large syringe to produce a
siphon. The connection of the tubes should be performed by
wrapping the tube in an alcohol soaked paper towel for 10 minutes
and then cutting it in the center of the paper towel and sliding it
onto the connecting tube. Remove the rack and wipe out the
autoclave with a moist sponge. Check the drain plug for
obstructions and empty it.

33

Adjust the values for fermentor pH, temperature, and agitation rate
to 7.0, 30°C, and 150 rpm, respectively. This is performed by
turning the selector knob to the desired variable (pH, temperature,
etc.) and turning the mode knob to set point. The control selection
on the mode knob shows the present value of the function on the
selector knob on the LED display.

Take a sample of the growth medium with a sterile pipette and
check the pH on a separate pH meter. If this value does not agree
with that given by the fermentor, adjust the desired setpoint
slightly to account for the difference. This fermentation is not
strongly affected by pH between 6 and 8, so errors of less than
half a pH unit are tolerable.

Transfer approximately 50 mL of the medium to the sterile,
screw-top sampling bottles to be used later as a spectrophotometer
blank and to dilute fermentation broth samples. Refrigerate until
needed to avoid possible microbial growth. Warm to room
temperature before using.

Transfer the inoculum culture (50 mL) into the fermentor to
initiate the fermentation.

B. Sampling the Fermentor

1.

Using a squeeze bulb, force some air through the sampling tube
before taking each sample, to ensure that the sample is fresh.
Record the pH.

Three mL samples should be taken for the turbidity assay
approximately every 20 minutes once growth has begun. The
samples should be immediately transferred to a cuvette and read in
the colorimeter at 710 nm versus a sterile growth medium blank.
Keep a running plot of ln(OD) versus elapsed time to follow the
progress of the fermentation.

Two milliliter samples are adequate for the glucose and ethanol
assays, and the same sample can be used for both.

Filter-sterilize the sample immediately using a disposable, 0.2 or
0.45 mm syringe filter. Fill the syringe with 1-2 ml of
fermentation broth collected from the sampling port. Attach the
syringe by screwing the filter onto the end of the syringe. Point
the nozzle of the filter into the sample vial or test tube and slowly

34
press the plunger to filter the liquid into the vial.

Collect the clarified filtrate in a small test tube, eap and label the
tube, and refrigerate for later analysis. Beeause ethanol is
volatile, it is important to control evaporative losses by minimizing
exposure of the samples to air. One sample should be taken soon
after inoculation to give the initial conditions. An appropriate
sampling strategy should be planned to give accurate measurements
of glucose consumption, as discussed previously. As an
approximate rule of thumb, 1% glucose is consumed for every 0.6
OD increase in the cell concentration during the exponential
growth phase.

C. Operation of the colorimeter

1.

Turn on the calorimeter using the switch on the left hand side of
the colorimeter.

Select the absorbance mode by pressing the MODE button in the
lower left until the display reads ABS in the right hand side of the
LED display. Turn the dial on the top to the desired wavelength
(710 nm) and insert your sample where in the front cuvette holder.
Allow 15 minutes for the optics to warm up.

Fill a cuvette with reverse osmosis (RO) water and place in the
rear cuvette holder and close the sample area lid. When handling
cuvettes, touch only the frosted sides of the cuvette and wipe down
the clear sides of the cuvette with a kimwipe before taking
absorbance readings. Turn the dial on the top of the colorimeter
towards the word blank until it stops. Then press the CAL button.

Fill another cuvette with R0 water, place it in the front sample
holder and read the absorbance. Ifthe absorbance is zero set aside
the cuvette for use and label it on the frosted side in some way.
Thisprocesseanberepeatedsothatawhole seriesofcuvettescan
be used without washing them until you have used the last
absorbance matching cuvette. An alternative method is to record
the absorbance if it is not zero and label the cuvette so that you
may subtract off that 'zero" absorbance form any readings tam
with that cuvette.

Remove the RO water from the cuvette and place your blank in the
rear cuvette holder. Turn the dial to blank and press CAL.

35

Place your sample in a cuvette and put the cuvette in the front
sample holder and close the lid.

Turn the dial to sample and record your absorbance reading. The
lid should be closed whenever cuvettes are not be added or
removed form the sample chamber.

D. Turbidity assay

1.

Place a 3 mL sample of fermentation broth in the sample cuvette
immediately after it is withdrawn from the bioreactor.

Insert into the spectrophotometer and read the OD (710 nm) versus
a sterile growth medium blank.

If the OD is greater than 1.0, dilute quantitatively with sterile
growth medium to bring the OD value below 1. When analyzing
the data, multiply the OD value by the dilution factor to put all
values on an equal basis.

Occasionally check the blank for signs of microbial growth
(cloudiness), and replace if necessary. Increases in the OD of the
blank may also be interpreted as growth but may merely be
recorded and accounted for while the absorbance reading is small.

E. YSI Autoanalyzer Setup (this may be necessary every two weeks)

1.

Set the RUN/STANDBY switch to STANDBY. Plug the
autoanalyzer into the wall socket. Only after you have plugged in
the autoanalyzer to the wall socket should the probe eable be
connected to the socket labeled probe.

Empty the supply bottle and rinse with R0 water. Prepare the
buffer by dissolving the buffer concentrate in the water according
to the directions on the package. Pour the buffer into the supply
bottle and screw on its cap.

Purge the sample chamber by pressing the CLEAR button and
holding it down until the buffer drains into the waste container.
If the pump does not begin pumping, the pump will have to be
primed. To prime the pump fill the bottle completely with buffer
and squeeze the bottle or use a buffer filled syringe to force fluid
into the pump.

Hold the clear button down for about another 30 seconds. Switch

36

from STANDBY mode to RUN, and press the clear button. Allow
the instrument to go through its clear cycle. When the
ZERO/INJECT light comes on, press the clear button. Check for
leaks and correct any that are found. Press the clear button twice
more and switch to standby. Remove the waste container, empty
it, rinse with water, and reinstall.

With the instrument in standby, unscrew the probe retainer from
the upper port and gently remove the Sensor Probe from the
temperature block, retrieving the O-ring from the block if it does
not come out with the probe. Remove the previous membrane,
being careful not to scratch the probe. Note that the membrane is
attached to the rubber o-ring and that a the new membrane will
also be attached to an o—ring.

Rinse the probe surface with distilled water and wipe clean with a
kimwipe removing any dirt or lint on the surface.

Remove the membrane foil pouch and snap open a eavity of the
plastic membrane holder. Place a drop of YSI 2392 NaCl solution
on the probe face. Using the plastic membrane holder, press the
O-ring membrane assembly onto the probe face with the membrane
side toward the probe surface. Return the plastic membrane holder
to the foil pouch and store as directed on the pouch label.

Inspect the probe and membrane assembly for hairs, dirts, bubbles,
wrinkling of the membrane and other signs of trouble. The O-ring
must fit snugly behind the guard at the tip. Replace the probe
back into the upper port on the temperature block being eareful in
seating the probe.

F. Ethanol Assay using the YSI Autoanalyzer

1.

Plush the sample chamber with buffer until no more air bubbles
ean be seen by holding down the clear button continuously and
switching between STANDBY and RUN every five seconds or so.

Allow the instrument to warm up until the small red light in the
sample chamber lights up.

Whenever the instrument is not being operated switch the unit to
standby. This keeps the pump running and prevents the membrane
from drying out. The digital display should read three eights (888)
in the standby mode but a minus sign or a one may lead the eights.
Any other meter reading indicates a loose connection or a defective

37
meter and all connections should be checked.

4. While in standby make sure that the sample chamber contains no
air bubbles and press the clear button. Switch to RUN and press
CLEAR and release.

5. The syringepet should be filled by depressing the plunger button
at the top and inserting the needle into the solution to be measured.
Slowly release the plunger earefully avoiding drawing up air
bubbles. Rinse the syringepet in R0 water by filling and emptying
it three times, then rinse the syringe three times with 300 mg/ml
(.3 % w/v) ethanol solution. If the 5 pl syringepet is not available
for use on the ethanol assay a hamilton syringe will work well if
air bubbles are avoided. If a hamilton syringe is used make sure
that you activate the read function by gently pressing on the
injection port until the display reads wait.

6. Fill the syringepet with 300 mg/dl (0.3 % w/v) standard and when
the ZERO/ INJECT light comes on turn the knob so that the
display reads zero and then inject the sample. The syringepet
should be inserted into the injection port through the rubber
septum and the plunger should be pressed firmly and evenly. Pull
the syringepet out the port keeping the plunger depressed to avoid
drawing out the sample.

7. When the READ light appears press the calibrate button and turn
the CAL knob until the display reads 300.

8. Press the clear button. Five seconds after the ZERO/INJECT light
comes on the reading should be between -1 and +3. If it is not,
press clear again and then adjust the zero after the second clear
cycle. Repeat the calibrations until they are stable within +/- 2.

9. Check the calibration by injecting 5 pl of water. The reading
should be between -2 and +5.

10. Check the linearity of the instrument by injecting 100 mg/dl (0.1
96 w/v) and 50 mg/dl (0.05 % w/v).

11. Once the calibration procedures have been earried out, all that is
required is the injection of the sample into the instrument.

G. Operation of the spectrophotometer

38

Turn on the spectrophotometer, and allow it to warm up for .15
min.

Set the desired wavelength by entering wavelength (in run) on the
key pad and pressing the Go To key 660 nm.

Fill both cuvettes with the blank solution (e.g. , sterile growth
medium in the case of the turbidity cell mass assay). Insert the
cuvettes into the spectrophotometer and close the cover. Handle
the cuvettes only by the frosted glass sides. The clear glass
windows must remain clean and dry; if they are not wipe them
with a kimwipe.

Zero the instrument by pressing the Zero key.

One of the cuvettes is the ”sample" cuvette (the closest one), and
the other is the ”blank“. Empty the sample cuvette, taking eare
not to get any liquid 0n the outside of the clear glass windows.
Rinse it with distilled water, and gently touch the mouth of the
inverted cuvette to a paper towel to siphon off any remaining
water. You may check to find cuvettes with identieal absorbances
as above.

Transfer the sample into the sample cuvette. Insert it into the
spectrophotometer and close the cover. Record the OD.

To analyze another sample, repeat steps 5 and 6.

H. Glucose Assays Using the Sigma Diagnostic Reagent Kit

1.

2.

Prepare the glucose trinder reagent according to the instructions.

Set the spectrophotometer to 505 nm and the absorbance to zero
with respect to a water blank.

Set up a series of test tubes labeled for reagent, blank, standard,
controls and experiment samples.

Pipet 3.0 ml of Glucose trinder reagent in to each tube and warm
to assay temperature.

At timed intervals, add lOuL (0.01 ml) of reverse osmosis water,
standard, controls, and experimental samples to the appropriately
labeled test tubes.

10.

11.

12.

39

Incubate each tube for exactly 18 minutes at ambient temperature.
If the assay temperature is 30°C or 37°C, incubate for 15 and 10

minutes respectively.

Read and record the absorbance of all tubes at 505 nm using the
same timed intervals from step 5.

Subtract the absorbance of the blank from the absorbance of the
experimental sample, standard, and controls to obtain the change
in absorbance due to glucose.

The calculation of the glucose concentration can use the following
equation:

(5)

 

A -A
W“ a“ xConcentration of Standard
Ame ' blank
If the results indieate concentration greater than 750 mg/dl, dilute

1 part sample with 1 part RO water and re-assay, multiplying the
results by two.

An alternate method involves running a series of known glucose
concentrations and recording their absorbances. The absorbances
for the known solutions are then linearized and used to determine
the concentration of the unknown samples. Both methods ean be
utilized. Use a sterile pipette when removing amounts of the
glucose standard solution.

Compare the results of the two methods.

I. Alternate Glucose Assay using the YSI Autoanalyzer

1.

Replace the ethanol membrane with a glucose membrane using the
procedures outlined in the YSI Autoanalyzer Setup Procedure
above.

Use a sample volume of 25 “L and the 25 ul syringepet.

Calibrate the analyzer with the glucose standard solution supplied
and check the linearity by diluting a small volume of the standard
as outlined in the ethanol procedure above. Sigma glucose
standards my also be used if they are available.

J. Dry-weight assay

1.

Withdraw an accurately measured sample (e.g. , 25.0 mL) of

10.

40
fermentation broth and place on ice in a 30 mL centrifuge tube.

Centrifuge at 8000 rpm for 10 min in the refrigerated centrifuge.

Remove the supernatant from above the cell pellet with a pipette.
Save a sample for glucose and ethanol assays.

Re-suspend the cell pellet in approximately 20 mL of deionized
water and centrifuge again, as before.

Repeat the deionized water wash (steps 3 and 4).
Weigh an aluminum weighing pan on the analytical balance.

Quantitatively rinse the cells into the weighing pan using a small
amount of deionized water.

Dry the sample overnight in a 105°C drying oven. The oven
should be set to about 3 with the vent slightly open.

Once dry, cool the pan in a desiccator to prevent water absorption
from the air.

Reweigh the pan on the analytical balance and calculate the mass
of dry cells by difference.

szymeKineties

Summary
The kinetics of the enzyme fumarase which eatalyzes the conversion of fumarate

to L-malate, were studied spectrophotometrieally at 300 nm using polymethacrylate UV
grade cuvettes and initial rate kinetic assays. The kinetic parameters, K. and V“, were
determined for fumarate, alone and in the presence of 22.4 mM citrate and 67 mM
phosphate, using Lineweaver-Burk and Hanes-Woolf plots. Neither linear analysis
technique produced superior fits to the experimental data in all of the eases studied.
Citrate was shown to be a wmpetitive inhibitor, which agreed with the literature and

phosphate demonstrated mixed-inhibitor behavior contrary to the literature.

Introduction

A catalyst is a substance that increases the rate of a chemieal reaction but is not
consumed in the process. Catalysts increase the rate of reaction by lowering the
activation energy without shifting the equilibrium of the reaction. Enzymes are eatalysts
that are produced by living systems to minimize the energy requirements for the reaction
of a substrate. A substrate is a reactant for the reaction eatalyzed by the enzyme.
Enzymes often have the ability to distinguish between very similar substrates and produce
highly specific products. Beeause of these properties, enzymes are useful in the
production of pharmaceutieals and other high-purity products such as a specific

stereoisomer of a compound. To design and optimize a reactor that utilizes an enzymes

41

42
as its catalyst, the enzyme’s kinetics must be known. An enzyme’s kinetics ean be

determined by measure the reaction rate as a function of the substrate concentration.
These data are modeled using a the appropriate rate form, which for most enzymes is the

Michaelis-Menten equation.

Background

Michaelis and Menten were pioneers in the field of enzyme kinetic studies who
classified enzyme behavior into two regimes: low and high substrate concentration.
Enzymes demonstrated first order behavior with respect to substrate concentration at low
substrate concentrations and zero order behavior at high substrate concentrations.
Michaelis and Menten developed a two-parameter model that emulated enzyme behavior
in both regimes. The two parameters, designated K. and V“, have physieal signifieance
related to the enzyme activity. The Michaelis constant, K_, which is also known as the
half-saturation coefficient, corresponds to the substrate concentration that produces one
half of the maximum reaction rate (Bailey and Ollis, 1986). The affinity of the substrate
for the enzyme is also represented by the value of its K_. The smaller the value of K_,
the higher the affinity of the enzyme for the substrate and vice versa. The maximum
reaction rate, V“, represents the maximum possible reaction rate that would occur at
an infinitely high substrate concentration for a specific amount of enzyme. Graphieal and
numerical techniques based on the saturation-kinetics model proposed by Michaelis and
Menten ean be used to evaluate K. and V“, from experimental reaction-rate data.

Reaction-velocity assays must be earried out to obtain reaction rate data to fit to

43

the kinetic model. An assay is an experiment to determine the concentration of a
chemical species. Reaction-velocity or enzyme-activity assays measure the rate of change
of the concentration of a species. An assay may be direct or indirect. A direct
spectrophotometric assay measures the concentration of a light-absorbing product or
reactant of the enzymatic reaction of interest. An indirect assay is required when the
reaction of interest does not contain a light absorbing compound called a chromophore.
The reacu’on of interest is chemieally coupled to a second reaction that involves a
chromophore. The rate of the first reaction can be followed indirectly by observing the
rate of appearance or disappearance of the chromophore. The reaction of interest must
be the rate-limiting step for the series of coupled reactions carried out for the indirect
assay technique to be valid. The electron earrier NAD‘INADH is commonly used to
couple reactions, since both the reduced and oxidized forms of NAD are chromophores
at different wavelengths. Both forms of NAD are usually compatible with enzymes since
they are often used as electron acceptors/donors within living organisms.

The enzyme fumarase catalyzes a reaction whose la'netics can be determined by
a direct assay. Fumarase catalyzes the hydration of fumarate to L-malate in the Citric
Acid Cycle. Fumarate’s double bond absorbs light in the ultraviolet spectrum at 300 nm.
A direct spectrophotometric assay can be used to monitor the concentration of fumarate
because on the absorbance of the solution at 300 nm decreases as its double bond is
hydrated to form L-malate. The fumarase reaction is very stereospecific; only a trans
configuration of fumarate will react with the enzyme to yield L-malate as the sole

product as shown in Figure 1 below (Dixon, 1979).

H COOH H H0 C0011
\ I I \ I
CH = CH + 0 fl CH - CH
I \ \ I \
HOOC H H HOOC H
fumarate 3,0 L-ntalate

Figure 1. Reaction Catalyzed by the Enzyme Fumarase
Fumarase is classified as a lyase because it removes water from fumarate by simple
extraction rather than by hydrolysis or oxidation.
Acids such as glycine, malate, citrate, adipate, trans-aconitate, glutarate,
succinate, and malonate can act as inhibitors of fumarase. An inhibitor is a substance

that interacts with the enzyme and reduces the rate of reaction.

Theoretical Analysis
The Lambert-Beer law relates the absorbance of fumarate to the concentration by

the following equation:

A = log(%) = abc (I)

where A = absorbance
I. = intensity of the incident light
I - intensity of the transmitted light
a = molar extinction coefficient
b = length of the light path
c = concentration in moles

The molar extinction coefficient, a measure of how strongly the chromophore absorbs
light, is a constant that depends on the wavelength of the light. The equation shows that

the absorbance is directly proportional to the concentration of the chromophore in the

45
solution. Application of the spectrophotometric method requires the use of a blank. A

blank is identical to the unknown solution except for the compound whose concentration
is to be measured. The blank’s absorbance is due to all the other species in solution and
is therefore subtracted from the absorbance of the unknown solution. Thus, only the
absorbance of the compound of interest is measured (Robyt and White, 1986).

Initial velocities for the enzymatic reactions are determined using a dynamic

version of the Lambert-Beer law given by the following equation:

 

= (_A£)_ = (M) = (MXC’IW‘ speed) (2)
At (A t)(a)(b) (distance)(a)(b)
where v -- reaction velocity
t = time elapsed

a = molar extinction coefficient

b = length of the light path (cuvette width)

c = concentration in moles

A = absorbance
The molar extinction coefficient is either determined experimentally using known
standards or obtained from the literature. The length of the light path is 1 cm for most
cuvettes. The enzyme is mixed with the substrate solution in the cuvette, and the cuvette
is placed in the spectrophotometer. As the reaction proceeds, the concentration of the
chromophore changes, causing the absorbance of the solution to increase or decrease.
The absorbance can be recorded as a function of time on chart paper or by computerized
data acquisition. The reaction rate can then be determined from the slope of the
absorbance-versus-time curve using the Lambert-Beer law. The initial slope of the

absorbance curve is used to determine the reaction rate characteristic of the initial

46
substrate concentration. When the slope is determined by a graphical procedure from

chart-recorder data, the chart speed is chosen such that the slope of the absorbance-
versus-time curve is between 30 and 60° from the x axis on the chart paper.
Alternatively, for computerized data acquisition, numerical differentiation can be used
to determine the reaction rate. Once reaction velocities are determined, they can be fit
to the Michaelis-Menten model.

The Michaelis-Menten equation for an enzyme catalyzed reaction of S -. P is as

follows:
v = E 2 —§ = g
K. + S d: d: (3)
where v = velocity of the reaction

V... = maximum reaction velocity

K. = half saturation or Michaelis constant

S = substrate concentration

P = product concentration

t = time
The Michaelis-Menten equation and its various forms were derived from elementary-step
mechanisms and rearranged into simplified forms that combined the rate constants of the
elementary steps. The Michaelis-Menten equation can be rearranged into several linear
forms whose slopes and intercepts are composed of the kinetic constants of the enzyme.
The constants can then be evaluated by using graphical or analytical line fitting
techniques. Two common linearized forms of the Michaelis-Menten equation are the
Lineweaver-Burk and the Hanes-Woolf plots (Segel, 1986; Robyt and White, 1986).

The Lineweaver-Burk equation is obtained by inverting both sides of the

Michaelis-Menten equation and algebraically rearranging it into the form of a line. The

47

Lineweaver-Burk equation is given below:

K. 1 + r (4)
Vans [S] VIII:

The slope and intercept of a plot of UV versus l/[S] are used to determine the K. and

 

l:
v

V... The Hanes-Woolf equation is obtained by diving both sides of the Michaelis-
Menten equation by [8] before inverting and rearranging it into linear form. The Hanes-

Woolf equation is:

 

m = .._1_. + K. (s)
v Yum] V"

The parameters for the Hanes-Woolf equation, determined from a plot of [S]lv versus
[S], are slightly different from those determined from the Lineweaver-Burk plot.

The effects of enzyme inhibition can be modeled if more parameters are added
to the Michaelis-Menten equations. The Michaelis-Menten equation for modeling
inhibition replaces V... and K. with the apparent maximum velocity, V“, and the
apparent Michaelis constant, K..." These apparent kinetic constants are functions of the
inhibition constant, K,; the inhibitor concentration, [I]; and the mechanism of inhibition.
If the presence of the inhibitor makes K... larger than K. for the substrate alone, the
enzyme is competitively inhibited by that compound. The larger K... is, the lower the
affinity of the enzyme for the substrate in the presence of the inhibitor. If the inhibitor
makes Vm less than V... then the enzyme is noncompetitively inhibited. A mixed
inhibitor makes both K... and V..." smaller than K. and V... respectively but not

necessarily by the same amount. An uncompetitive inhibitor decreases K..." and V...”

48

by the same amount and is a special case of mixed inhibition. The forms of
WV...” and 1N..." are given in Table l in terms of K.; V.,.; the inhibitor
concentration, [I]; and a, a factor of the decrease in V“ relative to K...

Table 1. Values of K..,/V.,.., and 1N..." for Different Types of Enzyme

 

 

Inhibition
Type of Inhibition K..,/V..m l/Vm
Competitive (l + [I]/K,)K./V.Ill llV.Ill
Uncompetitive K./V.. (1 + [I]/K9N..
Mixed (l + [l]/K,)K./V.. (l + [I]/(aK.))/V..
Noncompetitive (l + [I]/K,)K./V.III (1 + [I]/K1)/V..

 

The mechanism of inhibition can often be determined from the Lineweaver-Burk and
Hanes-Woolf plots. Bailey and Ollis (page 128) illustrate how the various types of

inhibition appear on the Lineweaver-Burk and Hanes-Woolf plots.

Experimental Equipment and Procedure

A Perkin Elmer lambda 3A spectrophotometer and R100A chart recorder were
used to determine the molar extinction coefficient of fumarate and measure initial
reaction velocities. The absorbance of the fumarate was determined at 300 nm using
polymethacrylate UV-grade cuvettes. The molar extinction coefficient was determined
using the same fumarate concentrations used in the kinetics study. Reaction velocities
were determined from the slope of the absorbance-versus-time data that were recorded

by the chart recorder. The slope of the initial linear region of the absorbance-versus-time

49
curve was estimated graphically using a ruler and a clear straight edge. The reaction

velocity was calculated by multiplying the slope by the molar extinction coefficient and
the length of the light path. The chart-recorder speed was adjusted to keep the slope of
the line between 30° and 60° from the x axis to minimize the error of the graphical slope
determination. The absorbance of the blank was used to zero the chart recorder. The
absorbance scale of the chart paper was set by marking the absorbance of the fumarate
solution without enzyme present at the corresponding position on the chart paper. A
small volume of enzyme was transferred from a refrigerated stock solution to a small test
tube to avoid the risk of contamination or denaturation of the stock. The enzyme was
kept on ice to avoid denaturation after removal from the stock solution. A Labsystems
Finnpipette (Helsinki, Finland) 5-40rrL repeat pipettor delivered reproducible 10 uL
aliquots of the enzyme from the tube to the cuvettes. After addition of the enzyme, the
cuvette was quickly capped with clean plastic film and rapidly inverted 3 to 4 times.
This mixing protocol minimized bubble formation which could denature the enzyme and
interfere with the absorbance measurements. Once mixed, the cuvette was immediately
placed in the spectrophotometer, and the absorbance was recorded on the chart paper as
a function of time.

The standard assay solution contained 2 ml of fumarate solution adjusted to pH
7.0 with 0.1 N NaOH and 1 ml reverse osmosis (RO) water. The fumarate
concentrations used for the velocity assays and the determination of the molar extinction
coefficient were 0.498, 0.622, 1.246, 2.492, 2.865, 4.983, 7.475, 9.967, 12.458 mM.

The concentrations stated for the assays are given in terms of the actual concentration in

50

the cuvette, not the concentration of the solution added to the assay. The concentrations
of the stock solutions for each of the assay ingredients were higher than the stated cuvette
concentrations to adjust for the dilution upon combination of the solutions in the cuvette.
The activity of the fumarase was also measured in the presence of 22.4 mM citrate and
66.4 mM phosphate, both of which were adjusted to pH 7 with 0.1N NaOH. The
inhibition experiments substituted 0.5 mL of the citrate or phosphate solutions for 0.5 mL
of RO water present in the standard solution. The fumarase used for this experiment was
Sigma Chemical (St. Louis, MO) extracted from porcine heart tissue. The 10 pL
aliquots of enzyme correspond to 2.4 x 10‘ activity units of fumarase. One activity unit
is defined as the amount of enzyme that will convert one umole of L-malate to one
pmole of fumarate per minute at 25°C and a pH of 7.5. This activity is for the reverse
of the reaction studied but should make substitution of fumarase from another source

simple.

Experimental Results and Discussion

The molar extinction coefficient for fumarate was determined to be 0.0363
absorbance units/cm mM by linear regression of the data shown in Figure 2. The kinetic
data were analyzed using both the Lineweaver-Burk and Hanes-Woolf plotting techniques
(Boyer, 1986). The kinetic constants were determined using linear-regression analysis
for both types of plots. The Lineweaver-Burk plot of the experimental data is shown in
Figure 3. The types of inhibition present are not clearly discemable from analysis of

Figure 3. Figure 4 shows the Hanes-Woolf plot of the experimental data. The lines with

51

3

N..

0.0 000 .0 8000080< 30.5000 00.. 0200 00080.30 .0 800mm

2:. 00200000000 0.0.00.0.
0F 0 .. 0 v N

 

 

— - _ _ _

 

0000.0 . 00.0000 0
0000.0 -\+ 0000.0 . 000.0...000 00:00.30 00.00. .. 0

 

 

0.0

0.0

6000506600)

52

05.80 002.0 .6 8005:0900 .e .20 30.9832: .0 200.0

.005: 00000000000 0.0.00.3:

0N N

06 .-

_. . 0.0

 

 

 

OO

0.0000000 20.. 0.00
0.02.0 20. 0.0.0
09.0.00. 00

E
O
o

 

 

000.0
000.0
000.0
000.0
5.0

0 F 0.0
30.0

90.0

—c E—0\:I.Eo—

P\t—XC >O—OO—H>~.

53
and without citrate are nearly parallel, suggesting competitive inhibition by citrate, which
agrees with Massey’s findings (Massey, 1952). The lines for the phosphate and the
fumarate intersected above the x-axis on the Lineweaver-Burk plot, which suggests
behavior resembling mixed inhibition. Figure 5 shows the reaction velocities calculated
by the two models and experimental data plotted versus the fumarate concentration. The
K., V... and the r2 values calculated by linear regression for both plots are given in
Table 2 below:
Table 2. Kinetic Constants for Fumarase Determined by Different Plotting

Techniques
—

 

Plot Technique K. V.III 11 value
Lineweaver-Burk 1.336 1271 0.9498

Hanes-Woolf 1.219 1236 0.9481

 

The r2 values suggest that the Lineweaver-Burk plot constants may fit the data
slightly better than the Hanes-Woolf constants. The plot of v versus [S] shown in Figure
6 demonstrates that the constants derived from the Hanes-Woolf plot model the
competitive-inhibition data for 22.4 mM citrate better than those from the Lineweaver-
Burk analysis. Bock and Alberty obtained a K. value of 1.37 d; 0.14 mM for fumarate
using a Lineweaver-Burk plot (Bock and Alberty, 1971). This value is within the
experimental error of the present study. The values of K.,", V“, K, and the r2
values for citrate are given below in Table 3 for both the linear plots.

The value for Kl determined by Massey for citrate at pH 6.35 and 23°C was 3.5 mM.

54

3

3:80:00 0095— 00 0000005900 000 .03 283.85: .0 800.0

3.0.. 00000000000 0.0.00.2 . .
NF 0.. . 0 0 0 N

 

 

— u a . _ _ —

 

0.0000000 20. 0.00 E
0.00.0 3.0. 0.00 0
02.0.00. 00 o

 

 

N000

000.0

000.0

000.0

..0.0

N_.0.0

0:00

0.0.0

0.350000%!) 0000\0x: >0-oo—~>~ E} E—C\=E°—

55

3

80.3050 000 0000080000 0.0.0300 33> 0500—00, 0000000 .n 8030

20.. 00202000000 0.0000030

 

 

 

 

NF 00 0 0 0 N 0
_ _ _ . _ _ _ O
.0.
0 0
0.1 00m _
. . E
0 . 0
w 1 00v 1
0...

>
0:. :0030000: 000 000: 000000 0x I 000 .
0:. 250-09.020.00... 0.0 000: 00:00 0 .00.. “.0
\w... .. 000 M
...........s.\ \x O . >

o o Q £ \s‘s\‘1©5§ o 1 OOO —.
.. .. I t .. I.....\\I ....... C
..n..uu..nu..n0s.. ..................... O . O
o - 003 ._
o o o
0
0 - 00: w

000—

56

.0820 80000 20. Yam 5? 2000050 .00 0000508000 30.0300 000.03 £00.05 000800 .0 8005

3:: 00203000000 0.000003.

 

 

bowou—oc >0—oo—~> 1§\E—0

E N— 00 0 0 v N 0
_ a _ _ _ _ . x. O
a... 4 000
. x...
0:. 0.0030000: 000 000: 000000 \ m 4 000
2: ..v_0:m-.0>00300_.. 0.0 000: 00:00 \.....©
w - 000
O \\\\\
..\Q. 00
o xxx-.0 o - m
0-
1 COO—-
.- CON—-
00v—

 

 

S7

3

.0805 0.0000000 2.0 0.00 5.3 0.0.0.000 00.. 0000-0000000 0.2.300 00000.» b.00_o> 0000000 .0 0.0.0.0

3:0 00:0..000000 0.0.0.00.
N0 00 m -. 0 v

 

 

_ _ q _ .

I

0.: 2003:0000: 0.0 000: 000000

0.: 0.000-033.0003 0.0 000: 00:00 0....

. m
. .\.
\

a
go-
to
00

 

 

000

000 ..

0000

000w

hoGOH—oc >o—oo—~> :Eo-\E—c

58 . .
Table 3. Inhibition Constants for the effect of Citrate on Fumarase Acuvrty

 

Plot Technique K.,," V” K, r2 value
Lineweaver-Burk 15 .03 2768 2. 187 0.95 86
Planes-Woolf 6.030 1345 5.678 0.9460

 

Experimental error and pH differences may account for the between the literature and
the present study. One of the experimentally determined values for K, is slightly larger,
and the other is slightly smaller than the literature value, indicating that the determination
was reasonably accurate. Figure 7 shows the experimental and model reaction velocities
for phosphate in which neither plotting technique produces a clearly superior fit to the
data. Table 4 shows the kinetic constants derived from the experiment with phosphate.
The phosphate causes behavior resembling mixed inhibition by increasing the K.,, but
it also signifieantly increases the V“ of the system. Massey’s data for the effect of

phosphate on fumarase show a different trend: K. was unaffected by phosphate but

<

M was increased (Massey, 1952). Massey also indieated that high phosphate
concentrations decreased the enzyme activity due to high solution ionic strength.

Table 4. Inhibition Constants for the effect of Phosphate on Fumarase Activity

 

 

Plot Technique K.,,” Vm KI a 1’2 value
Lineweaver-Burk 5.877 2591 17.38 3.488 0.968
Hanes-Woolf 6.637 2796 14.95 3.523 0.931

 

Figures 2 through 7 illustrate the scatter in the reaction-velocity data, which is

59
attributed primarily to the error involved in the determination of the slope of the

absorbance-versus-time data. Several previous experiments also demonstrated the need
for uniform delivery of the correct volume of enzyme to reduce data scatter.
Experimental error affects the two types of plots in different ways. The reaction
velocity assay exhibits the greatest error at low substrate concentrations. The data at low
substrate concentrations are the most heavily weighted by the Lineweaver-Burk analysis
since the technique uses the reciprocal of the substrate concentration. Figure 3
demonstrates that the points that correspond to higher fumarate concentrations are located
near zero and that the lower concentrations are located much farther from zero. Thus,
the slope determination, and hence the K. value is most strongly affected by the data
with greatest amount of experimental error. In contrast, Figure 4 shows that all of the
substrate concentrations are given equal weight by the Hanes Woolf Plot due to their
even spacing. The error of the Planes-Woolf analysis is greatest when the reaction
velocity is small because the uncertainty in the measurement of the velocity becomes
signifieantly large. This occurs at low substrate concentrations and has a stronger effect

when inhibition is studied.

Conclusions and Recommendations

The enzyme fumarase has been shown to follow Michaelis-Menten kinetics.
Citrate has been shown to be a competitive inhibitor of fumarase, and phosphate appears
to be a mixed inhibitor. The Hanes-Woolf technique presented a clearly superior fit to

the Lineweaver-Burk plot in only one case. The Lineweaver-Burk plots produced

60
slightly better linear fits to the data, but both plots yield kinetic constants that fit the data

well. The delivery of the correct amount of enzyme and the solution pH is crucial for
good experimental results.

It is recommended that the computer-controlled and monitored spectrophotometer
be used to earry out this experiment for the teaching laboratory. The computer-
controlled spectrophotometer possesses software which is designed specifieally for kinetic
assays and uses linear-regression techniques to obtain reaction velocities. It is also
recommended that a repeat pipettor be used for the crucial step of addition of enzyme to
the cuvette because of its speed and reproducibility.

Many further optional studies for this experiment are available. Several
documented inhibitors exist for inhibition studies. The reaction could also be studied in
the reverse direction by starting with L-malate and monitoring the reaction with and

without the presence of the inhibitors.

Symbok

a, a’ = constants that are functions of the type of inhibition
A = absorbance

a = molar extinction coefficient

b = length of the light path (cuvette width)

c = concentration in moles

I = intensity of the transmitted light

1. == intensity of the incident light

K; = inhibition constant

K. = half saturation or Michaelis constant

K.,." = apparent Michaelis constant

P = product concentration

3 = substrate concentration

I = time

V = reaction velocity

v-ax maximum reaction velocity

Van... = apparent maximum reaction velocity

61

[I] = inhibitor concentration

References
Bailey, LE. and Ollis, D.F.( 1986) Biochemical Engineering Mdamentals, pp. 100-130,
McGraw-I-Iill Book Co. , New York.

Bock, Robert M., and Robert A. Alberty, “Studies of the Enzyme Fumarase. 1. Kinetics
and Equilibrium”, J. Amer. Chem. Soc., 75, p. 1971, 1953.

Boyer, Rodney F.(1986) Modern Experimental Biochemistry,pp. 277-278, Addison
Wesley Pub. Co. , New York.

Dixon, Malcolm, Enzymes, 3rd ed., Aeademic Press, New York, NY, 1979, pp. 229,
264-265, 316318.396.

Massey, V., “Studies on Fumarase 2. The Effects of Inorganic Anions of Fumarase
Activity", Biochern. J., 53, p.67, 1952.

Massey, V., ”Studies on Fumarase 3. The Effects of Temperature", Biochern. 1., 53,
p.72, 1953.

Massey, V., "Studies on Fumarase 4. The Effects of Inhibitors on Fumarase Activity',
Biochem. J., 55, p.72, 1953.

Robyt, LP. and White, 3.1., Biochemistry Techniques Theory and Practice, Brooks/Cole
Pub. Co., Prospect Heights, 11., pp. 44.5, 1986.

Segel, I.H., Biochemical Calculations, 2nd ed., J. Wiley & Sons, Inc., New York, pp.
290-291, 1976.

62

Appendix

fumarate fumarase

L-malate citric acid
spectrophotometer and recorder polymethacrylate cuvettes
pH ealibration solutions pH meter

Na or K phosphate volumetric flasks

gloves parafilm
pipettes (SuL, lOuL, 20 uL, 2 mL, and 5 mL)

Experimental Procedure
I. Preparation of Stock Fumarate Solutions

1. Weigh out sufficient fumaric acid for 500 ml of 18.75 mM solution of fumaric
acid.

2. Adjust the pH of the fumaric acid using a dilute NaOH solution to 7.0.

3. Dilute the stock fumarate solution into more solutions following table 5 below
checking and adjusting the pH if necessary.

Table 5. Dilution Schedule for the Fumarate Solutions

Conc Conc in made added added runs
(mM) solution available

 

II. Determination of the Standard Curve
1. Remove any cuvettes from the sample and reference beams.

2. Turn on the spectrophotometer’s UV bulb using the UV ON switch on the front
lower right of the spectrophotometer.

10.

ll.

12.

13.

63

Turn on the power switch loeated on the back of the unit and allow 30 minutes
for the spectrophotometer to warm up.

Turn on the computer and type 'PECSS'.

Once the computer screen states ”ready for next command“, press Shift-F10 and
use the arrow keys to move the cursor to 'PARAM". After ORD type A for
absorbance, after speed type 120, after Autosave type Y, and after Autoprint type
Y unless the printer is not connected in which ease type N and hit enter.

Hit Shifi-FlO again and this time move to autozero. Always hold cuvettes by the
frosted sides and wipe the clear sides with a kimwipe before inserting them into
the spectrophotometer to obtain a reading.

Insert the cuvette containing the blank solution (RO water for the ealibration
curve) in the reference (rear) position and place a cuvette containing the blank
solution in the front position.

Under autozero type A after "mode" for absorbance and 300 after 'wave" for the
wavelength which is 300 am. When the cuvettes are in spectrophotometer and
the lid is closed type Y to begin the autozero procedure.

Press Shifi-FIO again and move to the CALIB menu. After “method" type
fumarate and after 'nwave' type 1. After “curve” type 1 this chooses a linear
calibration curve that passes through the origin.

. After “wavelength w1_' appears type 300 for 300 nm.

When the screen displays "Change or save the instrument parameters (Y IN)?“
type N-

Place the unknown in the front sample holder and record the spectrophotometer
reading and the concentration of the stock solution as well as the concentration
of the fumarate in the cuvette. The unknowns should contain 2 ml of each of the
stock solutions from table 1 and 1 ml of water. Mix the contents of the cuvette
by placing a clean piece of parafilm over the end of the cuvette and gently
inverting it several times. Practice mixing quickly producing as few bubbles in
the solution as possible.

When prompted ”Ready (YIN)? enter a sample id of CalOl and the concentration
of the sample in the cuvette after it is displayed. The next sample should
automatically call itself CAL02 so all you will need to do is type Y under ”Ready
(Y IN)?” and change the concentration under "conc'. When all the standards have

14.

15.

64
been recorded type N after ”Ready (Y/N)?".

The computer will then ealculate a ealibration curve and display it on the
screen.The slope is the molar extinction coefficient and is in the 2 nd column
after 'calib prms:" at the top of the screen. Record the slope and the residual
error ('resid errz').

Use the data to plot the concentration on the y-axis and plot the absorbance data
on the x-axis. Find the slope of the data using either a graphical technique or a
least squares fitting (preferred). The slope determined is the molar extinction of
the fumarate at 300 nm as defined by the Beer-Lambert Law.

III. Determination of K. and VIII, for Fumarate

1.

Make sure that the spectrophotometer is on and PECSS is started and autosave
is on under PARAM as outlined in section III. Autozero the spectrophotometer
with the two cuvettes you will be using by pressing Shift-F10 and moving the
arrow to AZERO. Enter A , 300 and Y to begin.

Obtain an ice bucket and fill with ice. Obtain gloves for handling of the enzyme.
The enzyme poses no real health danger, but skin has many proteases and other
substances on it that could denature the enzyme.

With a clean, sterile pipette remove a small aliquot of enzyme solution from the
bottle in the refrigerator. Place the aliquot on ice immediately and make sure the
main vial of enzyme is sealed tightly and replaced in the refrigerator.

Using all the solutions in listed in table I prepare solutions containing 2 ml of the
given fumarate solution and 1 ml of water in the sample cuvette. Cut out squares
of parafilm to serve as caps for the cuvettes during mixing of the cuvettes.

Press Shift-F10 and move the arrows to TDRIVE. Under "reg" type x, after
”wave” type 300, under "NoPts' type 1000, and after 'int" type 0.5 to have a
time interval of 0.5 seconds between the recording of each slope and press enter.

Use the arrows to move past 'ymin" and "ymax". Under sample ID enter
something that corresponds to the sample since each sample must have a different
sample id. A sample id of '15r1ak' could be used to indicate the 1 st run of the
15 mM fumarate by someone whose initials are A.I(. Remain on this screen and
move to the ”Ready (YIN)" put Y on the screen but do not press enter until the
cuvette is placed in the spectrophotometer.

Rinse the pipet used for the enzyme thoroughly with water. Measure out 10 uL
of fumarase and quickly add it to the cuvette. Cap the cuvette with the parafilm

10.

ll.

12.

13.

65

square and mix by gently but quickly inverting the cuvette, taking care not
produce bubbles.

Immediately place the cuvette in the sample holder close the lid and press Y and
Enter under ”Ready (Y/N)‘ in TDRIVE. After a few minutes after the line
displayed on the screen is clearly no longer linear press Esc to stop the run.

Type N to leave the TDRIVE menu so you may determine the reaction velocity
using the VIEW and SLOPE commands.

Press F9 to use the VIEW command. Enter x under ”reg" and press enter unless
yo wish to change the defaults. Once you have looked at the graph attempt to
narrow down the linear region of the absorbance versus time curve. Press F9
again and enter the times during which the slope appears linear under “start" and
'end'. Continue focusing in until you are satisfied with the linearity of the slope.
Ignore the initial linear period that may last about 1 second or so. Look for the
initial linear period after that.

When you are satisfied that you have isolated the linear region record the start
and end times and press Shift-F3 to use the slope command. After 'reg" type x
and enter the start and end times you just determined under start and end and
enter 1 for the factor to receive the slope in Alsec or 60 to receive the absorbance
in Almin. and press enter.

The slope is given by the 'SL" , the residual error is given by ”RE“, and a
linearity factor is given by "LF', and F is the factor by which the slope was
multiplied( l for Alsec, 60 for A/min).

ReturntoTDRIVEenteranew filenameandrepeattheprocesswhenreadyto
quit type stop and hit enter which will exit the program.

IV. Determination of K, for Citric Acid for Fumarate

l.

2.

Prepare a stock solution of 42 mM Citrate buffer to pH 7.

Autozero the spectrOphotometer using a new blank consisting of 2.5 ml water and
0.5 ml citrate.

Run activity assays for all the solutions in table 1 with 2 ml of fumarate solution,
0.5 ml of citrate stock solution, and 0.5 ml RO water. Use the procedures
outlined above in section 111.

V. Determination of the Effect of Phosphate on Fumarase Activity

66
Prepare a stock solution of 400 mM phosphate buffer to pH 7.

Autozero the spectrophotometer using a new blank consisting of 2.5 ml water and
0.5 ml phosphate.

Run activity assays using 2 ml fumarate solution, 0.5 ml phosphate stock solution,
and 0.5 ml water use the procedures outlined in section III.

Fermentation Mass Transfer

Summary

Experiments were performed to determine the volumetric mass-transfer
coefficient, k.a, for oxygen in water in a 1 L fermentor. The concentration of oxygen
was monitored as a function of time using a polarographic dissolved-oxygen probe after
a step change was made in the gas-phase oxygen concentration. The dissolved-oxygen
data were analyzed using unsteady-state mass balances to determine the k,a. The
experiment will eventually be performed in a 100 gallon stainless-steel fermentor that is

currently under renovation.

Introduction
Fermentation can be loosely defined as the production of chemicals from a
substrate using microorganisms as catalysts for the reaction. Fermentation is used to
produce a variety of commercial products including alcohol and pharmaceutieals. Many
fennentations are carried out using aerobic microorganisms, which consume dissolved
Oxygen from the fermentation broth. Oxygen is transferred to the liquid phase by
Sparging air or pure oxygen through the fermentation broth. The ability to accurately
masure and predict the oxygen mass-transfer rate is critical in bioreactor design since

oxygen transfer is often rate-limiting in commercial fermentations (Roberts et a1. , 1992).

liihcheroin“!

67

68

Fermentation rates are often limited by the amount of dissolved oxygen available
to the cells growing in the fermentor. Oxygen mass transfer to the liquid phase is
inherently slow due to its low solubility (Bailey and Ollis, 1986). The solubility of
oxygen in water in equilibrium with air at ambient conditions is about 10 parts per
million (ppm), and a typical aerobic yeast population requires over 750 times that amount
(Atkinson, 1983).

The rate of oxygen transfer to the liquid increases with the rate of agitation.
Impeller shear induces bubble breakup, thus decreasing the bubble rise velocity and
increasing the residence time for the gas bubbles in the liquid. The increased residence
time allows more mass transfer to occur before the bubbles exit the liquid. The
reduction in bubble size also enlarges the interfacial area of the bubbles available for
mass transfer, which further increases the rate of mass transfer. Other important
variables that affect the rate of mass transfer include the gas flow rate, the geometry of
the mixing vessel, the physical properties of the fluid, the type of impeller used, and the
power input to the system from mixing and gas sparging. The geometry of the mixing
tank, power input and the impeller style are specified during the design of the system.
The tank geometry may be characterized by several geometric ratios known as ”shape
factors" (McCabe, Smith, and Harriot, 1985). Mixing vessels are often designed to
match typical ”shape factors" given in the literature for which correlations exist.

The type of impeller used for agitation strongly affects both the mass-transfer
coefficient and power requirements of a system. Impellers are usually classified as either

axial or radial flow. Axial-flow impellers displace the fluid downward along the axis of

69
rotation, and radial-flow impellers push the fluid outward in the radial direction. Radial-

flow impellers generate higher shear rates and better gas dispersion, but they are more
costly to operate since they consume more power than axial-flow impellers (Oldshue,
1990).

Traditionally, commercial fermentors have used radial-flow impellers because of
their excellent mass-transfer capabilities. The high operating cost of radial-flow
impellers has initiated the development of advanced axial-flow impellers that promote
mass transfer and yet require less power than radial-flow impellers. These new impellers
were developed using complex hydrodynamic modeling and laser-doppler anemometry

(Oldshue, 1990).

Theoretical Analysk
The aqueous solubility of oxygen is controlled by the partial pressure of oxygen,
the temperature and the presence of other solutes. Sparingly soluble gases such as

oxygen are often modeled by Henry’s law:

C =22 (1)

where liquid phase concentration

C, =
p,3 = the partial pressure of the gas
H = Henry’s law constant

The solubility of oxygen is strongly affected by the presence of other solutes in a

fermentation broth that affect bubble coalescence and breakup. The accuracy of mass

70
transfer studies is signifieantly increased by using a fluid with properties as similar to the
fermentation broth as possible.

An unsteady-state mass balance on oxygen in the liquid phase of a stirred tank is

given below:

new

 

= kp(co; -coz)v—(- 01w (2)

where k = mass-transfer coefficient (length/time)
a = specific interfacial area (area/liquid volume)
Cm° = liquid-phase oxygen concentration in equilibrium with the
gas composition (mass/volume)
C02 = liquid-phase oxygen concentration (mass/volume)
= time

V = liquid volume in the reactor

-rm = rate of oxygen consumption (mass/liquid volume time)
The volumetric mass-transfer rate is given by the product of a mass-transfer coefficient
and a concentration driving force. The rate of consumption of oxygen, 40,, is
represented by a kinetic expression in terms of oxygen concentration. If the rate of
oxygen consumption is approximately constant, a quasi-steady state assumption can be
made for the system. The change in the partial pressure of oxygen with time can be
assumed to be approximately zero, resulting in the following solution for kLa (Roberts

et al., 1992):

-r
k,a ~ ——.°’— (3)

oz ’ C02
This method of determining kLa is sometimes called the steady-state method.

The static gassing out method is used to determine the hp in this experiment.

71

The value of to, is equal to zero since no oxygen-consuming reaction takes place, and

the mass balance becomes:

dC
a; a
7.- W<> <4)

The method consists of allowing a saturation concentration, Cm' , to be achieved in the
liquid phase and then making a step change in the gas-phase concentration and hence the
oxygen saturation concentration, Cog. The liquid-phase oxygen concentration is then
monitored as a function of time using a dissolved-oxygen electrode. The dissolved-
oxygen data may be analyzed using the mass balance without a reaction term in either
its differential form or one of its integrated forms. The integrated form of the equation

appropriate while sparging the fermentor with air is given by (Atkinson, 1983):

Col
ln(l " —T) = "(kLaN (5)
C0.

The integrated form of the equation for sparging with nitrogen is:

C

 

M f’ > = -k,a: (6)
Com»
where Co“; = oxygen solubility in equilibrium with air

The mass-transfer coefficient, kLa, is a function of the tank and impeller
geometry, the agitation power input to the system, the rate and method of sparging, and
many factors pertaining to mass transfer such as the bubble size. The mass-transfer

coefficient is often correlated in terms of sparging rate and power input in the following

form:
B
IcLa = «(9 0;, (7)
where a, B, 7 = constants dependant on hydrodynamic properties and the
vessel geometry

1” V = agitator power per reactor volume
Q.,. = volumetric flowrate of air

The volumetric flowrate of air ean results in either of two air flow regimes: free-bubble-
rise, which occurs in large scale equipment; and high-turbulence, which occurs in small
scale laboratory fermentors. More data exist for the high turbulence regime than for the
free-bubblerise due to the large—scale equipment required and proprietary nature of
fermentor design (Atkinson, 1983). The agitator power is a function of agitator rpm for
a fermentor containing a Newtonian fluid. Hence, the kLa for a Newtonian fermentation
broth and a constant air flow rate can be correlated in terms of the impeller rate by the

following equation (Roberts et al. , 1992):

kLa = a’(N)" (8)

where a’,B’ = constants
N = impeller rate , revolutions per minute

Experimental Equipment and Procedure

The equipment used for this experiment included a l L New Brunswick MultiGen
(New Brunswick, NJ) fermentor, an Ingold model 170 percent 02 amplifier with a
polarographic electrode (Wilmington, MA), a nitrogen cylinder, and a Dow Camile data

acquisition and control system (Midland, MI). Figure 1 illustrates the experimental setup

73
of the equipment. The impellers used in the fermentor were two equally spaced, 6 cm

diameter, 6-b1aded, Rushton, radial-flow impellers. The tank was 4.5 inches in diameter
and contained two 0.5 inch wide baffles.

The 0, probe and amplifier were calibrated after the fermentor reached 30°C. Air
was sparged through the fermentor at 2 L/min, and the agitation was set at 1000 rpm.
The 02 amplifier had 4-20 mA outputs which were connected to the data-acquisition
system. The mA output of the amplifier was monitored using the data-acquisition system
until steady state was reached. Then the amplifier was ealibrated to 20.9 percent oxygen
in air by turning the screw on the front of the unit. The amplifier was calibrated for zero
percent 0, by sparging nitrogen into the fermentor until a steady value of zero was
reached. The data-acquisition system was then ealibrated with respect to the amplifier
to convert the mA signals to percent 0,. The fermentor was sparged with air and
nitrogen at 1000 rpm repeatedly to verify that the ealibration of the amplifier and data-
acquisition system was stable.

The kLa was determined at 400, 600, 800, and 1000 rpm for air and nitrogen
flowrates of 2 L/min. Experiments began by sparging with air until oxygen saturation
was achieved. Then the air flow was replaced by nitrogen flow at the same rate. The
decrease in the dissolved-oxygen (DO) concentration was monitored and recorded using
the data-acquisition system. After the DO concentration reached zero, the experiment
wasruninreverse by sparging withair. ThekLaforeachrunwasdeterminedusing the
appropriate form of the static-gassing-out equation. The slapes of the DO-concentration-

versus-time data used in the equations were determined using linear regression.

74

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Experimental Results and Discussion
Figure 2 shows four sets of D0 data at different impeller speeds for the
determination of lqa when sparging an air saturated fermentor with nitrogen. The slope,
and therefore kLa, increased substantially with the impeller rate. Figure 3 illustrates the
fit of the experimental data to Equation (9) above. The constants a’ and B’ were
determined to be 1.6 x 10" min" and 1.4 1: 0.1 for agitation rate in units of min'l (rpm).
The correlation coefficient of the least squares fit used to determine a’ and 3’ was 0.923.
Experimental data collection about every 3 seconds was found to provide
sufficient accuracy while avoiding excessively large data files that can cause retrieval and
storage problems. The linear portion of the DO curves was usually about 40 seconds
long, so recording data every three seconds allowed about 12 data points for the linear
regression. The scatter in the data in Figure 3 is due to slight differences in the slopes
determined for each run. The variation of the slopes between runs is due primarily to

the differences in the selections of the linear regions chosen for each run.

Conclusions and Recommendations

The static gassing out method is a relatively quick method for estimating the k.a
fol‘ a system. The k.a also is a function of impeller rate for Newtonian fluids at a constant
air flowrate. This experiment demonstrates the basic principles of oxygen mass transfer
in a stirred tank and the correlation between agitation rate and ha The experiment

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78
on a long-term basis. This experiment is relatively straightforward and produces high-

quality data that ean be analyzed using simple mass-balance equations. It is

recommended that the 100 gallon fermentor currently being renovated for the laboratory
be used for this experiment to observe the characteristics of mass transfer of a much
larger seale fermentor. Determinations of ha in fermentors of two different sizes would

allow scale-up calculations to be performed and broaden the scope of this experiment.

Symbols
a, B, a’, B’, 7 = constants dependant on hydrodynamic properties and the vessel a =

interfacial area of the bubbles

a = specific interfacial area (area/liquid volume)

Co, = liquid phase oxygen concentration (mass/volume)

Co,’ = liquid phase oxygen concentration in equilibrium with the gas composition
(mass/volume)

C, = liquid phase concentration

H = Henry’s law constant
kl, = liquid phase mass-transfer coefficient (length/time)

N = impeller rate , revolutions per minute

pa = thepartialpressureofthegas
+P/V = agitator power per reactor volume, unit power per unit volume

Qfi. = volumetric flowrate of air
-r02 = rate of oxygen consumption (mass/liquid volume time)

t = time
V = liquid volume in the reactor

References
Atln'nson, Bernard, Biochemical Engineering and Biotechnology Handbook,
Nature Press, New York, 1983, pp. 239 - 269.

Bailey, James E. and David S. Ollis, Biochemical Engineering Fundamentals, 2
n<1. ed., McGraw-Hill, New York, 1986, pp. 498-494.

Dickey, David S., and Ramesh R. Hemrajani, “Recipes for Fluid Mixing",
'cal Engineering, March 1992, pp. 82-89.

79

McCabe, Warren L., Smith, Julian C., and Peter Harriot, Unit Operations in
Glenlical Engineering, 4 th. ed., McGraw-Hill, New York, 1985, pp. 208—252.

Oldshue, J. Y., and N. R. Herbst, A Guide to Fluid Mixing, Mixing Equipment
Company, Rochester, N.Y., 1990, pp. 1-3,.

Roberts, Ronnie 8., James R. Kastner, Maqsood Ahmad, and D. William Tender,
”The Effect of Agitation on Oxygen Mass Transfer in a Fermentor" Uremical
Engineering Education, vol. 26 no. 3, 1992, pp. 142-145.

80

Appendix

Experimental Equipment
Materials traded:
dissolved-oxygen probe
Multigen fermentor

Camile data-acquisition system
nitrogen cylinder and regulator

Experimental Procedure

1. Operation of the Multigen fermentor

1.

2.

3.

Turn on the power with the switch on the far right.
Turn on the switches for the air, agitation, and heat.

Adjust the dial for the temperature to the desired temperature and turn the dial for
the agitation until the desired rpm reading appears on the gauge on the upper left.

11. Operation of the Camile System and Calibration of the Dissolved-oxygen probe

1.

Consult with the other groups using the Camile system so that it may be used by
all the groups. The immobilized bioeatalysts, and the power and mass transfer
experiments use the Camile system. The eapabilities of the system for multiple
users is limited so cooperation between lab groups is important.

If the camile system is not already started, start up the Camile system by turning
on the computer and typing 'cd\camile" to get to the Camile directory. Then
type “menu” and the Camile logo will appear. Press any key and the main menu
will be displayed. Use the arrow keys to highlight 'run" and hit ENTER. Then
use the arrow keys to highlight the database called "HEA'ITRAN' and hit
ENTER. The computer will then ask you if you wish to initialize the Camile
control constants. Type "y” and hit enter.

When the computer prompts for the default log directory "C:\eamile\logs" should
be present and highlighted. If not, backspace and type it in then hit enter. The
log file screen should now be on the monitor. Use the arrows to move to log file
6 and type the name you have chosen for your log file. Make sure that “BIN“
and ”APP“ appear in the fields to the right of the log file name.

Wait for the other groups to enter their filenarnes before pressing the END key.
When all the groups have entered their filenames press END. If you have
repeated any log file name currently on file, the computer will prompt you to

81
change it. The computer will then ask you to enter a title. This and the

comments it prompts for next are optional, but your names and a few brief words

describing your experiment might save considerable confusion later. Leave a
blank line to finish and hit ENTER.

The computer will then inform you that the printer does not respond and will ask
youifyouwishtoretry. TypeNifthereisnoprinter.

III. Calibration of the Dissolved-oxygen probe and the Camile system

1.

Press the F4 button and then PAGE UP or PAGE DOWN until you are on the
screen that has the tag name "oxygen”. Look in the lower right hand corner next
tothebargraph. Checktoseethatthe slopeisequalto 1 andthattheintercept
and filter constant are both equal to zero. If they are not you may reset these
values by typing 'SL 1","IN 0",”FL 0" to change the slope, intercept and filter
constant, respectively.

Turnon theairandopenthevalveon therotameteralltheway. Alsosetthe
agitation to 100 rpm. Record the flowrate of the air as given by the rotameter.
You may use the on-line trending (F3) to make sure that the dissolved-oxygen
probe is fully equilibrated before adjusting the meter.

Once the response from the meter becomes constant, turn the screw on the front
of the dissolved oxygen meter to adjust the reading to 20.9 which is the
percentage of oxygen in air. It is important the meter is calibrated for each
temperature data is collected at since oxygen solubility is a function of
temperature.

On the F4 screen of the Camile system labeled "oxygen“, calibrate the eamile
system for the 0 - 20 mA output of the dissolved oxygen meter into units of 96
oxygen. Once the DO meter has equilibrated at 20.9 type "CAL HI 20.9", which
records the amperage that corresponds to 20.9% oxygen.

Shut off the air and carefully open the regulator by slowly turning the bar to the
right. Use the regulator to adjust the pressure and flow with the rotameter valve
open. Record the flowrate of the nitrogen.

Allow the nitrogen to sparge through the fermentor until the dissolved oxygen
content read by the meter stops changing. At that point type ”CAL L0" and the
value of the 96 oxygen read by the meter.

Type "CAL" again and the computer will calculate the a slope and an intercept
which are necessary to convert the mA signal from the meter into % oxygen.

82

IV. Determination of k.a at a specific rpm and flowrate

1.

Set the fermentor at the desired temperature for the experiment. Calibrate the
oxygen probe for that temperature, remember to set the slope and intercept to l
and 0 respectively before beginning the calibration.

If one of the other groups has not already started the question and answer menu
press F6 and type '52 ON ". This activates a question and answer sequence that
will prompt you for the parameters needed to log the data. You may leave a
question and answer screen at any time by pressing another one of the function
keys. The F1 key is help and a list of the commands for the function keys is
given by ALT-F1. You can then return to the question and answer screen by
hitting ALT-F8 at any time.

Set and record the rpm for the experiment and adjust the air flowrate for the
experiment.

Allow the oxygen concentration to reach steady state.

Once the oxygen concentration has reached steady state, make preparations to
begin logging data for your experiment by using the menus to get to the screen
that asks if you wish to begin logging for the oxygen mass transfer experiment.

Move through the screen into the highlighted areas to and type in the values you
desire. The logging period should be 3 seconds and the maximum length of the
experiment should be around 2 minutes. Change the "Do you wish to begin
logging?" to YES by typing "y". Nothing will occur from the changes made on
any of the question and answer screens until the END key is pressed. Make sure
to press the END key when you are ready.

Begin logging just before the air is shut off and the nitrogen is started unless the
number of users on the Camile allows you access to begin logging as the nitrogen
gas is started. You may record the rpm and gas flowrates in the log file by
pressing the F8 key and typing them in. When typing in comments include your
initials so that they may be distinguished from the comments recorded by the
other groups using the camile system.

Monitor the progress of you experiment by using the on-line trend screens (F3).
You may explore the functions of the Camile at this time as most functions that
will harm your experiment are denied access without a password. Do not change
your slope and intercept. An interesting feature of the on line trending screens
of the Camile system is the history trend. The history trend appears as graph 9
in the on-line trending screens and can be reached by paging up or down after
hitting F3. The history trend displays the data already logged into your file. To

10.

ll.

83

view a history trend type 'Read" while above graph 9 and then the cursor will
move to the middle of the screen next to the word tagnarne. Type in “oxygen”,
the tagname for the dissolved oxygen experiment, and then hit enter. The cursor
will move to the next row and which will say ”log file”. Enter 6 and press END.
At this point the computer should begin reading your data from the log file and
displaying it on the screen. If you or another lab group wishes to use the history
trend later you must first type ”Clear" and then re-enter the pertinent information.

After you have been logging data for the time you specified on the question and
answer screens, the Camile will automatically stop logging data. If you wish to
stop logging before the time you specified runs out press ALT-F8 to get the
question and answer main menu which will offer to stop logging for your
experiment. Enter the number corresponding to stopping logging for that
experiment on the next menu that is displayed and your group’s security code.
The security code is to prevent other groups from accidentally stopping logging
data for your experiment.

Repeat the experiment two or three times for each set of conditions and choose
a variety of rpms for each flowrate and use several air flowrates or temperatures
if time allows.

To get your log file off the hard disk for analysis you will have to exit run and
use the DATA subprogram to convert your binary log file into a comma separated
value ASCII file. At this time ask the teaching assistant or the instructor for the
password. Once it has been entered by pressing the F9 key and typing "LEVEL
ENGINEER" and the password, you may type ”BYE" and exit run.

III. Data Analysis

1-

Use the arrows to move the highlighting to DATA and press ENTER. The
screen should say ”output file typezASCII' and ”Report all time pointszyes' then
hit END. A whole list of options will then be provided for you to change.
Highlight a particular selection and then press the space bar to view the various
options and hit ENTER when the option you desire is shown. Make sure you
include comments, tag values, elapsed time, date, and the time of day. The
column delimiter must be a comma for easy retrieval of the log file into a
spreadsheet program. When the appropriate options have been selected, press
END. Highlight the two tag names (oxygen and timedo) and press the space bar.
An arrow should be present on the left of the names and then press END.

The computer will then show the prompt "EDIT filename: " and your log file title
with a ”.pm' extension will be displayed. Hit END and you will exit DATA and
then press escape to exit the Camile menu.

84

Import the log file into a spreadsheet as a comma separated value format (CSV).
(i.e. \\Import,CSV,\eamile\logs\oxygen.prn). You may do this from SuperCalc4
from cd\bin\sc4 or SuperCalcS (cd\bin\scS).

You will then need to find the time data and convert it from seconds to minutes.
Once the time data has been converted to minutes you must create a file that
contains only the time data in the left hand column and the concentration data in
the right hand column.

If the computer indicates that the memory is full when attempting to import the
data into the spreadsheet several things could have gone wrong. The log file may
become too long to import if the filenarne of the logging file was repeated, by
adding data to an already existing file; too short a logging period produced too
much data; or too many runs were performed. If this happens don’t panic simply
import the file into a editor such as WordPerfect and save the file in several
smaller pieces.

Fermentation Power Transfer

Summary

Power—transfer rates were studied for 3 different impellers in a clear plexiglass
mixing tank that was constructed to match geometric ratios specified in literature
correlations. A Lightnin Mixer LabMaster. 2510 (Lightnin Mixing Co., Rochester,
N.Y.) was used to measure power consumption outfitted with three impellers: a 6—bladed,
Rushton-style radial-flow impeller; a traditional marine-type axial-flow impeller; and an
Lightnin A310 high-performance axial-flow impeller. The power consumption was
correlated to the rotational speed for each impeller. The power number was also
correlated to the Reynolds number for all three impellers.

Introduction

Fluid mixing is an important industrial operation whose economies are affected
by the power consumed by the process. The power and mass-transfer characteristics of
a particular impeller style, rate, and tank geometry ean be predicted using correlations.
The impeller style used ean have signifieant effect on the economics of a process since
the power consumed by two different types of impellers operating at the same impeller
rate may differ by an order of magnitude. In biochemieal applieations, the choice of
impeller can be crucial to the economics of the process because of the dual requirements

of minimal operating costs and adequate oxygen mass transfer or mixing. The design

85

86

of a fermentation process must reflect the power consumption, gas dispersion, and the
shear characteristics of the impeller (Dickey, 1992).

Typically, a mixer consists of a motor, a drive mechanism, and a shaft with one
or more impellers mounted on it. Mixing power is transferred from the motor to the
fluid via the shaft and impeller. The amount of power transferred to the fluid is a
function of the impeller speed and type, the geometry of the mixing vessel, and the
physieal properties of the fluid being mixed (Rushton, 1950). There are many types of
impellers such as propellers, shrouded turbines, rakes, disk turbines, gates and paddles.
Each type of impeller requires a specific amount of power to overcome its
hydrodynamic resistance during rotation; thus different impeller types exhibit different
power-consumption characteristics (Rushton, 1950). There are two broad categories for
characterizing impellers: axial and radial flow (Oldshue, 1990).

Axial-flow impellers displace the fluid downward from the impeller, parallel to
the axis of rotation. Typical axial-flow impellers include marine-type propellers and any
impeller with pitched blades. Axial-flow impellers are more wonomieal to operate than
radial-flow impellers because they produce more fluid motion per unit of power
consumed (Oldshue, 1990).

Radial-flow impellers push the fluid outward from the impeller in the radial
direction (Oldshue, 1990). Radial-flow impellers consume more power than axial-flow
impellers but typically have superior mass-transfer characteristics. Radial-flow impellers

produce higher shear rates, resulting in increased bubble breakup which improves gas

87
dispersion and mass transfer. Typical radial-flow impellers include square paddles and

the 6-b1aded Rushton turbine.

Theoretical Analysis

The correlations from Rushton, Costich, and Everett’s 1950 dimensional analysis
of fluid mixing are still widely used for estimating impeller power consumption
(McCabe, Smith, and Haniot, 1985). The dimensionless groups that describe mixing
power consumption are the Power number, the Reynolds number, and the Froude number

which are given below:

P8,,- a &a recs (1)

P. a Power number =
p ("131) ‘5 inertial forces

 

233.2 . inertial forces (2)
u viscous jbrces

 

Re = Reynolds number

N31), inertial forces

 

Fr = Froude number = — = , (3)
8 8mm fvrm
where P = power output of mixer
gc = Newton’s Law unit conversion constant

pI = liquid density

N, = impeller rate

D, = impeller diameter

g = acceleration of gravity
p = liquid viscosity

The Power number is correlated as a function of the Froude number and the Reynolds

88
number and other dimensionless groups that represent the geometry of the tank and

impeller. The form of the correlation is given below:

_ .,r,H c,s L,W ,,J
P. KR!I"?(DMD-WE)(7):)‘(D-IXD‘){-1-}?I (4)

where T = tank diameter
= impeller diameter
H = liquid depth
C = height of impeller off bottom
= pitch of impeller
L = length of impeller blades
W = width of impeller blades
J = width of baffles
B = number of blades on impeller
B, = number of blades on the reference impeller
R = number of baffles
R, = number of baffles on reference tank

The lower-ease letters are the unknown exponents for the terms shown (Rushton, pt I,
1950). The characteristic dimensions for the tank and the impeller are shown in Figure
l. The last seven terms of the above equation are geometric parameters that have been
rearranged into dimensionless "shape factors". These 'shape factors“ designated S|
through S., are defined below, along with some common values used in correlations

(McCabe, Smith, and Harriot, 1985):

J 1 H (5)

~1L°
wln—

s,= s,=-§=r 3,:
I

If all the geometric parameters are fixed for a set of experiments, the constant K absorbs

all the geometric constants yielding an equation of the form:

89

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90

P. - K Re 'Fr ' (6)
The group log,o(P.lFr) is often plotted versus the log ,0(Re), and the slope gives the
exponent of the Re term. The effect of the Froude number is negligible when the tank

is baffled (i.e. n ~ 0), and the value of the (Fr)' is equal to 1.0 (Rushton et al., 1950).
The mixing conditions may be characterized into flow regimes defined by the
Reynolds number in a manner analogous to the friction factor. Viscous conditions exist
at Reynolds numbers below 10, with a transition range between Re values between 10
and 20,000. At Re greater than 20,000, the flow becomes turbulent, and the power
consumed by a radial-flow impeller in a baffled tank containing a Newtonian fluid is
proportional to the cube of the impeller rate. Log-log plots of power versus rpm in this

regime should yield lines with slopes equal to 3 for Rushton-style impellers.

Experimental Equipment and Procedure

The equipment used for the experiment consisted of a plexiglass tank fitted with
removable baffles, a Lightnin Mixer LabMaster. 2510 (Lightnin Mixing Co. , Rochester,
NY) outfitted with Lightnin Mixer impellers of several different types, and a Camile
2000 data-acquisition system (Dow Chemical Co. , Midland, MI). The setup of the
equipment is shown in Figure 2. The impellers used were A100 marine-type propeller
with a power number of 0.87, 8 R100 six-bladed paddle turbine with a power number

of 6, and an A310 high-performance axial-flow impeller with a power number of 0.3.

91

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92
The LabMaster. mixer motor measures the impeller speed and the power consumed and

sends the data to the Camile data-acquisition system via a serial cable. The mixer auto-
calibration procedure was followed before acquiring power-consumption data. The
power consumption of the impeller, shaft, and bearings was measured in air to determine
the losses due to fiiction within the mechanical couplings of the system for each impeller.
The power consumption for the same series of speeds was then measured in water for

each impeller.

Results and Discussion

The power consumption of the shaft and impeller in air was essentially zero for
all speeds and impellers tested, with the limitation that the set screw used to hold the
impeller on the shaft be as small as possible. Experiments performed with an excessively
large set screw produced vibratory deflections of the shaft and impeller at high impeller
speeds causing power fluctuations. Figure 3 shows the results of the power-measurement
experiments. The literature indicates that the power-meter data should increase with the
cube of the impeller rate for a Newtonian fluid in the turbulent regime (Oldshue, 1990).
However, linear regression of the power data produce slopes greater than 3 as shown in
Figure 3. Figure 4 contains a plot of the Power number versus the Reynolds number.
The R100, A310, and A100 impellers should asymptotically approach Power numbers
of 6, 0.3, and 0.87 respectively. The power numbers calculated from the experimental

data are about 1.5 times smaller than the asymptotic Power numbers. This may be due

93

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95
in part due to the inability of the current system to reach Re greater than 200,000 where

all impellers are said to reach their asymptotic Power number regardless of design
(Oldshue, 1990). Power measurements ean be taken only between Re of 11,000 and
about 100,000 using water as the mixing fluid because of the limitations of the power
meter and the mixer. In addition, the power cannot be measured in water by the mixer
below a certain range of impeller spwds, which varies with the type of impeller. At low
speeds, the power meter is not sensitive enough to detect a difference in power
consumption between water and air. Thus, the viscous regime of Reynolds numbers is
unavailable for study unless much more viscous fluids are used. Alternatively, Reynolds
numbers above 100,000 are difficult to achieve since the power consumed reaches the
maximum capacity of the motor and the power meter for the radial-flow impeller. The
axial-flow impellers approach the critical shaft speed above Re of 100,000 and shaft
vibration and deflection begins to become significant.

The mixer’s method of power measurement utilizes a microprocessor that may be
reprogrammed using input from the keypad and a series of commands (see Appendix 1).
Specifically, it may be possible to change the torque constant used by the microprocessor
to ealculate power-consumption values. This adjustment may allow the mixer to produce
data that more accurately fit the existing correlations for the Power number versus the
Reynolds number. A few preliminary runs after changing the torque constant indieate

that this method may produce the desired results, but much more analysis is required.

96

Conclusions and Recommendations

The mixer produces data that are highly precise but do not correspond to the
literature values. The power meter of the mixer should be calibrated to determine its
accuracywithrespecttotheliterature. Atrialanderrormethodcouldbeutilizedto
adjust the torque constant of the mixer to obtain the desired literature values for all the
impellers.

Both more- and less-viscous Newtonian fluids than water should be used to obtain
lower and higher Reynolds numbers. The use of higher-viscosity solutions such as
sucrose would decrease the relative contribution of the mechanieal losses in the power
consumption of the system by increasing the overall power consumption. The use of
lower viscosity fluids may allow operation at higher Reynolds numbers to ensure

operation in the turbulent regime.

Symbols

p. = liquid viscosity

B = number of blades on impeller

B, = number of blades on the reference impeller
C = height of impeller off bottom

D, = impeller diameter

D1 = imlxller diameter

Pr = Froude number = Ni’Dilg

g = acceleration of gravity

g, = Newton’s Law unit conversion constant
H = liquid depth

J = width of baffles

L = length of impeller blades

N, = impeller rate

97

P = power output of mixer

P,| = Power number = PgJ(p,N,’D,’)

R a number of baffles

Re 8 Reynolds number = Din/u

R, = number of baffles on reference tank
S = pitch of impeller

T = tank diameter

W - width of impeller blades

Bibliography
Bailey, James E. and David S. Ollis, Biochemical Engineering firndarnentals, 2 nd. ed.,
McGraw-Hill, New York, 1986, pp. 498-494.

Dickey, David 8., and Ramesh R. Hemrajani, “Recipes for Fluid Mixing“, Ozemical
Engineering, March 1992, pp. 82-89.

McCabe, Warren L., Smith, Julian C., and Peter Harriot, Unit Operations in Oiernical
Engineering, 4 th. ed., McGraw-I-Iill, New York, 1985, pp. 208-252.

Oldshue, J. Y., and N. R. Herbst, A Guide to Fluid Mixing, Mixing Equipment
Company, Rochester, N.Y., 1990, pp. 1-3,.

Rushton, J. H., Costich, E. W., and H. J. Everett, "Power Characteristics of Mixing
Impellers, Part 1" Chemical Engineering Progress, vol. 46 no. 8, August 1950, pp. 395-
404.

Rushton, J. 11., Costich, E. W., and H. J. Everett, "Power Characteristics of Mixing
Impellers, Part 11" Chemical Engineering Progress, vol. 46 no. 9, Sept. 1950, pp. 467-
476.

98

Appendix

Equipment and reagents needed:

Lightnin Labmaster T825 10

three impellers

tanks with removable baffles

Camile Data Acquisition and Control system
Glycerol

sugar (optional)

Experimental Procedure
1. Determination and Adjustment of Tank Geometric Constants

1.

Measure all the appropriate pieces of equipment to be used in the experiment to
obtain the values of the shape factors.

Look at the diagrams in the instruction manual to identify the each of the types
of impellers. The A310 impeller has a diameter of 3.4' with a Power number
of 0.3. The A100 impeller has a diameter of 2.7" and a Power number of 0.87.
The R100 is a 4" impeller..

Adjust the height of the impeller relative to the tank bottom according to the
values of the shape factors raise the water level to the appropriate height.

11. Operation of the Labmaster Mixer

1.

The power meter of the mixer must be autozeroed before collecting data for the
day. The shaft must be removed from the mixer to perform the autozero
procedure.

Loosen the two knobs on the arm that supports the mixer enough slide the mixer
up and down the track it is mounted on. Slide the metal bar out of the way above
and replace it once the mixer is above the level of the hole. Rest the mixer on
the bar above the tank.

Press the white shaft lock button located at the bottom center of the front of the
mixer. If the button does not go all the way in rotate the chuck slowly with your
fingers until the button travels all the way in. Never attempt to stop the mixer
with the shaft lock button always use the “RUN/STOP" button to stop the mixer.
The “RUN/STOP” button will have no effect in remote mode so the power must
be turned off in an emergency.

99

Loosen the chuck by turning it counterclockwise until the shaft glides freely out
of the mixer.

Press the 'ON' button and the “RESET” button at the same time and then release
the “RESET" button and then release the ”ON/OFF“ button. After the LCD
readout on the mixer says “diagnostic”, press '6' and then press ”ENTER". The
mixer will then perform a series of pre-set speeds and calibrate its power meter.
Be sure to bep hands and clothing away from the rotating parts of the mixer.

Replace the shaft into the mixer using the reverse of the above procedure. Make
sure that the chuck is hand tight but do not overtighten the chuck.

Press the ”ON/OFF" button twice to get to normal operating mode.

Usethe'MENU'keytomovetheflashingasterisksfromspeedtothe
temperature/power window. Use the item key pressed several times in succession
to show the temperature in “C and °F and the power in Watts. Use the “MENU“
key to move the asterisks to the pumping capacity and use the item key to select
the type of impeller used and enter the impeller diameter to one decimal place.
Enter the values from part A step 2 for both the A310 and the A100 and 4" for
the R100 impeller.

Press the RUN/ STOP button to start and stop the motor.

III. Measurement of Power Consumption

1.

Locate the impeller at the proper depth in the tank by sliding the shaft up and
down in the chuck while the mixer rests on the lowest bar in the track. It may
be nwessary to raise the mixer to adjust the shaft. The knobs that hold the mixer
in the track must be tightened before operation.

Fill the tank with reverse osmosis (R0) water.

MeasurethepowerwithROwaterintankforallthespeedsthatwereusedfor
the empty tank and record the rpm’s, temperature, and power allowing the system
to equilibrate at each speed. Measure the power consumption and rpm of each
impeller in the empty tank at a range of speeds between 50 and 400 for the R100
and spwds between 50 and 800 rpm’s for the other two impellers. Allow the
system to equilibrate at each speed. Install the R100 impeller with the hub facing
up. Install the A100 and the A310 with the convex side of the blades facing up.

100

IV. Operation of the Camile system with the Labmaster Mixer

1.

Consult with the other groups using the Camile so that it may be used by
everyone. The three experiments that use the camile system are: immobilized
bioeatalysts, and the power and mass-transfer experiments. The eapabilities of
the system for multiple users is limited so cooperation between lab groups is
important.

If the Camile system is not already started, start up the Camile system by turning
on the computer and typing "cd\eamile' to get to the Camile directory. Then
type 'menu" and the Camile logo will appear. Press any key to display the main
menu. Use the arrow keys to highlight 'run' and hit ENTER. Then use the
arrow keys to highlight the database called 'I-IEA'ITRAN" and hit ENTER. The
computer will then ask you if you wish to initialize the Camile control constants.
Type "y' and hit enter.

When the computer prompts for the default log directory 'C:\camile\logs" should
be present and highlighted. If not, backspace and type it in then hit enter. The
log file screen should now be on the monitor. Use the arrows to move to log file
6 and type the name you have chosen for your log file. Make sure that “BIN"
and 'APP" appear in the fields to the right of the log file name.

Wait for the other groups to enter their filenames before pressing the END key.
When all the groups have entered their filenames press END. If you have
repeated any log file name currently on file, the computer will prompt you to
change it. The computer will then ask you to enter a title. This and the
comments it prompts for next are optional, but your names and a few brief words
describing your experiment might save considerable confusion later. Leave a
blank line to finish and hit ENTER.

The computer will then inform you that the printer does not respond and will ask
you if you wish to retry. Type N if the printer is not connected.

If one of the other groups has not already started the question and answer menu
press F6 and type '82 ON " . This activates a question and answer sequence that
will prompt you for the parameters needed to log the data. You may leave a
question and answer screen at any tithe by pressing another one of the function
keys. The F1 key is help and a list of the commands for the function keys is
given by ALT-Fl . You can then return to the question and answer screen by
hitting ALT-F8 at any time.

10.

11.

12.

101

Select the number for the power transfer experiment on the main menu, enter it
in the highlighted space and press the END key. Move through the screens into
the highlighted areas to and type in the values you desire. The logging period
should be 30 seconds.

The speed of the mixer ean only be changed in manual mode. To change the
speed of the mixer press ALT-F8 to return to the question and answer screens.
Move through the menus like when beginning logging and then enter 'n" after the
question that asks if you want the mixer in remote mode and press ”END”.
When you have set the desired rpm on the mixer go back to that screen and type
'y" for both the remote mode and whether you wish to begin logging.

Before restarting the motor look at the shaft below the chuck and check for
scoring of the shaft, if there is consult with the teaching assistant. Make sure to
press the END key when you are ready.

Check the trend screen periodically to see if the values have become constant.
Go to the F6 screen and see if the number next to sequence '4. labmaster" is
constantly changing. If the number after 'labmaster' is constant, the
communications sequence must be restarted. To restart the communication
sequence, press F6 and type '84 OFF" and then type '84 ON”.

You may record the type of impeller and whether or not the reading is a
ealibration in water or air in the log file for your data by pressing the F8 key and
typing in any relevant notes. When typing in comments include your initials to
distinguish them from the comments recorded by the other groups using the
camile system.

Monitor the progress of you experiment by using the on-line trend screens (F3).
You may explore the functions of the Camile at this time as most functions that
will harm your experiment are denied access without a password. Do not change
your slope and intercept. An interesting feature of the on line trending screens
of the Camile system is the history trend. The history trend appears as graph 9
in the on-line trending screens and can be reached by paging up or down after
hitting F3. The history trend displays the data already logged into your file. To
view a history trend type ”Read” while above graph 9 and then the cursor will
move to the middle of the screen next to the word tagname. Type in ”power“ or
“rpm", the tagnames for the your experiment, and press enter. The cursor will
move to the next row and which will say 'log file". Enter 1 and press END. At
this point the computer should begin reading your data from the log file and

13.

14.

15.

102

displaying it on the screen. If you or another lab group wishes to use the history
trend later you must first type 'Clear" and then re-enter the pertinent information.

When ready to stop logging data press ALT-F8 to get the question and answer
main menu which will offer to stop logging for your experiment. Enter the
number corresponding to stopping logging for that experiment on the next menu
that is displayed and your group’s security code. The security code is to prevent
other groups from accidentally stopping logging data for your experiment.

Repeat the experiment with a variety of rpms for each impeller and with and
without baffles if time allows.

To get your log file off the hard disk for analysis you will have to exit run and
use the DATA subprograrn to convert your binary log file into a comma separated
value ASCII file. At this time ask the teaching assistant or the instructor for the
password. Once it has been entered by pressing the F9 key and typing “LEVEL
ENGINEER” and the password, you may type "BYE" and exit run.

V. Data Analysis

1.

Use the arrows to move the highlighting to DATA and press ENTER. The
screen should say ”output file typezASCII' and "Report all time points:yes' then
hit END. A whole list of options will then be provided for you to change.
Highlight a particular selection and then press the space bar to view the various
options and hit ENTER when the option you desire is shown. Make sure you
include comments, tag values, elapsed time, date, and the time of day. The
column delimiter must be a comma for easy retrieval of the log file into a
spreadsheet program. When the appropriate options have been selected, press
END. Highlight the tag names (power and rpm) and press the space bar. An
arrow should be present on the left of the names and then press END.

The computer will then show the prompt “EDIT filename: " and your log file title
with a ".pm' extension will be displayed. Hit END and you will exit DATA and
then press escape to exit the Camile menu.

Copy the file that is produced ”.pm' to a 3.5" diskette.

Import the '.pm" file into a spreadsheet as a comma separated value format
(CSV). (i.e. \\Import,CSV,mixer.pm).

Adjustment of the Labmaster. Mixer Torque Constant

Put the mixer in diagnostic mode using the directions for ealibration above.

103
Type “90" on the keypad and press the enter key.

Type "1723' on the keypad and press the enter key.

Type "75" on the keypad and press the enter key. The display should now read
"ARG'.

Press the enter key to see the current value of the torque constant. The factory
setting is ”519'.

Press the 'on/off' key.

To change the torque constant repeat steps 1 through 4 and enter in the new
torque constant using the keypad and press enter.

Press the "on/off” key.

Re-enter the diagnostic mode and perform a ealibration using the instructions
above. A calibration must be performed each time the torque constant is
changed.

Immobilized Cell Biocatalysts

Summary

The diffusive properties of CaCl, in alginate gel spheres were studied in an
unsteady state experiment by following the decrease in concentration of CaCl, in a well
stirred solution of finite volume. The alginate gel spheres were produced by dropwise
addition of sodium alginate into a CaCl, solution. A known volume of gel spheres was
added to a 10 g/l CaCl2 solution, and the rate of disappearance of salt was measured
using a conductivity meter. A computer program determined the effective diffusion
coefficient by fitting a mathematieal model to the experimental data and minimizing the

error between the model and the data.

Introduction

Enzymes and cells are often immobilized by attachment to a support to allow them
to be reused continuously. Immobilization techniques can be classified into two classes
for biocatalysts: cherrrical and physical. Chemical immobilization uses a covalent bond
between the immobilization material and the biocatalyst, which is typically an enzyme.
Physical immobilization often traps the biocatalyst using other types of interactions such
as entrapment within a porous matrix, containment by a membrane, or surface
adsorption.

Cells are most commonly immobilized by physical structures such as polymer

gels. The polymer gel is usually a bead which is formed by mixing the biocatalyst and

104

 

105

the monomer of the gel and then dripping the solution into a crosslinking solution which
polymerizes the monomer, entrapping the biocatalyst. The most common forms of
polymer immobilization are polyacrylamide, x—carrageenan, and sodium alginate.
Polyacrylamide is crosslinked using chemieal agents that are toxic to cells, but at-
carrageen and sodium alginate are both polysaccharides that can be crosslinked by
calcium solutions under mild conditions (Bailey and Ollis, 1986).

Alginate is a linear polysaccharide which acts as the skeletal component of the
seaweed and algae, from which it is normally obtained (Wang, 1990). The addition of
a polyvalent cation such as Ca+2 to a solution of alginic acid causes the formation of an
ionic-network polymer which is crosslinked by the Ca“2 ions between carboxyl ions.
Thus dropwise addition of the sodium salt of alginic acid to a solution of calcium
chloride will result in the formation of crosslinked alginate beads upon the exchange of
calcium for sodium in solution. The pore size, molecular permeability, and degree of
crosslinking of the beads depend primarily on the molecular weight of the alginic acid
used (Wang, 1990). The mild polymerization conditions for the alginate and its stable
structure between 0 and 50°C make it an ideal medium for immobilizing cells. However,
citrate and phosphate scavenge the Ca+2 ions, thus breaking the crosslinks. High
concentrations of Na+ ions also reverse the crosslinking reaction by replacing the Ca+2
with Na*.

Immobilization of biocatalysts presents advantages over non-immobilized
biocatalysts in separations and reaction engineering. A non-sterile feed may be used for

fluidized and packed-bed reactors because any contaminants not entrapped in the beads

106
will wash out of the reactor (Petersen, 1991). Downstream separation of the bioeatalysts

is not necessary since they are retained in the reactor. The retention of the biocatalysts
in the reactor also increases their concentration within the reactor, increasing the rate of
reaction and decreasing the need for renewal of the bioeatalysts (Bailey and Ollis, 1986;
Petersen, 1991).

Immobilization can present disadvantages for the engineer as well. Mass-transfer
limitations of the substrates and products ean limit the reaction rate of the bioeatalysts.
Systems that form inhibitory products may have a lower reactor performances than a non-
immobilized systems. Covalently attaching an enzyme to a support may decrease its
intrinsic kinetic properties (Bailey and Ollis, 1986).

The advantages and disadvantages of immobilization of biocatalysts vary with the
types of biocatalysts and immobilization technique used. The transport properties for all
the important species in the reaction must be considered before the system is
immobilized. The determination of effective diffusion coefficients for reactants and
products within the immobilization media is often required to analyze the transport

phenomena involved.

Theoretical Analysis

Simple diffusion without convection is most commonly described by Fick’s
law. Fick’s law relates the flux of molecules by diffusion to the concentration gradient
by a proportionality constant known as the effective diffusion coefficient. The form of

Fick’s law for radial diffusion in spherical coordinates is (Cussler, 1984):

107

6C, (1)
J, = -D.-—
6r
where J, = the diffusive flux of component i

D, = the effective diffusion coefficient

C, = the concentration of component i

r = radial coordinate
Equations describing the unsteady behavior of a diffusional system are derived by using
Fick’s law in the mass balance.

The basic unsteady-state mass balance equation describing the diffusion of a solute

into a sphere is the following:

 

6C BC 2
.__! = lib-ZD‘ ’) ( )
a: r2 Br Br
where C, = solute concentration in the beads
t = time

r = radial coordinate
D, = effective diffusion coefficient

The equation assumes that convective mass transfer within the sphere is negligible. The
following initial and boundary conditions are used for the diffusion of a solute into

spheres from a well stirred solution of limited volume (Crank, 1975):

108

att=0; 0<r<R; c,=o (3)

(4)
atr=0; DR; CL=Cb
8C
att>0; r=0: -—‘S=0 (5)
6r
6C (6)

:>0- =R; VaC‘=KAD '|
’ r 1.7 p s e— r-R

where R = radius of the beads
CL = concentration in the liquid phase
CL, = initial concentration in the liquid phase
V, = volume of the liquid phase
K, = partition coefficient between liquid and beads
A, = surfaceareaofthebeads

This model assumes negligible mass transfer resistance in the liquid film surrounding the
spheres. Crank gives the following series solution for the liquid phase concentration of
solute in terms of the diffusion coefficient, the ratio of the liquid volume to the bead

volume (a), the radius of the beads, and several qII values:

 

 

 

- Aft
aC a. 6(l+a)exp(. 2 ) (7)
CL: “(1+2 2 2
H: "=1 9+9a+q a

Values for the q,’ s are given by the non-zero solutions of the following equation:

34.. (8)
3 + aq.

 

tam.) =

Determination of the effective diffusion coefficient for CaCl2 within an alginate

109

gel sphere requires that the other mass transfer resistances must be made negligible. The
limiting transport step in the system must be the diffusion of the CaClz into the polymer
itself. The film theory of mass transport states that a significant amount of resistance to
mass transfer may exist within the film that surrounds any object immersed in a fluid.
Film theory also states that the film thickness decreases with the velocity of the fluid
motion across a surface. Therefore to reduce the film resistance, the velocity of the
alginate spheres relative to the solution must be high; this is accomplished by rapidly
swirling the beads in solution.

Film theory defines the film thickness (5) with the following equation (Nguyen,
1986):

8 =5 (9)

where D, is the diffusivity of CaCl, into free water and k is the external mass transfer
coefficient. The external mass transfer coefficient is often defined by the following

relation in terms of the total flux of component i, N,:

10
N, =rc(c, -K,c,) ( )

The equilibrium concentrations of the liquid and solid phases are related by the partition
coefficient K. Correlations for the value of k are given in terms of the Schmidt number,

the Reynolds number, and the Sherwood number:

110

(l 1)
Sir = f(Re,Sc)

where Sh = Sherwood number = kd/DIII
Sc = Schmidt number = ulpD,
Re = Reynolds number = pod/u.
d =' bead diameter
p = fluid viscosity
p = fluid density
The variable u is the liquid velocity relative the to beads, and it is dependent on the
shaker speed, orbit size of the shaker, the density of the beads, and the density and

viscosity of the fluid in which they are immersed.

Experimental Equipment and Procedure

The equipment used to produce the alginate beads included a magnetic stirrer,
plastic tubing, a funnel, a plastic nozzle, and a clamp for the tubing. The equipment was
set up as shown in Figure l. The clamp on the tubing was adjusted until the alginate
flowed out the nozzle in a dropwise fashion into the CaClz solution where it was
crosslinked into beads. The buds were incubated in the CaCl, solution at room
temperature for about an hour after the alginate was completely added to the solution.

The beads were then repeatedly rinsed with reverse osmosis (RO) water and
placed in the shaker at 400 rpm and 30°C with fresh RO water. The water was replaced
every 5-10 minutes until its conductivity matched that of pure RO water for 15 minutes.
Once the beads contained no detectable free CaClz, 25 beads were measured to determine
the average diameter.

The equipment used in the determination of the effective diffusion coefficient,D,,

111

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Fli,

 

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112
included a conductivity probe with meter, water bath shakers with a circular orbits of 0.5

and 1 inch, and the Camile Data Acquisition and Control System to record the data. The
general setup of the equipment is shown in Figure 2.

Solutions of 2, 5, 8, and 10 g/L CaCl2 were used to create a calibration curve.
The voltage output from the conductivity meter was registered by the Camile System for
each of the standards. The calibration curve for each of the standards at 30°C is shown
in Figure 3.

The experimental data were analyzed using an existing Fortran program that fit
Equation 7 to the data by changing the parameters D, and a to minimize the deviation
between the model and the experimental data. The program uses Newton’s Method to
find the roots (q,) to Equation 8. The program utilizes the non-linear optimization

subroutine PATERN. A copy of the program is given in Appendix II.

Results and Discussion

The results were obtained using both 0.5 and 1 inch orbit shaker operating at 400
rpm. Figures 4 and 5 show experimental data as well as theoretieal curves. The
deviation between the model and the data is greatest for the earliest time points. Periodic
fluctuations in the meter output rate are primarily due to poor temperature control of the
shaker. Figure 6 illustrates these characteristic trends of the larger 1" orbital shaker.
The 1" orbital shaker had superior temperature control and more reproducible shaker
speed settings. The use of larger beads also produced better results. Possible reasons

for the improved results include increased inertia causing greater flow around the beads

113

 

 

 

 

 

 

 

 

I 1 serial cable
- E-Zl

/ \

Computer

 

 

 

 

 

 

 

 

 

 

 

Camlle Data Acqulsltlon
and Control System

 

 

 

 

 

 

 

 

 

 

voltage signal
conductlvlty probe 0 - 2 v on
thermocouple
I erlenmeyer flask
water bath shaker conductlvlty meter

Figure 2. Experimental Setup for Determination of Effective Diffusion Coefficients

114

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118

and an increase in the diffusion path of the experiment. Increasing the diffusion path of
the experiment increases the diffusion time reducing the relative magnitude of the timing
errors. Four experiments with identical amounts of beads and CaCl2 solution were
carried out using the 1" orbital shaker, and the results are presented in dimensionless
form in Figure 7. Note that as the shaker speed increases up to 250 rpm the final
concentration of the solution increases. Also, the data for 250 rpm fit the model more

accurately than the data at 350 rpm. The better fit of the data taken at 250 rpm is
explainable by the fact that forced convection within the bead may be occurring at 350
rpm, invalidating the assumption of no convective flux. Unfortunately correlations of
the mass transfer coefficient for the case of an orbital shaking motion were not found in
the literature. Therefore the mass transfer limitations can only be assumed to be
overcome for these experiments.

The periodic fluctuations in the data can be attributed mostly to temperature
fluctuations in the water bath. The water bath shaker temperature did fluctuate in
sinusoidal fashion, as can be expected from the control system.

The experimental values of the effective diffusion coefficient, .D,, ranged from 5
x 10" to 8 x 10“ cmz/min and the literature values ranged between 2 x 10‘ and 8 x 10"
cm2/ min (Itamunoala, 1987). This indicates that the experimental procedure produces

results that are accurate enough to be consistent with the literature.

Conclusions and Recommendations

The experiment can be used to determine the effective diffusion coefficients for

119

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0:... 000.00.00080

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0.0. 000 n. 0.0. 000 x E0. on: + E0. 00 .

 

 

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120

diffusion into or out of porous spheres with sufficient accuracy to match literature values.
The shaker speed and temperature control of the shaker are crucial for the data
collection. High agitation rates are required to minimize mass-transfer resistance in the
liquid film surrounding the spheres. Effective diffusion coefficients determined by this
approach would be useful for mathematical models for packed- and fluidized-bed
bioreactors.

Modification of the experimental apparatus to include temperature compensation
at the level of the conductivity meter or at the level of calculations within the data
acquisition system could greatly improve the quality of the data. The use of a baffled
flask and experimentation at different rotational rates might provide interesting insight
into the interphase mass transfer regimw of the shaker as well. Modification of the
experimental apparatus to use a fluidized bed of the gel spheres in recirculated CaCl2

solution might allow the mass-transfer properties of the beads to be studied.

Symbols

0: = ratio of liquid volume to bead volume
5 = film thickness

It = fluid viscosity

p = fluid density

A, = surface area of the beads

C, = the concentration of component i

CL = concentration in the liquid phase

C1,, = initial concentration in the liquid phase
C, = solute concentration in the beads

d = bead diameter

D, = effective diffusion coefficient

D, = the effective diffusion coefficient

D, = diffusivity into water

J i = the diffusive flux of component i

k = external mass transfer coefficient

121

K, = partition coefficient between liquid and beads
n = eigenvalue index

N, = total flux of component i

q, = eigenvalues of the solution for CL/CL,
r = radial coordinate

R = radius of the beads

r = radial coordinate

Re = Reynolds number = pud/u

Sc = Schmidt number = a/pD,

Sh = Sherwood number = kd/Dl

t = time

u = liquid velocity relative to beads

VL = volume of the liquid phase

References

Crank, 1., Mathematics in Dmitsion, Claredon Press, Oxford, 1975,
pp. 56-60, 93-97.

Cussler, E. L. , Dzfiiaion: Mass Transfer in Fluid Systems, Cambridge University Press,
New York, 1984, pp. 19-21.

Freund, Vicki, "Using DIFF to Determine Diffusion Coefficients" , Department of
Chemical Engineering, Michigan State University, photocopy

Itamunoala, G. F . , ”Effective Diffusion Coefficients in Calcium Alginate Gel",
Biotechnology Progress, 3, June 1987, pp. 115-121.

Wang, Nam Sun, "Experiment No. 7 - Supplement B: Enzyme Immobilization Protocol
Entrapment in Alginate Gel” University of Maryland Laboratory Manual, 1990 photocopy

Kennedy, John F. and Cabral, Joaquim M. S., "Immobilized Living Cells and Their
Applications" Applied Biochemistry and Bioengineering Volume 4: Immobilized Microbial
Cells, Academic Press, New York, 1983.

Nguyen, An-I.ac, and J. H. T. Luong, ”Diffusion in K-Carrageenan Gel Beads”
Biotechnology and Bioengineering, vol. 28,pp. 1261-1267, J. Wiley and Sons, 1986

Petersen, James N., Davidson, Brian H., and Charles D. Scott, ”Minimizing the Errors
Associated with the Determination of Effective Diffusion Coefficients when using
Spherical Cell Immobilization Matrices” Biotechnology and Bioengineering, vol 37, pp.
386-388, John Wiley and Sons, Inc., 1991.

122

Appendix 1. Experimental Equipment and Procedure

Equipment and Reagents N wded:
sodium alginate

calcium chloride

graduated cylinders

funnel

rubber tubing
screw clamps
conductivity meter

Reverse osmosis (RO) water
balance

I. Preparation of the Alginate Solution and Beads

1.

Check to see if any alginate solution has been prepared for you. If not, weigh
out sufficient alginic acid to prepare a 1-3 wt. % solution of alginic acid in R0
water. Otherwise skip to step 4.

Slowly add alginic acid to 500—1000 ml of water while heating and stirring
vigorously on a stirrer/hot plate. The recommended method is to slowly scrape
enough alginate to barely cover the spatula into the vortex to prevent clumping.

Once the alginate solution has completely dissolved, allow the solution to stand
and cool. Make sure that the air trapped within the alginate is allowed to

completely escape.

Set up the apparatus as shown in Figure 1. Make sure to completely pinch off
the tube with a screw clamp. For best results, the plastic nozzle chosen should
be of the largest size available. Make sure that the ring holding the funnel is as
high as possible on the stand. This allows the beads time to form a spherical
shape as they fall and avoids splashing from the beaker onto the nozzle.

Prepare about 200 ml of a 15 g/l CaClz in water solution in a 400 ml beaker.
Place the beaker on the stir plate and add a stir bar to the solution.

Adjust the speed of the stirrer so that the surface of the fluid is just barely
disturbed by the vortex. If the stirring rate is too high, the beads will deform due
to shear before they cure.

Slowly open the clamp and allow the alginate solution to drip out. Open the

. clamp enough to allow the alginate to leave the nozzle as individual drops. Poor

beads will be formed if the dripping rate is too fast. When the funnel containing
the alginate is empty, let the beads cure in the calcium chloride solution for 30-60

10.

ll.

12.

123
minutes.

While the beads are curing, turn on the main power on the shaker and adjust the
shaker to the desired temperature of operation. Use the conductivity meter to
determine the conductivity of RO water.

Create several standard salt solutions in the range of 5-10 g/l CaClz.

Start up the Camile system by turning on the computer and typing "cd\eamile"
to get to the Camile directory. Then type ”menu" and the Camile logo will
appear. Press any key and the main menu will be displayed. Use the arrow keys
to highlight "run" and hit ENTER. Then use the arrow keys to highlight the
database called ”HEA'ITRAN" and hit ENTER. The computer will then ask you
if you wish to initialize the Camile control constants. Type 'y" and hit enter.
The computer will then prompt for the default log directory. "C:\eamile\logs"
should be present and highlighted. If not, backspace and type it in then hit enter.
The log file screen should now be on the monitor. Use the arrows to move to log
file 4 and type the name you have chosen for your log file. Check with the other
lab groups using the computer to enter in their file names before continuing.
Make sure that ”BIN” and “APP” appear in the fields to the right of the log file
name. When you have finished press END. If you have repeated any log file
name currently on file, the computer will prompt you to change it. The computer
will then ask you to enter a title. This and the comments it prompts for next are
optional, but your names and a few brief words describing your experiment might
save considerable confusion later. Leave a blank line to finish and hit ENTER.
The computer will then inform you that the printer does not respond and will ask
you if you wish to retry. Type N.

Press the F4 button and then PAGE UP or PAGE DOWN until you are on the
screen that has the tag name 'COND". Look in the lower right hand corner next
to the bar graph. Check to see that the slope is equal to 1 and that the intercept
and filter constant are both equal to zero. If they are not you may reset these
values by typing ”SL l","IN 0",”FL 0" to change the slope, intercept and filter
constant, respectively.

Place the capped standard solutions in the shaker bath and allow them to come to
the desired temperature (eg. 30°C). Always turn off the shaking on the shaker
before adding glassware to or removing glassware from the platform. Place the
conductivity probe into each solution and record the voltages and the
corresponding concentrations in g/l. Use the on-line trending (F3) to make sure
that the solution temperature is fully equilibrated before moving on to the next
solution. It is important that a ealibration be carried out for each temperature you
will be experimenting at since the conductivity of CaCl2 solutions is a fairly
strong function of temperature.

13.

14.

15.

16.

124

Linearize the concentration versus voltage data to yield an equation for the
calibration curve. Use a calibration curve of the form: concentration = slope
x voltage + intercept.

On the F4 screen of the camile system you must change the slope and intercept
values to the ones you determined using the commands in step 11, substituting
your slope and intercept values for l and 0, respectively. Make sure the values
for the constants you determined for your calibration curve appear on the screen
in the lower right comer so you will have an on-line representation of the CaCl2
concentration. Press F6 and type '82 ON". This activates a question and answer
sequence that will prompt you for the parameters needed to log the data. You
may leave a question and answer screen at any time by pressing another one of
the function keys. The F1 key is help and a list of the commands for the function
keys is given by ALT-F1. You can then return to the question and answer screen
by hitting ALT-F8 at any time.

Once the beads have cured, transfer the beads to a 250 ml erlenmeyer flask.
Rinsethebeads with ROwaterthenfilltheflasktoabouttheZOOmlmarkwith
RO water and place the flask in the shaker at 250 rpm with the conductivity probe
capping the solution. Periodically drain off the water using a wire screen placed
against the mouth of the flask. Repeat the process of replacing the water and
putting the flask in the shaker until the water over the beads gives the same
conductivity reading as pure RO water for 10 minutes.

Prepare a sufficient amount of 10 g/l CaCl, solution for 4 experiments and label
the bottle with your group letter, names, and contents and place it in the
refrigerator.

11. Determination of Gel Permeation

1.

Set the water bath shaker at the desired temperature for the diffusion experiment.
On the NBS G76D this ean be accomplished by turning the MODE SELECT
knob to °C and toggling the switch below it to ”SET" and changing the displayed
temperature using the switch with the arrows.

Fill a 250 ml graduated cylinder with somewhere between 100 and 130 ml of
water and record the volume. Then drain the beads and add them to the
graduated cylinder containing the water and record the final volume.

Drain the water offthe beads using the wire screen and place the beads on a clean
cloth or paper towel. Do not thoroughly dry the beads, use the towel to absorb
the excess water only.

10.

11.

125

Measure out somewhere between 100 and 170 ml of your 10 g/l solution, record
the volume, and place it in the water bath with the conductivity probe in the
solution.

Securely mount the conductivity probe into the flask in the shaker. The speed of
the shaker can be adjusted by turning the MODE SELECT switch to "RPM" and
using the rocker switch with arrows. The shaking action can be turned on or off
without changing the set point using the switch labeled shaker. Never attempt to
add or remove anything to the bath while the shaker is running. Set the shaker
at a speed that allows the probe to obtain an accurate reading by keeping the
solution slightly above the level of the hole on the side of the probe.

Turn on the power to the conductivity meter and begin monitoring the
concentration on the Camile system for your experiment. Make sure that the
slope and intercept for the COND tag are set to your constants from the
calibration curve. You should log your data in intervals of about 30 seconds for
the first 1/2 hour of the experiment and about l/min for next 1/2 hour after that.

Use a wide mouth funnel and ring stand to transfer the beads from the towel to
an erlenmeyer flask and cover it with parafilm. Place the flask in the water bath
to allow it to come to temperature.

Leave the CaCl, solution in the shaker until the Camile indicates that the
concentration is equal to 10 g/l. This lets you know that the probe is responding
properly and that the solution is at the proper temperature for your calibration
curve.

Once the solution has reached the proper temperature, go to the question and
answer screen that asks if you wish to begin logging for the conductivity
experiment. Make sure that the logging period is correct and that it says "yes"
after the question "do you wish to begin logging?". If it does not, use the arrows
to move the cursor onto the box and type over the current answer and hit return.
When you are ready to add the beads press END and logging will begin. Wait
30 seconds after you have pressed the END key and then remove the flask
containing the CaCl, solution and the beads from the bath and add the CaCl,to
the flask containing the beads. Place the probe into the flask containing the beads
and the CaCl2 into the bath.

Make sure that the stopper containing the conductivity probe is securely fastened
and then set the shaker to 350 rpm. Carefully move the flask into the shaker.
Avoid rough handling of the wire connected to the probe.

You may monitor the progress of you experiment by using the on-line trend
screens (F3). You may explore the functions of the Camile at this time as most

12.

13.

126

functions that will harm your experiment are denied access without a password.
Do not change your slope and intercept. An interesting feature of the on line
trending screens of the Camile system is the history trend. The history trend
appears as graph 9 in the on-line trending screens and ean be reached by paging
up or down after hitting F3. The history trend displays the data already logged
into your file. To view a history trend type ”Read” while above graph 9 and then
the cursor will move to the middle of the screen next to the word tagname. Type
in ”cond" and then hit enter. Then the cursor will move to the next row and
which will say log file. Enter 4 and press END. At this point the computer
should begin reading your data from the log file and displaying it on the screen.
If you or another lab group wishes to use the history trend later you must first
type "Clear” and then re-enter the pertinent information.

After you have been logging data for the time you specified on the question and
answer screens, the Camile will automatically stop logging data. To get your log
file off the hard disk for analysis you will have to exit run and use the DATA
subprogram to convert your binary log file into a comma separated value ASCII
file. At this time ask the teaching assistant or the instructor for the password.
Once it has been entered by pressing the F9 key and typing ”LEVEL
ENGINEER" and the password, you may type "BYE” and exit run.

While one of your group members converts the log file into a form suitable for
analysis by the provided program, (directions are given below) at least 20
diameter measurements of the beads must be taken by the other members to
obtain a statistically significant average value.

III. Data Analysis

1.

Use the arrows to move the highlighting to DATA and press ENTER. The

' screen should say "output file typezASCII" and ”Report all time points:yes" then

hit END. A whole list of options will then be provided for you to change.
Highlight a particular selection and then press the space bar to view the various
options and hit ENTER when the option you desire is shown. Make sure you
include comments, tag values, elapsed time, date, and the time of day. The
column delimiter must be a comma for easy retrieval of the log file into a
spreadsheet program. When the appropriate options have been selected, press
END. Highlight the two tag names (COND and CTEMP) and press the space
bar. An arrow should be present on the left of the names and then press END.

The computer will then show the prompt ”EDIT filename: " and your log file title
with a ”.prn" extension will be displayed. Hit END and you will exit DATA and
then press escape to exit the Camile menu.

Import the log file into a spreadsheet as a comma separated value format (CSV).

10.

11.

12.

13.

14.

127

(i.e. \\Import,CSV,\camile\logs\cond.prn). You may do this from SuperCalc4
from cd\bin\sc4 or SuperCalcS (cd\bin\scS).

You will then need to find the time data and convert it from seconds to minutes.
Once the time data has been converted to minutes you must create a file that
contains only the time data in the left hand column and the concentration data in
the right hand column.

You can isolate the data by using the 'lReplicate,Range,Values' command to
copy the cells containing the time and concentration data.

At this point you may delete everything on the spreadsheet except the values of
the time and concentration. Then you will need to move the time and
concentration data to the upper left hand corner making sure that the time is in
column A and the concentration is in column B using the move command (i.e.
\Move,Block,Range). The alternative is to export only the range containing the
copies of the time and concentration data. This can be done using the
"\\Export,CSV,Part,Range" command. The time data and the concentration data
must still be in adjacent columns with the time on the left for this to work.

Record the number of time data pairs in your file along with the filename.

Either obtain a copy of DIFFTR5 or use the copy on the Camile computer to
analyze your data.

To run DIFFI'RS simply type DIFFI‘RS or the path name (i.e. ”cd\diff' then
"difftrS" or "C:\dift\difftr5" for the lab computer).

The computer will then ask you whether you wish to solve case 1 or 2. Enter 1
since you wish to determine the diffusion coefficient from diffusion of solute into
initially solute free spheres.

Then the computer will prompt you for the name of the " .csv" file where you
stored your data and the number of data points. You must enter the name
including the path in single quotes and then follow that with a comma and the
number of points (i.e. ’a:\cond.csv’,10)

The computer will then prompt you for the number of q, values you wish to use.
Six is usually sufficient though you may use more if desired.

The computer will then ask for the radius of the beads in cm. Enter that value -
and press ENTER. The screen will then flash many values across the screen.

When the screen stops scrolling and reports that the program is finished, record

15.

16.

128

the cost, parameter 1, parameter 2, and the 6 or so values that correspond to your
q, values. Parameter l is the effective diffusion coefficient in cm’lmin and

parameter 2 is a.

To obtain a theoretical curve for the solute concentration it is necessary to use
the q, values calculated by the computer. The q, values, a, and D, can then be
plugged into equation 4 to generate the curve.

Plot your experimental data points and the theoretical curve in a fashion similar
to Figure 6.

..-1

3”
4

129

Appendix II. Difftr5: Program for Evaluation of D and a

C
C
C

SUBROUTINE PROC FOR PROGRAM CALLED PATERN

PURPOSE: TO ESTIMATE DIFFUSION COEFFICIENTS BY READING

IN DATA

C

00000

“000

CONTAINING TIME -VS- CONCENTRATION VALUES.

MAIN PROGRAM
PROGRAM CHE46O

IMPLICIT DOUBLE PRECISION(A-H,O—Z)

INTEGER NDATA,NP,NPASS,IO, NED

COMMON C(4000), T(4000), Q(10000),NDATA, x, NQ, R
COMMON NTYPE, x13

DIMENSION P(10), STEP(10)

CHARACTER CONCEN*20

SEARCH INITIALIZATION
P(1)=5.0E—4

P(2)=4.00

STEP(1)=1.0E-5
STEP(2)=0.1

NP=2

NPASS=3

IO=3

READ IN DATA

WRITE(*,*)’WHAT TYPE OF DIFFUSION PROBLEM DO YOU WISH TO’
WRITE(*,*)’SOLVE? ENTER THE NUMBER FOR THE DESIRED TYPE.’
WRITE(*.*)

WRITE(*,*)’1. DIFFUSION FROM LIQUID INTO INITIALLY’
WRITE(*,*)’ SOLUTE FREE SPI-IERES.’

WRITE(*,*)’2. DIFFUSION FROM SPHERES INTO INITIALLY’
WRITE(*,*)’ SOLUTE FREE LIQUID.’

READ(*,"‘) NTYPE

WRITE(*,*)

IF(NTYPE.EQ.1) THEN
WRITE(*,*)’ENTER INITIAL LIQUID CONCENTRATION IN glL’
READ(*,“') x
WRITE(*.*)

130

ELSEIF(NTYPE.EQ.2) THEN
WRITE(*,*)’ENTER INITIAL BEAD CONCENTRATION IN g/L’
READ(*,*) XB
WRITE(*.*)

ELSE
WRITE(*,*)’YOU DID NOT ENTER A 1 OR A 2. TRY AGAIN’
WRITE(*.*)
GOTO 5

ENDIF

WRITE("',*)’ENTER THE NAME OF THE TIME-CONCENTRATION FILE’
WRITE(*,*)’AND THE NUMBER OF DATA POINTS’

READ(*,*) CONCEN, NDATA

WRITE(*,*)

OPEN(UNIT =20,FILE=CONCEN,STATUS = ’OLD’)

WRITE(*,*)’ENTER THE NUMBER OF Q VALUES DESIRED’
READ(*.*) NQ
WRITE(*,*)

WRITE(*,"‘)’ENTER THE RADIUS OF THE BEADS’
READ(*,"‘) R
WRITE(*,*)

WRITE("‘.*)
WRITE(*,*)’CONCENTRATION(g/L) TIMECMIN)’
DO 150 J=1,NDATA
READ(20,*)t(J),C(-I)
WRITE(*.350)C(J).T(J)
FORMAT(6X,F6.2,18X,F6.2)
CONTINUE

START SEARCH

CALL PATERN(NP,P,STEP,NPASS,IO,COST)

SEARCH COMPLETE, PRINT RESULTS
PRINT 300, P(1), P(2), COST

300 FORMAT(F10.3,10X,F10.3)

OPEN (UNIT =30,FILE=’FOR30.DAT’,STATUS=’NEW’)
WRITE (30,300) P(1),COST

131

300 FORMAT(E10.3,5X,F6.3,5X,E10.3)
DO 346 L=2,NQ+1
WRITE (*.*)Q(L)
346 CONTINUE
STOP
END

THIS FILE IS A PAIR OF SUBROUTINES WRITTEN TO BE
COMPATIBLE WITH THE OPTIMIZATION SUBROUTINE PATERN.
THEY SIMULATE A PROCESS USING DISCRETE DIFFERENCE
EQUATIONS AND COMPARE THE SIMULATION OUTPUT WITH
THE ACTUAL OUTPUT (READ IN THROUGH A DATA FILE),
CALCULATING AN ERROR OR ”COST” ASSOCIATED WITH THAT
SIMULATION. PATERN USES THESE SUBROUTINES ITERATIVELY
IN ORDER TO FIND THE OPTIMUM SET OF TRANSFER FUNCTION
PARAMETERS TO FIT THE DATA.

OOOOOOOOOOOOOO

SUBROUTINE PROC(P,COST)

IMPLICIT DOUBLE PRECISION (A-H,O-Z)

COMMON C(4000), T(4000), Q(10000), NDATA, x, NQ, R
COMMON NTYPE, XB

DIMENSION P(IO), STEP(10), CONC(100)

INITIALIZE ARRAYS AND DEFINE PARAMETERS

000

D =P(1)
ALPHA = P(2)
ERROR=0.0
TOTAL=0.0
C
C PURPOSE: TO CALCULATE THE Q VALUES BASED ON THE ALPHA
GIVEN '
C
C
* Program solver
*Solves for the first N solutions of the variable QN given alpha
*USING NEWTON ’8 METHOD
* DEFINE THE FUNCTION F WHICH MUST = 0 TO OBTAIN A QN VALUE
*FP = THEDERIVATIVEOFTHEFUNCTIONF
C
C

132

"' TOLl IS THE CONVERGENCE CRITERION
TOLl = .00000001
* QNOLD IS THE CURRENT VALUE OF QN

QNOLD = 3

NC = l
"‘ ALL OF THE IF STATEMENTS BELOW INVOLVING ALPHA GIVE THE
COMPUTER

* A FIRST GUESS CLOSE TO THE TABULATED VALUES FROM CRANK
IF (ALPHA .LT. .6667) THEN

QNOLD = 4
ENDIF
IF (ALPHA .LT. .4286) THEN
QNOLD = 4.18
ENDIF

* THIS IS THE MASTER LOOP IT IS CONTROLLED BY THE NUIVIBER OF QN
VALUES DESIRED
110 IF (NC .LE. NQ) THEN

FPOLD = 1/((DCOS(QNOLD))**2)-(3 *ALPHA*QNOLD**2
+ -6*ALPHA*QNOLD+9)/((3+ALPHA*QNOLD**2)“2)
FVAL = DTAN(QNOLD)- 3*QNOLD/(3 +ALPHA*QNOLD**2)
IF (FPOLD .EQ. 0) THEN
WRITE (*,*) ’NEWTONS METHOD FAILS’
NC=NQ+1
ELSE
QNNEW=QNOLD-(FVAL/FPOLD)
QNOLD=QNNEW
NED=NED+1
ENDIF
IF (ABS(FVAL) .LT. TOLl) THEN
NC = NC + 1
QNOLD =QNOLD +2
C WRITE 0.120) ’QN’.’F(QN)’.’FP(QN)’
C120 FORMAT (15X,A6,15X,A6,25X,A6)
C WRITE (*,*) QNNEW,FVAL,FPOLD

Q(NC) = QNNEW
WRITE (*3) NC, Q(NC),NED,ALPHA
NED = 0

ENDIF
GOT O l 10
ENDIF

GOO

10

20

40

U)

00

0000

133

CALCULATE COST

IF(NTYPE.EQ.1) THEN
DO 20 J=1,NDATA
DO 10 I=2,NQ+1
TERMI =(6*(1+ALPHA)*EXP(-D*Q(I)**2*T(J)/R**2))
TERM=TERM1/(9+9*ALPHA+Q(I)"2*ALPHA"2)
TOTAL=TOTAL+TERM
CONTINUE
CONC(J) = ((X*ALPHA)/(1 +ALPHA))*(1+TOTAL)
ERR=ABS(C(J)-CONC(J))
ERROR=ERROR+ERR
COST=ERROR
TOTAL=0.0
CONTINUE
GOTO 300
ELSE
DO 30 J=l,NDATA
DO 401=2,NQ+1
TERMl =(6*(l +ALPHA)*EXP(-D*Q(I)*“'2*T(J)/R"2))
TERM=TERM1/(9+9*ALPHA+Q(I)**2*ALPHA"2)
TOTAL=TOTAL+TERM
CONTINUE
CONC(J) = (XB/(l +ALPHA))*(1-TOTAL)
ERR=ABS(C(J)-CONC(J))
ERROR=ERROR+ERR
COST=ERROR
TOTAL=0.0
CONTINUE
ENDIF
RETURN
END

SUBROUTINE BOUNDS(P,IOUT)

IMPLICIT DOUELE PRECISION (A-H,O-Z)
COMMON C(4000),T(4000),Q(10),NDATA, x, NQ, R
COMMON NTYPE, XE

DIMENSION P(1), STEP(1)

IOUT=0

IF(P(1).LT.0.0R.P(2).LT.O) IOUT=1

134

RETURN
END
C
SUBROUTINE PATERN(NP,P,STEP,NRD,IO,COST)
C---THE SIZE OF B1,B2,T,AND S NEED ONLY BE EQUAL TO THE NUMBER
OF PAR
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIIWENSION P(1000),STEP(1000),B1(100),B2(100),T(100),S(100)

 

THE FOLLOWING COMMAND ALLOWS PATERN TO USE AN INTEGER
VARIABLE AS THE THIRD PARAMETER P(3).

GOOD

NSRC =3
P(NSRC) = IDINT(P(NSRC))
C
C----STARTING POINT
L=l
ICK=2
ITTER=0
D05 I=1,NP
B1(I)=P(I)
E2(I)=P(I)
Ta) =P(I)
5 S(I)=STEP(I)*10.
Can-INITIAL BOUNDARY CHECK AND COST EVALUATION
CALL BOUNDS(P,IOUT)
IF(IOUT.LE.0)GOT010
IF(IO.LE.0)GOTO6
WRITE(*,1005)
WRITE(*,1000)(J.P(J).J =1.NP)
6 RETURN
10 CALL PROC(P,CI)
IF(IO.LE.0)GOT011
WRI'I'E(*,1001)I'I'I‘ER,C1
WRITE(*. 1000)(J.P(J)J =1.NP)
Can-«BEGINNING OF PATTERN SEARCH STRATEGY
11 D099 INRD=1,NRD

 

 

 

D012 I=1,NP
12 S(I)=S(I)/10.
C
S(NSRC) = 1.0001
C
IF(IO.LE.O)GOT020

WRITE(*, 1003)

20

135

WRITE(*,1000)(J,S(J),J=1,NP)
IFAIL=0.0

C----PRETURBATION ABOUT T

21

22
23

24

25

30

31
32

33

34
35

D030 I= 1,NP
IC =0
1’0) =T(1)+ 3(1)
IC =IC + 1
CALL BOUNDS(P,IOUT)
IF(IOUT.GT.0)G0T023
CALL PROC(P,C2)
L=L+1
IF(IO.LT. 3)GOT022
WRITE(*,1002)L,C2
WRITE(*.1000)(J.P(D.J=1.NP)
IF(Cl-C2)23,23,25
IF(IC.GE.2)GOT024
3(1) =-S(1)
GOT021
IFAIL=IFAIL+1
P(I) =T(I)
GOTO30
T(I) =P(I)
Cl =C2
CONTINUE
IF(IFAIL.LT.NP)GOTO35
IF(ICK.EQ.2)GOTO9O
IF(ICK.EQ. 1)GOT035
CALL PR0C(T,C2)
L=L+1
IF(IO.LT.2)GOTO31
WRITE(*,1002)L,C2
WRITE(*.1000)(J,T(J),J =1,NP)
IF(Cl-C2)32,34,34
ICK =1
D033 I= 1,NP
B1(I) =B2(I)
P(I) =BZ(I)
T(I) =B2(I)
GOT020
C1 =C2
IE1 =0
D039 I=1,NP
B2(I) =T(I)
IF(ABS(BI(I)-B2(I)).LT. 1.0E-20)IB1 =IE1 +1

39

136

CONTINUE
IF(IB1.EQ.NP)GOTO90
ICK=O
ITTER=TITER+ 1
IF(IO.LT.2)GOTO40
WRITE(*,1001)I'ITER,C1
WRI'I'H'“.1000)(J.T(J)J =1.NP)

C----ACCELERATION STEP

40

SJ=1.0
D045 II= 1,11
D042 I=1,NP
T(I)=B2(I)+SJ*(B2(I)-B1(I))

 

IF(I.EQ.NSRC)T(I)=IDII~IT(T(I))

 

45
46
47

90
91
99

Pa) =T(I)
SJ=SJ-.1

CALL BOUNDS(T,IOUT)
IF(IOUT.LT. 1)G0TO46
IF(II.EQ.11)ICK=1
CONTINUE

D047 I=1,NP
B1(I)=B2(I)

GOT020

D091 1: 1,NP
T(I)=B2(I)
CONTINUE
D0100 I=1,NP

100 P(I)=T(I)

COST=C1
IF(IO.LE.0)RETURN
WRITE("‘,1004)L,C1
WRITE(*.1000)(J.P(J).J=1.NP)
RETURN

1000 FORMAT(3(35X,I7,5X,E13.6/))

1001 FORMAT(//1X13HITERATION NO. ,15/5X,5HCOST= ,E15.6,20X,
1 10HPARAMETERS)

1002 FORMAT(10X3HNO.,I4, 8X5HCOST=,E15.6)

1003 FORMAT(I1X28HSTEP SIZE FOR EACH PARAMETER

1004 FORMAT(1H113HANSWERS AFTER

EVALUATION S //

1 5X5HCOST=,E15.6,20X,18HOPTIMAL PARAMETERS )
1005 FORMAT(1H135HINITIAL PARAMETERS OUT OF BOUNDS

END

,I3 , 2X,23HFUNCTIONAL

Membrane Filtration

Summary

A hollow-fiber system with a molecular weight cutoff of 100,000 and membrane
areaof0.3 m’was usedtoaconcentratecell suspension on. mobilis from 8t030g/l.
The recirculation rate for the hollow-fiber unit was 1000 ml/ min with a pressure drop
and total system operating pressure of 5 psig. The rejection coefficient of the cells was
0.744 at a flux of 31.9 :1; 0.49 IJm2 min. An aqueous blue dextran solution was
concentrated from 0.5 to 1.4 g/l using a spiral ultrafiltration cartridge with a molecular
weight cutoff of 30,000 and membrane area of 0.0929 m’. The spiral cartridge was
operatedatarecirculationrateoflOOOml/minat30psigwithaSpsigpressuredrop
across the cartridge. The blue dextran was concentrated, yielding a rejection coefficient

of 0.872 and a flux of 14.66 l/m2 min.

Introduction

Membrane separations are frequently used in the growing biotechnology industry.
Polymer membranes separate dissolved and suspended material from a pressurized fluid
streams based on molecular size and properties. Substances smaller than the pore size
of the polymer membrane pass through the membrane with the solvent, and larger solutes
are retained by the membrane (Tutunjian, 1985). Two types of filtration exist: dead-end
and crossflow filtration. Dad-end filtration produces a cake that rapidly builds up on

the membrane reducing the filtration rate, while, in crossflow filtration, the fluid moves

137

138
across the surface minimizing the build up of retained particles, as illustrated in Figure
1 (Murkes, 1988).

Crossflow filtration processes are categorized by the size of the particles retained
by the membranes and the pore size. Ultrafiltration (UF) generally relates to species of
molecular weights ranging from 10 to 100 Angstroms in size (500 to 1,000,000 daltons).
Microfiltration refers to pore sizes ranging from 0.01 to 10 microns. Microfiltration is
used to retain suspended particles such as cells, while ultrafiltration is used to remove
macromolecules such as proteins, peptides, and viruses. Reverse osmosis uses even

a
smaller pore sizes that retain salts and only allow water to pass through the membrane

(Imunjian, 1985).

Commercially available membrane geometries are usually classified into two
categories: hollow fibers and flat sheets. Hollow fibers are self-supporting polymer tubes
contained in cartridges. Hollow fibers are able to be backflushcd, facilitating cleaning
and product recovery, but are currently limited to pressures below 40 psi. Flat-sheet
membranes exist inmany forms, including conventional plate-and-frame filters and Spiral
cartridges. Flat sheet membranes may operate at higher pressures but can be diffith
to clean (Tutunjian, 1985).

Membrane filtration can be used to concentrate, diafiltrate, or purify a mixture.
Solutions are concentrated when processing is inconvenient or expensive for a dilute
solution. Diafiltration removes low-molecular-weight solutes, such as salts, from
solution by exchanging them for water through the membrane while retaining the higher-

molecular-weight product.

Suspension

 

139

CL...

I
3 g
.“C .. l—>

—>
;_..
'—>
|—>

Suspension

 

 

 

Filtrate

Filtrate

Crossflow filtration

Dead End filtration

Figure 1. Schematic Comparison of Dead Erd and Crossflow Filtration

140
Purification is the isolation of the final product from other solutes (Tutunjian, 1985).

The advantages of using microfiltration and ultrafiltration for separations over
conventional processes are numerous. Membrane filtration produces a high-purity
filtrate, operates at low temperatures, allowing separation of heat-sensitive products and
minimizing energy costs since no heating is required (Murlres, 1988). Membrane
separations also facilitate other downstream-processing steps. The filtrate is essentially
free of colloids and microorganisms, allowing other purification steps, such as ion-
exchange or affinity chromatography. Since no other chemicals are required for
membrane filtration, later recovery and disposal steps can be avoided (Beaton, 1980).
If the products are retained by the membrane, they may be purified and concentrated in
one step. Products permeable to the membrane are separated with minimal dilution. An
example that uses all of the advantages of crossflow filtration is the concenhation of a
cell suspension. The performance of the membrane is not a strong function of cell size,
and is not dependent upon a density difference between the cells and suspending media,
eliminating the need for flocculating agents (Cheryan, 1986).

Despite its utility, membrane filtration also poses some disadvantages. Low
membrane filtration rates are common, requiring relatively large membrane areas and
therefore substantial capital investment. Technical or economic limitations of the
membranes may exist for the maximum amount of solids that may be retained by the
membrane (Beaton, 1980). Many common anti-foaming agents used in fermentations
adhere to the membrane and rapidly foul it (Murkes, 1988). Crossflow filtration often

damages shear sensitive products, such as mammalian cells or proteins. High viscosity

141
solutions, such as mycelial fungi fermentation broths require large pumping rates to
minimize fouling and concentration polarization to maintain a suitable flux (Cheryan,
1986). Concentration polarization, the formation of a viscous and gelatinous boundary
layer on the surface of the membrane, increases the resistance to flow, lowering the
membrane flux. The membrane flux is maintained at high levels by operating the
membrane using high flow rates that minimize the boundary-layer thickness (McGregor,
1986). In some documented cases, concentration polarization has reduced the flux to 5 96

of the maximum in 25 seconds (Cheryan, 1986).

Theoretical Analysis

The effect of transmembrane pressure difference on permeate flux varies with the
properties of the membrane, the permeate and the solute. In general, the flux is directly
proportional to the pressure difference across the membrane at low pressures and
independent of the pressure difference at high pressures. Mathematical models have been
proposed for both of these regimes.

At low operating pressures the membrane flux may be described by the Hagen-

Poiseuille law for stream-line flow through channels. The form of this relation useful

 

for modeling ultrafiltration is:
= e rzP (1)
8 11 (Ax)
where J = membrane flux

r = channel (mean pore) radius
P = applied transmembrane pressure
p = fluid viscosity

142

Ax = membrane thickness (or pore length)
6 = surface porosity of the membrane

prurewaterisusedas the feed tothe filtration, P = APT. Otherwise, the net driving

force, P, is given by :

P - APT-Art - '(P,-P,)-(rr,-rr,) (2)

where APT = transmembrane pressure drop
Ar = osmotic pressure gradient = f(C,_.)

The osmotic pressure gradient for macromolecules is usually assumed to be small
compared to the transmembrane pressure drop, so P is equal to APT in most cases. The
Hagen-Poiseuille model is based on assumptions of steady state; laminar flow through
the pores; an incompressible, Newtonian fluid; and negligible end effects. It predicts that
flux should be directly proportional to the applied pressure and inversely proportional to
the viscosity. The viscosity at the membrane surface may differ from the bulk fluid
viscosity due to concentration polarization. Flux is directly proportional to pressure only
when concentration polarization is minimized, i.e. when the feed composition is low, the
pressure is low, and at high crossflow velocities (Cheryan, 1986).

The high pressure, mass-transfer controlled regime may be described using film
theory. Figure 2 shows two film resistances in series: the stagnant-liquid boundary layer
and the concentration-polarization layer. The rate of solute transport to the membrane

by convection, 1,, is given by the following equation (Cheryan, 1986):

isa

71' Opt

143

J - JC, (3’

where J, = rate of solute transport by convection, moles (or mass)/time
I = permeate flux, volume! time
C., = bulk concentration of the retained (rejected) solute
The accumulation of high concentrations of solute at the membrane surface results in a
concentration gradient that drives diffusion of the solute back into the bulk solution.
Neglecting axial diffusion, the rate of diffusive transport back into the bulk phase is

given by Fick’s law:

= E (4)
J, Ddx

where D is the diffusion coefficient and dC/dx is the concentration gradient over a
differential element in the boundary layer. At steady state, the two mechanisms of
transport will be equal and equations (3) and (4) can be combined to eliminate 1,. The

resulting equation may be integrated over the boundary layer to give the following result

(Cheryan, 1986):
D g, C (5)
= _. = I: .1
0 1n( C.) 1n( C.)
where k = mass transfer coefficient

6 = film (boundary layer) thickness

C, = gel concentration at the membrane surface

C., = concentration solute in the bulk fluid
This model is valid when flux is independent of transmembrane pressure drop. The flux
is controlled by rate of solute transfer back into the bulk phase. The physicochemical

properties of the fluid control C, and C.,, so increasing the mass transfer coefficient, k

144

concentration
polanzauon

layer

membrane

-:2:3'?'.3:i:1:1:l:3'
'.:.;~;.~._'.:.:.;.
. .....

   
    

.;.;.-..._'.-_.:.§.-, .

conveCtive flow
permeate C

ififfilj‘iiif diffusion

Figure 2. Schematic of Concentration Polarization and Boundary Layer

145

is the only way to increase the flux. The mass-transfer coefficient in increased by
increasing the flowrate, which minimizes the boundary layer. Increasing the operating
pressure of the membrane has only transient effects on the flux since the change in
pressure ultimately affects the boundary layer and the mechanisms of transport into the
bulk phase (Cheryan, 1986). .

The mass-transfer coefficient can be correlated using dimensional analysis by a

correlation of the general form (Cheryan, 1986):

Sh = Ame)" (36)“ 6%)“ (6)

where d. = hydraulic diameter
perimeter)

L = channel length
Sh = Sherwood number = deD
Re = Reynolds number = pudJu
Sc = Schmidt number = u/pD
D = diffusion coefficient
,4 = fluid viscosity
p = fluid density
11 = fluid velocity
a,B,w,A = constants

4(cross sectional area)/(wetted

For tubes and circular cross sections, d. = diameter (d). For slits of width a and height

b, d. is of the form:

ab) (7)
2M+M

 

d,=4(

If a > > b for slits, d. is equal to 2b. For laminar flow with fully developed velocity
and concentration profiles, a and B are zero. The correlation for laminar flow, when Re

<1800,L,, < Lanch > L:

146

Sir - 1.86Re°'”Sc°” (2141,)” (8)

where L, = length required for a fully developed concentration profile
L., = length required for a fully developed velocity profile

The correlation forlaminarflow withL, > Land L, > L:

Sh - 0.664Re°"Sc°'” (db/L)” (9)

For turbulent flow, Re > 4000 the correlation is given by (Cheryan, 1986):

Sh = 0.02311e‘".<rc"-’3 (10)

A third model to describe the pressure-flux behavior of ultrafiltration for both
pressure regimes combines the two previous models. In the pressure-controlled regime

the Hagen-Poiseuille equation shown in Equation (1) can be rewritten as:

 

g BAP, 3 AP, (11)
v R.
where B = membrane permeability coefficient
R. = intrinsic membrane resistance using pure water as the feed

= “/13

The model predicts that the flux is directly proportional to the driving force and inversely
proportional to the resistance. Since the resistances of both the membrane and
concentration polarization are in series, they may be added in the equation as shown

below:

Apr (12)
RM,

J:

 

where R.’ = intrinsic membrane resistance including fouling

147

R, = resistance due to concentration polarization
The resistance due to concentration polarization is a function of the applied pressure,

suchthat:

13
R’Hw,’ (1

where 4) is an empirical constant that reflects the degree of concentration polarization.

Combination of the equations (11), (12) and (13) results in the following:

AP: (14)

J = _I_._
R..+¢AP,.

When R, > R.’ then the flux approaches the value of 1M» (Cheryan, 1986). The flux
will increase linearly with the transmembrane pressure at relatively low fluxes and
pressure drops. The filtration rate may be controlled by adjusting the operating pressure
and recirculation rate is this regime. Upon the formation of a gel by concentration
polarization, the flux becomes relatively insensitive to pressure. The filtration rate in this
regime may be increased by increasing the flow velocity to reduce the thickness of the
concentration polarization and boundary layers. Crossflow velocity has a strong effect
on the flux of systems with particulates, such as bacteria (Tutunjian, 1985).

A batch concentration process removes a volume of permeate, V.,, from a
suspension through the pores of the membrane, decreasing the retentate volume from the
initial value, V., to its final volume, V. The retentate is the fluid that is retained by the
membrane, and the permeate is the fluid that passes through the membrane. The fluid

volumes are related by a simple material balance i.e. V = V° - V,. The membrane pores

148

may hold a significant volume of fluid, so the calculated value of V may not be exactly

equal to the actual final volume (Cheryan, 1986).

Diafiltration removes low-molecular-weight solutes by exchanging them for water

molecules across the membrane. Diafiltration removes the lower-molecular-weight

solutes without affecting the concentration of the higher molecular weight solutes.

Typically, the solutes removed are salts that were used to precipitate proteins out of

aqueous solution (Tutunjian, 1985). The concentration of the removed solute decreases

exponentially as the total volume of water added increases as described by the following

equation:

where

C, - Cgm-VJV) (15)

C, = concentration of removed solute

C3. = initial concentration of removed solute
V., = total volume of water added

V. = initial volume of solution

Purification operates similarly to diafiltration in that smaller molecules are

separated from larger ones. The permeate usually contains the product in purification

operations. The overall recovery, R, is given by the following equation:

where

 

R g VEC, =1- VC (16)
VOCO VOCO

C, = solute concentration in the permeate
C = retentate solute concentration

C. = initial retentate solute concentration
V = volume of retentate

V, = permeate volume

The rejection coefficient, a, is an important variable that characterizes the membrane’s

149
ability to retain the solute. The rejection coefficient may be determined using the

following equation:

C (17)
a = 1 —_£
C
where C = concentration of the solute in the retentate

C, = solute concentration in the permeate
A rejection coefficient value of 1 indicates that the solute is completely retained, while
a = 0 implies that the solute freely passes through the membrane.

The filtration process can be represented in terms of the probability, P, of a solute
passing through the membrane. The value of P is assumed to be constant for most
filtration processes. Solutes that freely pass through the membrane i.e. those with or =
0, have P = 1. Solutes with that are completely retained by the membrane have a P of
zero. The rejection coefficient can be defined in terms of the probability, P, in the

following form:

1
o=l-P (8)

The probability, P, can be defined as the ratio of C, to C. The mathematical model
developed below is derived from a material differential balance and is based on the
volume-concentration ratio, VCR, which is defined below (Cheryan, 1986):

V ' (19)

VCR=-—’
V

The concentration of the solute in the retentate is given by:

20
C-MV ()

where C = concentration of the solute in the retentate
V = volume of the retentate during ultrafiltration
N = number of solute particles in the retentate
Each volume of liquid, AV, that passes through the membrane results in a corresponding
change in the number of solute particles, N, which is equal to AN and is given by

(Cheryan, 1986):

(21)
AN - (C A V)P

Dividing both sides by N, substituting in C = NW, and rewriting it in differential form

yields (Cheryan, 1986):

iv . .42 (II)
N V
Integrating and rearranging:
, (23)
N a K V
Substituting this equation into the expression for C yields (Cheryan, 1986):
(24)

C a KV"’

Putting C in terms of VCR, and defining P in terms of the rejection coefficient yields:

151

C -C,(VCR)° (25’

Thus, a logarithmic plot of C versus VCR should yield straight lines with a slopes of 0.
Deviation from the model suggests solute absorption by the membrane or that the
rejection coefficient of the membrane varies with concentration. The yield, Y, is the
mass of the solute present in the retentate divided by the mass of the solute that was
initially present in the retentate and is given by the following equation (Cheryan, 1986):

CV
C

Y = = (ya-mod (26)

 

.V

Experimental Equipment and Procedure

The equipment used in this experiment included a hollow-fiber cartridge, a spiral
cartridge, two peristaltic pumps, and a spectrophotometer. The hollow-fiber cartridge
was an Amicon H1P100 cartridge (Danvers, MA) with a molecular weight cutoff of
100,000, and a membrane area of 0.3 m1 which consisted of 55 1.1 mm inner diameter
fibers. The spiral cartridge was an Amicon SlY30 cartridge with a molecular-weight
cutoff of 30,000 and a membrane area of 0.0929 m’. The pumps used were both
Masterflex Model 7523-00 peristaltic pumps (Chicago, IL). The spectrophotometer used
for concentration determinations was a Perkin Elmer Lambda 3A (Norwalk, CT). The
hollow-fiber and spiral cartridge were attached to the pumps as shown in Figures 3 and

4.

152

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154
The cell concentration was measured spectrophotometrically at 770 nm based upon

the calibration curve for dry weight versus O.D. shown in Figure 5. The blue dextran
concentration was also determined spectrophotometrically at 660 nm, and the calibration
curve for blue dextran at 600 nm is shown in Figure 6. The time, volume of permeate,
and the volume of retentate were recorded as the liquid level reached the volume
gradations in the retentate reservoir. The permeate volume was monitored by collection
in a graduated cylinder. Samples of about 3 ml were removed from both the permeate

and the retentate whenever volumes were recorded.

Results and Discussion

The data were analyzed in terms of the volume-concentration-ratio theory and the
flux. The fits for the concentration and yield data to the VCR theory for the hollow-fiber
and spiral cartridges are shown in Figures 7 and 8 respectively. Linear regression
yielded rejection coefficients of 0.873 d: 0.024 for the cells and 0.744 :1; 0.019 for the
blue dextran with correlation coefficients of 0.992 and 0.995 , respectively. The fluxes
were determined from the slope of a plot of permeate volume versus time divided by the
membrane area as shown in Figures 9 and 10. After an initial adjustment period of
about 6 seconds, the flux in both cases became constant, yielding lines with correlation
coefficients of 0.999 for the hollow-fiber and 0.991 for the spiral cartridge. The flux for
the hollow fiber was 31.9 :L- 0.48 l/rn2 min, and the flux for the spiral cartridge was
14.66 :1: 0.68 l/m2 min.

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161
Conclusions and Recommendations

The experiment demonstrated the application of microfiltration for concentration
of cell suspensions and ultrafiltration for concentration of blue dextran and other polymer
solutions. The two systems studied were fit by the VCR model well. The high
correlation coefficients determined for the concentration versus VCR data indicated that
the rejection coefficients remained relatively constant for both the cells and the blue
dextran, validating the use of the VCR model.

Further experiments using a series of recirculation rates and pressure drops should
allow modeling of the dependence of the flux on the operating pressure and recirculation
rate. The experiments are of relatively short duration, so several runs can be performed

with different operating conditions.

Constants

6 = film (boundary layer) thickness

Ar = osmotic pressure gradient

a,fl,0,A = constants

APT = transmembrane pressure drop

Ax = membrane thickness (or pore length)

6 = surface porosity of the membrane

a = fluid viscosity

p = fluid viscosity

p = fluid density

0 = empirical constant reflecting the degree of concentration polarization
B = membrane permeability coefficient

C = concentration of the solute in the retentate

C., = bulk concentration of the retained (rejected) solute
C, = gel concentration at the membrane surface

C,II '2 retentate concentration at the membrane surface
Co = initial retentate solute concentration

C, = solute concentration in the permeate

C, = concentration of removed solute

Ca, = initial concentration of removed solute

162

D = diffusion coefficient
dC/dx = concentration gradient over a differential element in the boundary layer
d. = hydraulic diameter = 4(cross sectional area)l(wetted perimeter)
J = permeate flux, volume/time
J, = rate of solute transport by convection, moles (or mass)/ time
k = mass transfer coefficient
L - channel length
I.c - length required for a fully developed concentration profile
L, - length required for a fully developed velocity profile
N — number of solute particles in the retentate
P - net driving force for an ideal membrane
r = channel (mean pore) radius
Re= Reynolds number = pudJu
R. = intrinsic membrane resistance using pure water as the feed = “/8
R.’ = resistance of the membrane including fouling
R, = resistance due to concentration polarization = «MPT
Sc = Schmidt number = u/pD
Sh = Sherwood number = deD
u = fluid velocity
V = volume of the retentate during ultrafiltration
V. = total volume of water added
= final volume of the permeate
V, = initial volume of retentate solution
V, = permeate volume

References

Bailey, LE. and Ollis, D.F.(l986) Biochemical Engineering Fundamentals, pp. 100-130,
McGraw-Hill Book Co., New York pp. 726 -.

Beaton, N. C., "The Application of Ultrafiltration to Fermentation Products“, Polymer
Science and Technology, Volume 13. Ultrq'iltration Membranes and Applications,
Plenum Press, New York, 1980, pp. 381 -385.

Cheryan, Munir, Ultrqfiltration Handbook, Technomic Publishing Co. , Lancaster,
Pennsylvania, 1986, pp. 74-120, 280-284.

Meireles, Martine, Pierre Aimar, and Victor Sanchez, " Albumin Denaturation During
Ultrafiltration: Effects of Operating Conditions and Consequences on Membrane
Fouling,” Biotechnology and Bioengineering, vol. 38, pp. 528-534, 1991.

163

McGregor, W. Courtney, ed. , Membrane Separatioru' in Biotechnology Marcel Dekker,
Inc., New York, 1986, pp. 61-79.

Murkes, Jakob, and Claes-Goran Carlsson, Crouflow Filtration: Theory and Practice,
John Wiley and Sons, New York, 1988, pp.l-3,

Tutunjian, Robert S. , ”Scale-up Considerations for Membrane Processes“ , Biotechnology,
vol 3, July 1985, pp. 615 - 626.

164

Appendix
Equipment and Reagents Needed:

cells

hollow-fiber apparatus

CoCl;

Blue Dextran (M.W. 100,000)
polymeric disposable membrane with 30,000 MW cutoff

spectrophotometer
1. Calibration of the Peristaltic Pump

1.

2.

Disconnect the pump from the filtration apparatus.

Turn the pump on to forward and adjust the flow rate until the display reads the
desired flowrate.

Measure the flow rate using a graduated cylinder and a stopwatch for about 5
minutes to determine the flow rate.

If the measured flow rate does not match the flow rate on the display, adjust the
calibration screw with a screwdriver until the display reads the measured
flowrate.

II. Determination of Pure Water Flux

1.

3.

4.

Loosen the knob at the top of the reservoir and pull off the lid. Flush the
appropriate membrane with water and refill the reservoir.

Setthepumpatthefirstflowrateandtheappropriatepressuredropforeach
membrane type (see the instructions for each type below).

Place the permeate line in a large graduated vessel.

Record the time and permeate volume for the water.

111. Concentration of Blue Dextran from a Mixture

1.

Develop a calibration curve by measuring the absorbance of blue dextran at 660
or 650 nm for several known concentrations ranging from O to 2 gll.

Flush the membrane and determine the pure water flux for your first flow rate
and pressure drop.

Loosen the knob at the top of the plexiglass reservoir for the to remove the lid.

10.

ll.

12.

13.

14.

15.

165
Remove the lid and pour the blue dextran mixture into the tank.

Openthevalveatthebottomofthetankbyturningthehandlesothatisinline
withthetank.

Placetheendofthepermeatelineinagraduatedvesseltocollectthewaterthat
flows through the membrane.

Make sure that the backpressure valve at the top of the spiral filter cartridge is
fully open (in line with the pipe).

Makesurethatthepumpissetfortheappropriate tubingsize(18), andtumon
the pump by flipping the switch to ’forward’. Set the flowrate somewhere
between 800 and 1,800 ml/min.

Slowly close the backpressure valve until the pressure on the top gauge rises to
about 30 psi. Always make sure that the lower pressure gauge is no more than

4psihigherinpressurethattheuppergauge,orthefiltermaybedarnaged.

Record the time, pressures, absorbance, and volume of both the permeate and the
retentate at regular intervals.

When the concentration is complete, drain the fluid from the cartridge. The tank
can be drained by disconnecting the tubing which feeds the pump. Once the tank
is empty, the pump can be used to move air through the mrtridge to remove
excess process fluid.

Refill the tank with reverse osmosis (R0) water and run the system with a low
backpressureatahighpumpingratekecping thepressurebelow 8psi.

DrainthewaterandrefillwithcleanROwaterandrunthepumpinreverse
mode.

Determine the pure water flux, re-dilute the retentate, and then restart the
experiment at a different flow rate or pressure drop.

Aftereach flowrateflush thesystemwithwateranddeterminethepurewater
flux.

Flush the membrane thoroughly after the final run, and clamp off the filtrate tube
and store wet. Ifthe filter is to be stored for the weekend add a small amount of
sodium azide solution or other bacteriostatic agent to the reservoir and recirculate
it through the filter. Wear gloves when handling bacteriostatic agents since they
are poisonous and label the filter and reservoir clearly after it is added to the

166

system. Do not pour sodium azide down the drain as an explosive reaction may
take place.

IV. Concentration of Cells using Hollow Fibers.

1.

10.

Obtain the cell culture that was saved form the previous fermentation experiment
or the culture that was prepared for this experiment. Filter sterilize 2-3 ml of
fermentation broth to produce a cell free blank for absorbance readings. Swirl
the suspension until it is uniform, remove 2-3 ml of cell suspension, place in a
cuvette, and record the absorbance at 660 or 710 nm using the cell free broth as
a blank.

Loosen the knob at the top of the plexiglass reservoir for the to remove the lid.
Remove the lid and pour the cell suspension into the tank.

Openthevalveatthebottomofthetankbytumingthehandlesothatisinline
withthetank. ‘

Placetheend ofthepermeatelineinalargegraduatedcollection vesselthathas
sufficient volume to collect the filtered broth that permeates the membrane.

Make sure that the backpressure valve at the top of the hollow-fiber cartridge is
fully open (in line with the pipe).

Makesurethatthepumpissetfortheappropriatetubingsize(18),andtumon
the pump by flipping the switch to ’forward’ . Set the flow rate somewhere
between 800 and 1,800 ml/min.

Slowly close the baclqiressure valve until the pressure on the gauge rises to about
8 psi.

Note the time and record the pressure, absorbance and volume of both the
perrneateandtheretentateatregularintervals. Notethatthepressureofthe
filtrate is atmospheric, so obtain a barometer reading from the lab downstairs
(rm. 287).

When the concentration is complete, drain the fluid from the cartridge. The tank
can be drained sliding the tubing that feeds the pump ofl’ the nozzle on the tank.
Once the tank is empty, air can be pumped through the cartridge to remove
excess process fluid by turning on the pump.

Refill the tank with reverse osmosis (RO) water, and run the system with a low
backpressure at a high pumping rate but not in excess of 8 psi.

ll.

12.

14.

15.

167

Re-dilute the retentate with the permeate and repeat the experiment at a different
flowrateorpressuredrop. KeepthepressuredropbelowSpsig.

Repeat steps 10, 11, and 12 after each run.

DrainthewaterandrefillwithcleanROwaterandrunthepumpinreverse
mode.

Clamp off the filtrate tube and store wet.

 

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