Microelectrode measurement of local mass transfer coeffecient in biofilms
by Shunong Yang
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Environmental Engineering
Montana State University
© Copyright by Shunong Yang (1995)
Abstract:
Recent studies revealed that biofilm structures are heterogeneous. The immediate consequence of this
structural heterogeneity is the non-uniformity of local mass transfer processes in biofilms. So far, no
theoretical or experimental approach has been provided to describe it.
This thesis presents an experimental technique to measure local mass transfer coefficients in biofilms.
Local mass transfer rates in an aerobic biofilm was measured using a limiting current technique in an
electrochemical microsink formed by a mobile microelectrode. Viable cell count and time-lapse
photography results show that the technique is applicable to biofilm system. Local mass transfer
coefficients calculated from the measured limiting current varied both horizontally and vertically in the
biofilm. Mapping of the biofilm with the electrode verified the existence of an irregular biofilm
structure comprised of microbial clusters surrounded by torturous water channels. Unexpected
increases of local mass transfer coefficient within 300 ¨m above biofilm surface suggested the existence
of local turbulence in this region. As expected, the influence of bulk flow velocity on the local mass
transfer rate decreased with increasing depth into the biofilm. Mass transfer coefficients fluctuated
significantly inside biofilm cell cluster, suggesting the existence of internal channels. A new conceptual
model of biofilm cell cluster structure is proposed to account for such biofilm microstructure
irregularities.
The limiting current technique was also used to measure local shear rate on microelectrode surface. A
flow field model on the surface of circular-disk microelectrode was developed to describe the
relationship between local mass transfer coefficient and local shear rate. Initial results show that local
shear rate on the microelectrode surface increases exponentially with the increase of bulk flow
velocity. 
MICROELECTRODE MEASUREMENT OF LOCAL MASS TRANSFER
COEFFICIENT IN BIOFILMS
by
Shunong Yang
A thesis submitted in partial fulfillment 
of the requirements for the degree
of
Master of Science 
in
Environmental Engineering
MONTANA STATE UNIVERSITY 
Bozeman, Montana
March, 1995
ii
APPROVAL 
of a thesis submitted by 
Shunong Yang
This thesis has been read by each member of the thesis committee and has 
been found to be satisfactory regarding content, English usage, format, citations, 
bibliographic style, and consistency, and is ready for submission to the College 
of Graduate Studies.
4„/£ r, IM i_____________
Date Chairperson, Graduate Committee
Approved for the Major Department
Date
/f (phod
O '
\
Tie ad, Major Department
Approved for the College of Graduate Studies
YMlIlL
Date Graduate Dean
iii
STATEMENT OF PERMISSION TO USE
In presenting this thesis in partial fulfillment of the requirements for a 
master’s degree at Montana State University, I agree that the Library shall make 
it available to borrowers under rules of the Library.
If I have indicated my intention to copyright this thesis by including a 
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consistent with “fair use” as prescribed in the U.S. Copyright Law. Requests for 
permission for extended quotation from or reproduction of this thesis in whole or 
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Signature
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iv
ACKNOWLEDGMENTS
First I would like to express my gratitude to my academic and. research 
advisor Dr. Zbigniew Lewandowski for his guidance and support. I would also 
like to thank Dr. Warren Jones, Dr. Phil Stewart and Dr. Al Cunningham for 
serving as my thesis committee members. Dr. Frank Roe was appreciated for 
proof-reading this thesis.
Along every step, my wife, Yibin, is always there with me. I would like to 
thank her for her love and support. Thanks a|so to my parents and other family 
members for their love and care.
In the past two and one-half years, my life cannot be so joyful without the 
support and sharing from all my friends, Mark, Duy, Dong, Grace, Xiaoming, 
Ricardo, and many others.
My research has been sponsored by the National Science Foundation and 
the Associates of the Center, my thanks to them.
VTABLE OF CONTENTS
Page
LIST OF TABLES.......... ............................................................................  ix
LIST OF FIGURES ................................................................................... x
ABSTRACT ...............................................................................................  xii
INTRODUCTION ......................................................................................  1
THEORY .................................................................................................... 7
Mass transfer coefficient calculation ............................................  7
Calculation of shear rate on electrode surface ........................... 9
Mathematical model .................................................................  10
Solutions ........... ........................................................................  11
MATERIALS AND METHODS ............................................................15
Biofilm growth ............................................................... ................  15
LOT experimental setup ...............................................................  16
Electrodes and electrolyte solution .......................................  16
Gravitational flow setup .........................................................  18
LOT applicability tests ..................................................................  18
Measuring Fe(CN)63" concentration in biofilms ..................... 19
Measuring limiting current at various Fe(CN)63'
concentration.............................................................................  19
Monitoring biofilm structure ............  19
Local mass transfer coefficient measurements..................... ......  20
Measuring vertical profiles of local mass transfer
coefficient.....................................................   20
Measuring horizontal distributions of local mass transfer
coefficient ................................. ;............................ ................  22
Combination of CSLM velocimetry and LCT
measurements...........................................................................  24
RESULTS ................................................................................................  26
Fe(CN)63' concentration distribution of in biofilms .....................  26
Independence of mass transfer coefficient on Fe(CN)63"
concentration ................................   26
Biofilm structure and viability ............................    26
Vertical profiles of local mass transfer coefficient ...................  27
3%calcium alignate layer ...............................................    27
Biofilms ....................................................................................  28
Horizontal distribution of local mass transfer coefficient ........  29
Mass transfer coefficient at various flow velocities ................. 29
vi
Vertical profiles of local velocity and mass transfer coefficient
in biofilm void ............................      30
DISCUSSION ......................... :.............................................,........... 43
Experimental conditions influencing mass transfer
coefficient.....................................................................................  43
Microelectrode cleaning ....................................................  43
Reacting electrolyte selection ...........................................  44
Applicability of LCT to biofilm system .....................................  45
Estimation of measurement errors on mass transfer
coefficient ..............................        46
Possible error in measuring sensing area of
microelectrode ...............................    46
Possible error in measuring bulk Fe(CN)63"
concentration .........................................................................  47
Possible error in measuring limiting current ........    47
Other possible error .......................................................   47
Influence of convective flow velocity on mass transfer
coefficient ..........................   48
Analysis of horizontal distribution of local mass transfer
coefficient ....................................................................   49
Secondary structural heterogeneity of biofilms ......................  51
vii
Local shear rate on microelectrode surface ............................. 53
Correlation of local flow velocity and local mass transfer
coefficient .......................................................................................  54
SUMMARY .............................................   60
RECOMMENDATION FOR FUTURE RESEARCH ..........................  62
REFERENCES .........................      63
NOMENCLATURE ...........   69
yiii
APPENDIX 71
Table
1.
2 .
ix
LIST OF TABLES
Page
Viable cell counts of the biofilm under LCT measurement
condition .......................................................... ...................... 27
Analysis of horizontal distribution in Fig. 10 ..................... . 50
XLIST OF FIGURES
Figure Page
1. The existing steady-state biofilm model ...........................  2
2. Flow field model on the surface of circular-disk
microelectrode ..................................................................... 10
3. Relationship between Peclet number and Sherwood
number for circular-disk microelectrode .....   14
4. The schematic diagram of LCT experimental setup ....... 25
5. Mass transfer coefficient vs. Fe(CN)63" concentration ..... 32
6. Vertical profile of mass transfer coefficient through a
alginate layer ............................................................    33
7. Vertical profile of mass transfer coefficient through a
alginate layer ........     34
8. Vertical profiles of local mass transfer coefficient taken
in a biofilm void (a) and through a biofilm cluster (b) ..... 35
9. Vertical profiles of local mass transfer coefficient measured
at two different locations in the same biofilm cluster ....  36
10. Horizontal distributions of local mass transfer coeffocient
at V= 1.59cm/sec 37&38
xi
11. Horizontal distributions of local mass transfer coefficient at
z=50 gm under various flow velocity................................... .....  39
12. Influence of bulk flow velocity on horizontally averaged mass
transfer coefficient at z=50 |im ................................................ 40
13. Influence of bulk flow velocity on horizontally averaged mass
transfer coefficient at three vertical depths .... i..................... 41
14. Vertcal profiles of local flow velocity and local mass transfer
coefficient in a biofilm void ..... .................................... ........... 42
15. Vertical profile of horizontally averaged mass transfer
coefficient through a biofilm cluster .......................................  55
16. Vertical profile of horizontally averaged mass transfer
coefficient for a 200 jim high biofilm cluster ......................... 56
17. Proposed structural model of biofilm clusters .....................  57
18. Relationship between local shear rate on circular-disk
microelectrode and bulk flow velocity ..................................  58
19. Correlation between local mass transfer coefficient and
local flow velocity in a biofilm void ........................................  59
xii
ABSTRACT
Recent studies revealed that biofilm structures are heterogeneous. The 
immediate consequence of this structural heterogeneity is the non-uniformity of 
local mass transfer processes in biofilms. So far, no theoretical or experimental 
approach has been provided to describe it.
This thesis presents an experimental technique to measure local mass 
transfer coefficients in biofilms. Local mass transfer rates in an aerobic biofilm 
was measured using a limiting current technique in an electrochemical microsink 
formed by a mobile microelectrode. Viable cell count and time-lapse photography 
results show that the technique is applicable to biofilm system. Local mass 
transfer coefficients calculated from the measured limiting current varied both 
horizontally and vertically in the biofilm. Mapping of the biofilm with the electrode 
verified the existence of an irregular biofilm structure comprised of microbial 
clusters surrounded by torturous water channels. Unexpected increases of local 
mass transfer coefficient within 300 |im above biofilm surface suggested the 
existence of local turbulence in this region. As expected, the influence of bulk 
flow velocity on the local mass transfer rate decreased with increasing depth into 
the biofilm. Mass transfer coefficients fluctuated significantly inside biofilm cell 
cluster, suggesting the existence of internal channels. A new conceptual model 
of biofilm cell cluster structure is proposed to account for such biofilm 
microstructure irregularities.
The limiting current technique was also used to measure local shear rate 
on microelectrode surface. A flow field model on the surface of circular-disk 
microelectrode was developed to describe the relationship between local mass 
transfer coefficient and local shear rate. Initial results show that local shear rate 
on the microelectrode surface increases exponentially with the increase of bulk 
flow velocity.
1INTRODUCTION
Steady-state biofilm models 9' 32, 33 commonly assume that internal mass 
transfer (inside biofilms) is diffusion controlled and that external mass transfer 
(outside biofilms) is dominated by convection. Consequently, it is believed that 
the diffusivity is the only parameter needed to describe mass transfer rate inside 
biofilms. Mass transfer and reaction are thus incorporated into a mass balance 
equation as follows:
r j ’d2^  _ C1Cx m
dZ2 Kc + C
The mass transfer rate from the bulk fluid to the biofilm surface is commonly 
approximated by assuming that the mass boundary layer above the biofilm
I
surface is uniform and stagnant. Thus, the flux across the external mass transfer 
layer is treated as a boundary condition and can be expressed as
J = D x  = k x  AC ' (2)
o
A descriptive diagram of the existing biofilm steady state model is shown in 
Fig. I.
2______C0
External mass transfer: 
mass transfer coefficient 
k=D/8
Internal mass transfer: 
diffusivity-D
Substratum<— j< *3'0^ r^n-------------->|<->|------------>.bulk
external mass 
transfer resistant 
layer
Fig. 1 The existing steady-state biofilm model 
This simple mass transport model in biofilms has been challenged by the 
observations of Light Microscopy (LM )31119, Atomic Force Microscopy (AFM)2, 
Scanning Electron Microscopy (SEM)7'26, and Confocal Scanning Laser 
Microscopy (CSLM)5'6'39. Recent studies by CSLM reveal that the structures of 
aerobic biofilms are not uniform but consist of microbial cell clusters separated 
by interstitial voids. According to this concept, mass transport in interstitial voids 
is mainly facilitated by convective flow while mass transfer inside microbial 
clusters is entirely due to molecular diffusion. Therefore, the mechanism of local 
mass transport is determined by the structural heterogeneity of biofilms.
3Consequently, mass transfer rates can no longer be considered the 
same at different locations in a biofilm due to variable porous structure and 
subsequent reactivities that vary in space. Rather, mass transfer rates depend 
on complex interactions among local biofilm activity, structure, and 
hydrodynamics. The situation is even more complicated because that biofilms 
are viscoelastic and microscale hydrodynamics near such surfaces has not been 
characterized analytically. Since there is no adequate mathematical model 
describing mass transfer in a growing three dimensional irregular structure, it is 
necessary to study the mass transfer rate inside heterogeneous biofilms 
experimentally.
A few attempts have been made to describe the relationship between 
biofilm structure and hydrodynamics..Lewandowski et a /21 described liquid flow 
in a biofilm reactor using Nuclear Magnetic Resonance Imaging (NMRI) with 
limited spatial resolution. De Beer et a l6 and StoodIey et a l39 measured liquid 
flow velocity in biofilm voids by using Particle Image Velocimetry (PIV) which 
traces the horizontal movement of fluorescent beads in the voids of biofilms 
using CSLM. While these papers quantify factors influencing mass transport rate, 
none of them provides the means to actually measure it.
This thesis describes measurements of local mass transfer coefficients in 
biofilms using a modified Limiting Current Technique (LCT).. LCT uses a particular 
electrochemical reaction that proceeds at the highest possible rate on an electrode
surface. Under mass transfer limiting conditions, the magnitude of electrical current 
measured in the external circuit depends only on the mass transfer rate and is 
directly proportional to the mass transfer coefficient to the electrode.
Historically, Lin e ta l22 made a systematic study of mass transfer rates of ions 
and other reacting species in electrochemical processes and measured the mass 
transfer coefficients in laminar and turbulent flows using LCT. Ranz29 discussed 
problems associated with applying LCT to liquid flow velocity measurement.
Mitchell and Hanratty13,24 developed LCT into a wall shear-stress meter and used 
it in the study of turbulence at a wall. D.A.Dawson and O.Trass4 used LCT in the 
study of mass transfer rates at rough surfaces. The basic principle and 
applications of the conventional LCT were reviewed in several publications25'35'41.
This well-known technique was also used to study local mass transfer rates 
8,16,17,18,3410 f|at surfaces. The electrodes used were flush mounted to the 
reactor's wall. Sizes of electrodes range from several hundred micrometers to a 
few centimeters.
Our application of LCT is different from the conventional method in two 
aspects: (1) the microelectrode used here was mobile and could be positioned at 
any location in biofilms; (2) the size of the electrode was reduced to a few 
micrometers to prevent damaging the biofilm structure and disturbing the 
hydrodynamics.
5The tip of the microelectrdde formed a microsirik for the electroactive 
species purposely added to the reactor. Measured limiting current was directly 
proportional to the local mass transfer rate at the tip of the microelectrode. The 
magnitude of the limiting current was dependent on a combination of all factors 
influencing the local mass transfer rate, e.g., the local hydrodynamics and the 
local structure of the biofilms. Consequently, the local mass transfer coefficient 
calculated from the measured limiting current to the microelectrode is related to 
the local effective diffusivity that is a function of local hydrodynamics and local 
biofilm structure.
Hydrodynamic flow in biofilm reactors does not just influence mass transfer 
rate. Another important aspect of its influence is on biofilm shearing, i.e., the loss 
of biomass from biofilm reactor as a result of shear forces. The mechanism of 
shearing loss is still unknown due to its complexity. Because of differences in 
time scale and types of biofilms and reactors investigated, some completely 
contradictory results have been drawn from various studies. Gantzer et a/10 
concluded that higher biomass levels in streambed biofilms were found at the 
faster acclimation velocities. Lau and Liu20 discovered that biofilm biomass 
accumulation was substantially reduced as flow shear stress increased and that 
the maximum accumulation occurred under very low flow conditions. To 
understand the mechanism of biofilm shearing loss, it is very important to 
measure local shear stress on biofilm surface under the defined hydrodynamic
6condition and correlate local shear stress data with biofilm acumulation or biofilm 
detachment. LCT is a potential tool for acquiring such information. Besides 
measuring local mass transfer coefficient, application of LCT has been extended 
by Hanratty et a l12 to measure wall shear stress on the surface of sensing 
electrodes. With a hydrodynamic model for the flow field on the surface of an 
electrode, the relationship between wall shear stress and mass transfer 
coefficient can be established. A flow field model and its solutions for the 
circular-disk microelectrode will be discussed in the next chapter.
7THEORY
Mass transfer coefficient calculation
During LCT measurement, the ions reacting on the sensing electrode are 
transferred from the bulk of the solution to the surface of the electrode principally 
by (a) migration due to the potential field, (b) diffusion due to the concentration 
gradient, and (c) convective flow. Fe(CN)63" is one of the commonly used reacting 
species in LCT. The electrochemical reduction of Fe(CN)63' occurs on the surface 
of the microelectrode as
+g--4»Fg(CAD6^ (3) .
By adding an excess amount of non-reactive supporting electrolyte, e.g., KCI, to 
the electrolyte solution, there should be little potential gradient formed near 
electrode surface. Thus, the electromigration process becomes negligible and 
almost all of the electrolyte current arises from the reaction of ions that reach the 
electrode surface by diffusion and/or convection. The flux of the reacting species 
onto the electrode surface is related to mass transfer coefficient, k,
J = Mc0-Cs) (4)
8
I
By increasing the polarization potential, the current will increase until the 
concentration of Fe(CN)63" at the electrode surface reaches zero (Cs=O). The 
current corresponding to a zero surface concentration of the reacting species is 
called “the limiting current." The flux of ferricyanide ion, J, to the surface of the 
microelectrode with sensing area A is related to the limiting current, I
The relation between mass transfer coefficient and limiting current can be found 
by combining Eqn. (4) and (5) for Cs=O
k  =  — - —  (6)
nAFCo
With the elimination of migration effect, the information obtained from LCT 
can be applied to non-electrochemical process. Furthermore, the analogy 
between heat and mass transfer becomes valid as discussed by A ga r1. Thus 
mass transfer results obtained by LCT may be correlated with the knowledge of
heat transfer.
9Calculation of shear stress /t) at the electrode surface
As pointed out in the previous chapter, LCT has a potential application in 
investigating local shear stress in biofilm reactors. To obtain local shear stress, a 
flow field model on the microelectrode surface has to be established.
Due to the fabrication capability and experimental convenience, the tip 
surface of the microelectrode used in this study was a circular disk with its 
diameter on the order of a few micrometers. The flow field on the surface of 
circular-disk microelectrode is illustrated in Fig. 2.
The basic assumptions implied in this figure are:
(a) the scalar boundary layer is within the region where V=Sz;
(b) the flow is homogeneous over the electrode surface;
(c) the velocity components other than in the Z-direction are negligible.
Generally, for large Sc and small A, the concentration boundary layer over
the microelectrode will be so thin that it lies within a region in which the velocity 
field is a simple shear flow with a constant shear rate.
Theoretical issues of above assumptions have been discussed in detail by 
Phillips27, Hanratty and Campbell13 and Stone 38.
10
Mathematical model
The steady-state mass balance equation on the electrochemical reacting 
species for the described flow field can be written as
DV2C = (7)
oX
sensing area
insulation glass
V=Sxz
X
Fig. 2 Flow field model on the surface of circular-disk microelectrode
The boundary conditions are 
C=O for z=0, (j) = r
11
—  = O for z=0, (b > r 
- dZ
C = C0 as(x2 + y2 + Z2 ) 1/2 °°
The equation can be written in terms of dimensionless form
V^e = (8)
By solving the mass balance Eqn. (8), The relationship between 
dimensionless mass transfer coefficient, Sb, and dimensionless shear rate, Fe, 
can be established.
Solutions .
Analytical solution by Reiss and Hanratty30: By neglecting diffusions in X- 
and Y-directiohs, Eqn. (8) is simplified
329
dn2
= Pex\ 30 (9)
Eqn. (9) was solved analytically and a relation between Sherwood number and 
Peclet number was obtained
5% = O.d&dJ&fg", + (10)
12
or the shear rate can be calculated explicitly from S=1.45649xkxr1/3xD"2/3. The 
numerical solution obtained by Stone 38 for Eqn. (8) shows that the error in using
I
Eqn. (10), because of neglecting diffusions in X- and Y-directions, is less than 
5% for Pe>400. The high Pe situation can be encountered when sensor diameter 
is big, and/or velocity gradient is large, and/or diffusivity of reacting species is 
small.
Analytical solution by Phillips27: The limitation of using Eqn. (10) lies in its 
one dimension diffusion assumption. Generally, the diffusion problem is fully 
three dimensional or the edge effect cannot be neglected. By using the method 
of matched asymptotic expansions, Phillips solves Eqn. (8) analytically. The final 
solution is written as
= 4-0.11268 Pem }
n i l -0.20281 Pela)
Results calculated from Eqn. (11) were compared with Stone's numerical 
solutions. Both results agree within 2% from Pe=O-OOI up to Pe=2. The smallness 
of Pe means that on the scale of microelectrode surface, convection, represented 
by the right-hand side of Eqn. (8), is weak. It results in a small perturbation of a 
purely diffusive solution. This solution is applicable when the microelectrode is 
used in low velocity flow.
13
Numerical solution by Stone 38: Numerically, Stone evaluated the mass 
transfer rate over a wide range of Peclet numbers (0.001 <Pe<4Q0.Q). Without 
making, additional assumption to the problem represented in Eqn. (8), Stone used 
one of the boundary integral methods to calculate overall mass transfer rate at 
different Pe values. By performing the regression on his numerical results, Stone 
proposed a correction term for Eqn. (10) at high Peclet number (Pe>10). The new 
equation is written as
Sh = 0.68658 Pe1/3 +1.13000 Pe1/6 (12)
The results calculated from this equation have good agreement with the 
numerical solution in the high Peclet number range (10<Pe<400).
To calculate Peclet number from Sherwood number, or shear rate from mass 
transfer coefficient, for a wide range of Peclet numbers (from 0.001 to 400), it will 
be very convenient to have a single analytical formula that applies to the entire Pe 
range. Eqn. (11) fits the numerical solution very well up to Pe=2 and results given 
by Eqn. (12) lie within 3% of the numerical solution for Peclet numbers as low as 
10. By fitting the data provided by Eqn. (11) from Pe=0.001 to 2 and Eqn. (12) from 
10 up to 400, we generated Eqn. (13) that is valid Pe from 0.001 to 400. A curve 
fitting software, TabIeCurve 2D of Jandel Scientific, was used.
■J¥e = -20.5 + 40.3 x Sfc -  31.7 x Sh2 +12.9 X Sfc3 -  2.47 x Sfc4 + 0.183 x Sfc5 (13)
Solutions of Eqnsi (11), (12), and (13) are presented in Fig. 3.
Pe
cl
et
 N
um
be
r
14
from Eq.(13)
■ from Eq. (11 & 12)
0.001
2 2.5 3
Sherwood Number
Fig. 3 Relation between Peclet number and Sherwood number for a 
circular-disk microelectrode
15
MATERIALS AND METHODS
Biofilm growth
The open channel biofilm reactor used in this research was made of 
transparent polycarbonate. It was 2 cm deep, 4 cm wide, and 75 cm long.
Nutrient solution consisting of KH2PO4(2.2 mM), K2HPO4 (4.8 mM), (NH4)SO4 
(0.25 mM), MgSO4 (0.04 mM) and yeast extract (0,1 g/l) was recycled through 
the reactor at a rate of 10 ml/s by a magnet drive vane pump (Cole-Parmer, 
Chicago, IL.). Oxygen was supplied by pre-aerating the nutrient solution. The 
operating volume of the recycle loop including the reactor was 450 ml. After 
inoculation, the reactor was operated batchwise for 12 h. The inoculum consisted 
of the aerobic organisms: Pseudomonas aeruginosa, Pseudomonas fluorescens 
and Klebsiella pneumoniae. Use of this defined mixed population to form biofilms 
was described by Stoodley e ta l39. After 12 h of batch operation, the reactor was 
switched to a continuous flow mode. Nutrient solution was added by a peristatic 
pump (Masterflex; Cole-Parmer, Niles, IL.) at a rate of 15 ml/min to achieve a 
hydraulic residence time of 30 min. The same peristatic pump was used to
16
maintain the effluent flow at the same flow rate  ^ Biofilm was allowed to grow for 4 
to 7 days before LCT measurements.
Just before LCT measurement, the flow of nutrient in the reactor was 
stopped, the nutrient solution in the reactor was slowly drained and replaced with 
the electrolyte solution formulated for the LCT measurements. The reactor was 
then connected to a gravitational flow system designed for LCT measurement.
LCT experimental setup
Electrodes and electrolyte solution
Microelectrodes used for LCT measurements were made of 100 |im 
platinum wire, 99.99% Pt (product of Engelhard, Carteret, NJ), with the tips 
etched electrochemically in 2M KCN solution to a diameter of less than 1 |im. 
The wire was then rinsed with double-distilled water and carefully inserted into a 
glass capillary. Location of the wire’s tip in the capillary was observed under a 
microscope. The glass capillary was positioned in a Micro Electrode Puller 
(Stoelting Co., Wooddale, IL.) with the tip of the wire 1 to 1.5 cm higher than a 
Ni-Cr heating coil. Heat was gradually increased until the glass around the 
platinum wire melted and adhered to the wire while the entire capillary dropped 
down and cooled in the air. The tip of the wire was then exposed by grinding on 
a rotating diamond wheel (Model EG-4, Narishige Co, Tokyo, Japan). Surface of
17
the microelectrode was cleaned in a sonication bath first with deionized water, 
then with acetone. Tip diameter was measured under the microscope and the 
surface area of the electrode calculated. Electrical connection with the 
microelectrode was made by inserting a small piece of solder and a bare copper 
wire into the capillary and melting the solder in a stream of hot air to form a 
metallic droplet connecting the platinum and copper wires.
The counter/reference electrode was a commercial calomel electrode 
(Model 13-620-51, Fisher Scientific, Pittsburgh, PA). A Hewlett Packard 4140B 
multimeter was used as voltage source and picoammeter. The microelectrode 
was polarized cathodically to -0.8 V against the reference electrode that was 
placed next to it within reactor in the downstream direction. Voltammetry tests 
were performed for each microelectrode to check their performance. Voltage 
between the microelectrode and the reference electrode was scanned from 0 to - 
1.2 V. Microelectrodes with limiting current in the voltage range between -0.6 to - 
0.9 V were considered useable.
The reaction/diffusion solution was an electrolyte solution consisting of 0.5 
M of KCI and 25 mM of K3Fe(CN)6. KCI was Used as supporting electrolyte to 
suppress the contribution of electromigration to the overall mass transfer rate to 
microelectrode. Viscosity of this solution, j i , as measured with a falling ball 
viscometer (Model GV-2100, Gilmont Instruments, Barrington, IL) was 0.9888 cp.
18
Density of the solution, p, was 1*017 g/ml. Actual concentrations of Fe(CN)63" 
were determined by iodimetric titration40 before each measurement.
Gravitational flow setup
The reaction/diffusion solution was recycled through the biofilm reactor 
using a gravitational flow system to ensure that flow rates were constant and 
without pulsation. Flow rates were adjusted by a control valve and continuously 
monitored by flowmeter (Model GF-1500, Gilmont Instruments, Barrington, IL). 
The recirculating electrolyte was filtered through a quartz wool plug to remove 
any large aggregates of cells. Before any measurement, electrolyte solution was 
allowed to flow through the biofilm reactor for 30 min to attain uniformity 
throughout the reactor.
LCT applicability tests
In order to apply LCT to measure local mass transfer coefficients in biofilms, 
a few critical conditions need to be met. They are: (I)  the concentration of 
Fe(CN)63' is uniformly distributed in biofilm reactor or its local concentration can 
be mesasured, (2) the calculated mass transfer coefficient is independent of the 
concentration of Fe(CN)63' used in the measurement, and (3) biofilm structure 
remains intact during the measurement.
19
Measuring Fe(CN)c3' concentration in biofilms
The tip of a microelectrode described in the Electrodes and electrolyte 
solution section was coated with a thin layer of cellulose acetate membrane so 
that it was not sensitive to mass transfer rate but only to the concentration of 
Fe(CN)63'. The electrolyte solution was allowed to recycle through the biofilm 
reactor for 30 min. Then vertical profiles of Fe(CN)63' concentration in biofilms 
were measured by using this Fe(CN)63" sensing microelectrode.
Measuring limiting current at various Fe(CN)c3' concentrations
For the electrolyte solutions used in the experiment, the concentration of 
KCI was kept constant and the concentration of Fe(CN)63' was varied from 
2.5mM to SOmM. Under the same flow velocity V=2.2 cm/sec, a microelectrode 
was positioned in the bulk flow and limiting current was measured for different 
concentration of Fe(CN)63" . A relation between the measured mass transfer 
coefficients and Fe(CN)63' concentrations was obtained.
Monitoring biofilm structure
The biofilm reactor was positioned on the stage of an inverted microscope 
(Model CK-2, Olympus, Japan). Biofilm structure was observed through the 
transparent bottom of the reactor. During the LCT measurement, micro- 
photographs of biofilm were taken hourly to check for structural integrity of the
20
biofilms and samples of biofilm were taken for R2A agar plate counts to 
determine the viability of biofilm at time 0, 2, 4, and 22 h.
Local mass transfer coefficient measurements
Measuring vertical profiles of local mass transfer coefficient
A microelectrode was mounted on a micromanipulator (Model M3301L, 
World Precision Instruments, New Haven, C l)  that was equipped with a stepper 
motor (Model 18503, Oriel, Stratford, CT) and manipulated by a computer 
controller (Model 20010, Oriel, Stratford, CT). The microelectrode was 
introduced from the top of the reactor. To ensure that the viscous flow profile at 
the location of the measurement was fully developed, the distance from chosen 
measurement location to the entrance of reactor was always larger than the 
hydrodynamic entrance length as estimated according to Schlichting’s equation14, 
L=0.04xRHxRe, where Rh is the hydraulic radius in centimeters and Re is the 
Reynolds number.
The microelectrode was introduced into the biofilm perpendicularly to the 
bottom of the reactor. Location of the tip in the biofilm was monitored through an 
inverted microscope. To measure the vertical profiles of mass transfer 
coefficient, the microelectrode was slowly moved down from the bulk liquid and 
into biofilm at preset increments by the computer controlled micromanipulator.
Limiting current was measured at various vertical positions and stored by the 
data acquisition system. The minimum distance between two adjacent positions, 
for microelectrodes with a tip diameter of 10 pm, was set greater than 20 pm.
To establish the vertical Z-coordinate, the position of the reactor’s bottom 
plate (the substratum for the biofilm) was arbitrarily set as z=0. The vertical 
position of the microelectrode, z, was then measured as the distance from tip of 
microelectrode to the bottom of the reactor. The lowest limiting current was 
always measured at z=0.
Custom software was used to control microelectrode movement and collect 
limiting current data. The vertical profile of limiting current was displayed on the 
computer’s monitor in real time. At each vertical position, the data acquisition 
system (Model CIO-DAS08PGL, ComputerBoards, Inc., Mansfield, MA) collected 
22 separate readings at a sampling frequency of I KHz. The highest and the 
lowest values were rejected and the remaining 20 measurements were 
averaged. Standard deviation was calculated for each set of 20 data and 
compared with a preset standard deviation defining the desired precision of the 
measurement. If the measured standard deviation was smaller than the preset, 
the measurement was accepted, the data stored, result displayed on the screen, 
and the microelectrode moved to the next vertical position. If the calculated 
standard deviation was higher than the preset, the.measurement was repeated. 
A compromise between the precision and practicality had to be accepted; to
21
22
complete the measurement in a reasonable time. A standard deviation of 5% 
was set for all measurements.
To study mass transfer rate over a homogeneous viscoelastic surface and 
to test the performance of the technique, a layer of 3% calcium alginate was 
fixed on the bottom of the reactor. The thickness of the layers varied from 300 to 
700 pm. Vertical profiles of limiting current through alginate layers were 
measured.
Limiting current profiles were measured through both the biofilm clusters 
and the interstitial voids. Vertical position of a top of the cluster was estimated 
from the mass transfer coefficient profile: a point at which the mass transfer 
coefficient showed the first dramatic decrease. Estimations of the cluster 
locations were confirmed by microscopic observations.
Measuring horizontal distributions of local mass transfer coefficient
/
Fig. 4 is the schematic diagram of the experimental setup. The biofilm 
reactor was positioned on an X-Y micropositioner stage (Model CTC-462-2S, 
Micro Kinetics, Laguna Hills, CA) with the microelectrode attached to a linear 
micropositioner (Model CTC-322-20, Micro Kinetics, Laguna Kills, CA) and 
positioned above the reactor. The micropositioners were computer controlled ■ 
through a controller (Model CTC-283-3, Micro Kinetics, Laguna Hills, CA) with a 
positioning precision of 0.1 pm. Custom software was used to simultaneously
23
control the stage movement, microelectrode movement, data acquisition, and 
distribution display in real time. The software allowed sampling a horizontal grid 
over a certain area. The usual grid setting was a 10x10 matrix, with step size of 
25 pm in both horizontal directions. A similar data acquisition protocol used in the 
vertical profile measurement was applied. The microelectrode was first 
manipulated manually to the first grid point at a predetermined position in the 
biofilm. Once the limiting current was measured and the data was accepted, the 
linear micropositioner moved the microelectrode out of the biofilm into bulk liquid, 
the motorized X-Y stage moved the reactor to the next grid point, the 
microelectrode was lowered to the predestined position, and the limiting current 
was measured after a 40 ms delay. The procedure was repeated for the entire 
grid. The horizontal distribution of limiting current was displayed on the 
computer's monitor in real time. The real time result display permitted, on many 
occasions, early detection of experimental problems, such as data acquisition 
malfunction, that could have otherwise remained unnoticed until the 
measurements were completed.
To evaluate the influence of convective flow on mass transfer rate, the 
horizontal distributions of mass transfer coefficient at the same vertical position 
were measured at various bulk flow velocities.
I
24
Combination of CSLM velocimetry and LCT measurements
. An experiment was set up to measure local velocity profile and local mass 
transfer coefficient profile at the same location in biofilm voids. The similar setup 
described in Monitoring biofilm structure was used. Instead of using a 
conventional inverted microscope, a CSLM was used. Local velocity profile in _ 
biofilm voids was measured by P IV 6’39. The vertical profile of local mass transfer 
coefficients was measured at the exact same location using LCT.
25
.
HP4140B
I \ %
Fig. 4 The schematic diagram of LCT experimental setup. 1,1’ -- electrolyte 
reservoir, 2 -  pump, 3 -  microelectrode, 4 -- X, Y microposition stage, 5 -  
reference/counter electrode, 6 -  open channel biofilm reactor, 7 -  linear 
micropositioner, 8 -  micropositioning controller, 9 -  potentiostat, 10 -  computer.
26
RESULTS
Fe(CN)g31 concentration distribution in biofilms
By using the concentration sensitive microelectrode, Fe(CN)63" 
concentrations were measured at various locations in the biofilm reactor and 
were found constant throughout the reactor.
Independence of mass transfer coefficient on Fe(CN)g3lConcentration
Limiting current was measured at various ferricyanide concentrations. 
Results are plotted in Fig. 5. By changing the concentration of Fe(CN)63" from 2.5 
mM to 50 mM, the measured limiting current increased linearly with the 
concentration as shown. For each concentration, a mass transfer coefficient was 
calculated from the corresponding limiting current according to Eqn. (6).
Biofilm structure and viability
Microscopic observation supported by time-lapse photography revealed that 
the biofilm overall structure remained intact for more than 20 hours under the
27
continuous recycle flow of the reaction/diffusion electrolyte solution. No visible 
detachment or sloughing was recorded during the mass transfer measurement. 
Although it was assumed that the biofilm was inactive under the conditions of the 
mass transfer experiments, results of plate counts showed that the number of 
viable cells in the biofilm remained relatively constant in the first four hours.
Table 1 presents the results of the viable cell count for biofilm samples taken as 
a function of time since the onset of electrolyte recycling.
Table 1. Viable cell counts of the biofilm under LCT measurement condition
Time of sampling (hr) 0 2 4 22
Viable cell count (CFU/cm2) 4.8x107 3.6x10s 1.2x108 1.2x104
Vertical profiles of local mass transfer coefficient
3% calcium alginate layer
Fig. 6 and 7 are vertical profiles taken through uniform alginate layers. The 
bulk flow velocity was 1.15 cm/sec. The thickness of the alginate layer was 460 
jim for Fig. 6 and 650 (im for Fig. 7. A significant decrease of local mass transfer 
coefficient was observed in both profiles when the microelectrode penetrated the 
surface of the alginate layer.
28
Biofilms
Fig. 8 illustrates two typical vertical profiles of the local mass transfer 
coefficient. Curve (a) was measured in a water-filled void and is similar to that 
measured in a clean reactor (results not shown). This profile shows that the local 
mass transfer coefficient in the void decreased gradually toward the bottom of 
the reactor as the local fluid flow velocity decreased. Curve (b) was measured 
through a 170 pm thick biofilm cluster. For vertical positions above z=700 pm, 
the local mass transfer coefficient held constant at the pure fluid value. Between 
z=400 and 700 pm, a decrease of the local mass transfer coefficient was 
observed. Just above the top of the cluster, between z= 200 and 400 pm, the 
local mass transfer coefficient increased slightly. Inside the biofilm cluster, the 
local mass transfer coefficient fluctuated significantly.
In a separate experiment, two profiles presented in Fig. 9 were taken at 
two horizontal locations, 200 pm apart, in a 450 pm thick section of biofilm.
Profile (a) demonstrates a randomly fluctuating mass transfer coefficient similar 
to that observed in Fig. 8. Profile (b) shows a rather smooth decrease in the local 
mass transfer coefficient.
29
Horizontal distribution of local mass transfer coefficient
Measurements of the local mass transfer coefficient at various vertical 
positions above a horizontal plane were conducted in the reactor without biofilm 
(results not shown). No significant variation was observed within each individual 
distribution.
Similar measurements at various horizontal planes were conducted in the 
reactor with a 200 pm thick biofilm cluster at a constant flow velocity, V= 1.58 
cm/sec. Three horizontal distributions were taken in the bulk solution at different 
vertical positions in the bulk solution to study the change of mass transfer rate 
above biofilm clusters. Three other horizontal distributions were taken on or 
inside the biofilm matrix. These six distributions are presented as Figures 10a to 
10f. Their corresponding vertical positions above the biofilm substratum are: 
1000, 500, 300, 200, 100, 50 pm, respectively.
Mass transfer coefficient at various flow velocities
Fig. 11 presents the change in horizontal distributions of local mass transfer 
coefficients in biofilms corresponding to the change in flow velocity. For a 200 
pm thick biofilm cell cluster, horizontal distributions of local mass transfer 
coefficients were taken at z=50 pm. The flow velocity was varied from 0.41
30
cm/sec to 1.4 cm/sec. For each distribution, the horizontally averaged value of 
the mass transfer coefficient was calculated and plotted against the flow velocity 
in Fig. 12.
In a separate experiment, horizontal distributions of local mass transfer 
coefficient were measured at various vertical positions and various flow 
velocities. The average mass transfer coefficient for each distribution was 
calculated. The relationships between average mass transfer coefficient and the 
bulk flow velocity are presented in Fig. 13. The average thickness of biofilm 
under investigation was estimated at 120 pm. Measurements were conducted at 
three vertical positions: ( I)  z=5000 pm in the bulk solution; (2) z=100 pm just 
below the top of the biofilm; (3) within the biofilm at z=10 pm. Average mass 
transfer coefficients were calculated from horizontal distributions taken from a 
typical 250 pmx250 pm grid area. Curves (1) to (3) show the average mass 
transfer coefficients measured at these three vertical positions under various 
bulk flow velocities. The slopes of these curves indicated the sensitivity of mass 
transfer coefficient to the change in flow velocity. The intercepts provided mass 
transport information in no convective flow condition.
Vertical profiles of local velocity and.mass transfer coefficient in void
At the same location in a biofilm void, the vertical profile of local flow 
velocity and the vertical profile of local mass transfer coefficient were measured
31
and presented in Fig. 14. Both local velocity and local mass transfer coefficient 
decreased toward the base of the biofilms, but the rate of decrease of local flow 
velocity was much more significant than that of local mass transfer coefficient.
Li
m
tin
g 
C
ur
re
nt
 (
10
 7A
)
32
■ Limiting current
▲ mass transfer 
coefficient
------Linear regression
Concentration of Ferricyanide Ion (mM)
5.00E-04
4.00E-04
3.00E-04
2.00E-04
1.00E-04
0.00E+00
Fig. 5 Mass transfer coefficient vs. concentration of ferricyanide ion
M
as
s 
Tr
an
sf
er
 C
oe
ffi
ci
en
t (
m
/s
)
Lo
ca
l M
as
s 
Tr
an
sf
er
 C
oe
ffi
ci
en
t (
m
/s
)
33
1.402-04
1.202-04
1.002-04
8.002-05
6.002-05
the top of the 
alginate layer
4.002-05
2.002-05
0.002+00
200 400 600 800 1000 1200 1400
Vertical Position (jiim)
Fig. 6 Vertical profile of local mass transfer coefficient through an alginate layer
Lo
ca
l M
as
s 
Tr
an
sf
er
 C
oe
ffi
ci
en
t (
m
/s
)
34
1.40E-04
1.20E-04
1.00E-04
8.00E-05
6.00E-05
4.00E-05 the top of 
the alginate layer
2.00E-05
0.00E+00
Vertical Position (gm)
Fig. 7 Vertical profile of local mass transfer coefficient through an alginate layer
Lo
ca
l M
as
s 
Tr
an
sf
er
 C
oe
ffi
ci
en
t (
m
/s
)
35
4.00E-05
3.00E-05
2.00E-05
1.00E-05 -
the top of 
the cluster
0.00E+00
Vertical Position (jim)
Fig. 8 Vertical profiles of local mass transfer coefficient measured in a void (a) 
and through a cluster (b). The insert is the schematic diagram that shows 
locations of measurement. The Shaded areas represent biofilm clusters.
Lo
ca
l M
as
s 
Tr
an
sf
er
 C
oe
ffi
ci
en
t (
m
/s
)
36
2.00E-04
1.50E-04 - -
1.00E-04 • *
5.00E-05 • ■
the top of 
the cluster
0.00E+00
Vertical Position (fim)
Fig. 9 Vertical profiles of local mass transfer coefficient measured at two
different locations through a biofilm cluster. The insert is the schematic 
diagram that shows locations of measurement. The shaded area 
represents biofilm cluster.
37
Y(gm)
(b) z=500 (im
2.00E-04'
1.60E-04-
1.20E-04-
8.00E-05-
4.00E-051
0.00E+00'
Y(gm)
(c) z=300 gm
2.00E-04'
1.60E-04-
1.20E-04-
8.00E-05-
4.00E-05-
0.00E+00' X (gm)
Y(|im)
Fig. 10 Horizontal distributions of local mass transfer coefficient at v=1.59cm/sec
38
(d) z=200  pm
I t
1 1
I !o
(e) z=1 OO pm
Y  ( L i m )
X ( L i m )
Y  ( L i m )
(f) Z=SO pm
1S S
I l</) O
I IO
Y ( L i m )
Fig. 10 (continued)
39
V=I .40 cm/sec
V=0.88 cm /sec
V=0.76 cm /sec
V=0.41 cm /sec
I
I
Y (|im)
1.10E-04
1.00E-04
I 9.00E-05
8.00E-05
7.00E-05
O
M M m
X (fim )
Y (fim)
1.10E-04
1.00E-04
E, 9.00E-05
8.00E-05
7.00E-05 X (|xm)
7.00E-051 X (|im)
Y(gm)
Fig. 11 Horizontal distributions of local mass transfer coefficient at z=50 gm. 
The thickness of the biofilm cluster was 200 |im.
H
or
iz
on
ta
lly
 A
ve
ra
ge
d 
M
as
s 
Tr
an
sf
er
 
C
oe
ffi
ci
en
t (
m
/s
)
40
1.04E-04
(1.30e-6) ♦
1.00E-04
9.60E-05
♦  (4.72e-6)
9.20E-05
♦  (5.73e-6)
(5.68E-06) ♦8.80E-05
8.40E-05
Flow Velocity (cm/s)
Fig. 12 Influence of bulk flow velocity on Horizontally averaged mass transfer 
coefficient at z=50 |im for a 200 (im thick biofilm cluster. The values 
labeled next to data symbols are standard deviations of distributions
H
or
iz
on
ta
lly
 A
ve
ra
ge
d 
M
as
s 
Tr
an
sf
er
 
C
oe
ffi
ci
en
t (
m
/s
)
41
2.00E-04
1.60E-04 --
1.20E-04 • -
8.00E-05 - -
4.00E-05 ■ ■
0.00E+00
Bulk Flow Velocity (cm/s)
Fig. 13 Influence of bulk flow velocity on horizontally averaged mass transfer
coefficient. As shown in the insert: (1) measured in bulk fluid at z=5000 |im; 
(2) measured in biofilm at z=100 |im; and (3) measured in biofilm at z=
10 (j,m. The shaded area represents biofilm cluster. Dashed lines show 
where horizontal distributions were taken from.
Lo
ca
l F
lo
w
 V
el
oc
ity
 (c
m
/s
)
42
2.50E-04
2.00E-04
1.50E-04
1.00E-04
- flow velocity
— mass transfer coeff. 5.00E-05
0.00E+00
200000 1000 15(
Vertical Position (|im)
Fig. 14 Vertical profiles of local flow velocity and local mass transfer 
coefficient in a biofilm void
Lo
ca
l M
as
sT
ra
ns
fe
r 
C
oe
ffi
ci
en
t (
m
/s
)
43
DISCUSSION
Experimental conditions influencing mass transfer limitation
To successfully apply LCT to mass transfer measurement, the overall 
electrochemical reaction occurring on the electrode tip, oxidation or reduction, 
has to be limited by mass transport. The most important experimental conditions 
are: (a) the surface condition of microelectrode, (b) the electrochemical reaction 
rate of reactive electrolyte. Both of them can be controlled experimentally. The 
surface condition of the microelectrode can be changed by polishing and 
cleaning and the electrochemical reaction rate is determined by properties of 
reactive electrolyte selected and electrochemical potential applied to the 
microelectrode.
Microelectrode cleaning
To ensure that the electrochemical reaction proceeds at the maximum 
possible rate and that the electrode response is reproducible, the surface of the
r '
electrode has to be prepared properly. In the literature35, several cleaning 
procedures for large electrodes were proposed. The procedure mostly includes
44
acid rinsing and cathodic treating. We found these procedures unsatisfactory, 
results of voltammetry tests showed that electrodes prepared following these 
procedures did not provide a reasonable length of limiting current plateau. In 
many cases, electrodes showed a resistor-like behavior, i.e. measured current 
increased linearly as the applied potential increased. The mechanism of this 
behavior is believed to be due to the formation of a passive layer on the 
electrode surface. Instead of using reported cleaning procedures, a simple 
cleaning procedure involving sonication in water and acetone was described in 
the Methods and Materials. The method was found to be satisfactory and 
reasonable limiting current plateaus were achieved for microelectrodes.
Reacting electrolyte selection
The choice of electrochemical reactant for LCT applied in biofilm systems is 
narrowly restricted by the following criteria35: chemical stability; (b) high solubility; 
(3) low cost; (4) a reaction electrode potential that is sufficiently different from 
that of hydrogen evolution (or oxygen evolution) to give long, well-defined limiting 
current plateaus; and (5) less toxic or destructive to biofilm structure.
Commonly, ah acidified copper sulfate solution is used from which copper 
is deposited on the electrode surface. However, because of the small surface 
area of the microelectrode such deposition will significantly alter the sensing 
area. An oxygen reduction system is also frequently used because of a long
45
limiting current plateau on platinum electrode surface. However, because oxygen 
is consumed by microorganisms in biofilm, local oxygen concentration can vary 
dramatically making it difficult to Calculate mass transfer coefficient from 
measured limiting current according to Eqn. (6). An electrolyte system (Fe(CN)63"
/ Fe(CN)64") was considered to meet most of the listed criteria and was chosen to 
be used in biofilm mass transfer studies.
Applicability of LCT to biofilm system
The uniform distribution of Fe(CN)63" concentration in biofilms suggests that 
Fe(CN)63" either does not react with biofilms or reacts very slowly. Since n, A, F, 
and C0 are all constants, the mass transfer coefficient only depends on limiting 
current according to Eqn. (6) and can be calculated easily.
Fig. 5 presents the linear relation between the measured limiting current 
and Fe(CN)63" concentration employed. Mass transfer coefficients were 
calculated for different.ferricyanide concentrations. The average mass transfer 
coefficient was 2.19x10"4±0.20x10"4 m/s. Because the standard deviation was 
small (<10%), the measured mass transfer coefficient is assumed independent of 
the concentration of reacting species.
The major concern of applying LCT to determine local mass transfer 
coefficients in biofilm systems was whether the. biofilm structure would remain
46
unchanged during the measurement. The time required to complete a set of 
measurements ranged from 2 to 10 hours. Observations by inverted microscope, 
supported by time-lapse photography, confirmed that biofilm structures remained 
intact throughout the measurements. In addition, the viable cell count 
demonstrated that many biofilm microorganisms remained viable, despite the 
harsh conditions during the experiments. Since the mass transfer rate of 
Fe(CN)63" to the microelectrode was mainly influenced by the hydrodynamics and 
the biofilm structure, we concluded that LCT was applicable to biofilm systems 
and did not alter mass transfer process in biofilms.
Estimation of measurement errors on mass transfer coefficient
Since the mass transfer coefficient is calculated according to Eqn.(6), the 
possible measurement error for mass transfer coefficient mainly comes from 
errors in measuring A, C0, and I.
Possible error in measuring sensing area of microelectrode
The diameter of the microelectrode was measured under a microscope with 
a IOOx magnification lens. For a 10 pm diameter microelectrode, the possible - 
measurement error was estimated to be ± 0.2 pm or 2% of measurement error in 
diameter which translated into a ± 4% error for the sensing area estimation..
47
Possible error in measuring bulk concentration of Fe(CN)c3'
The possible error in measuring C0 by the titration method can be estimated 
as follows: a typical 25 ml of 25 mM Fe(CN)63' solution consumes 6.25 ml of 0.1 
M- Na2S2O3 titrant. During the titration, the possible titration error was ± 2 drops of 
titrant which was measured to be 0.14 ml of the titrant volume. The error of C0 
measurement was then estimated to be ± 2% (=0,14 ml/6.25 ml).
Possible error in measuring limiting current
The limiting current was measured using HP-4140 multimeter whose 
measuring accuracy in current is at the level of 10'12 Ampere. The typical current 
value measured in this study was in the range of IO'7 to 10'9 Ampere. Therefore, 
the error in measuring current was negligible.
Other possible error
Besides measurement errors discussed above, another source of error 
comes from the contribution of electromigration to the limiting current. The 
migration contribution provides a positive error because the existence of 
migration process will increase the limiting current. For Fe(CN)63' /  Fe(CN)64' 
system, it is estimated35 that the migration contribution is less than 1% with
48
the addition of excess amount of non-reacting electrolyte, KCI, to the electrolyte 
solution.
By combining all possible error sources, the maximum measurement error 
for the obtained mass transfer coefficient was estimated to be between + 7% and 
-5%.
Influence of convective flow velocity on mass transfer coefficient
)
In these studies, the flow velocities used ranged from 0.2 to 1.6 cm/sec and 
the corresponding range of Reynolds numbers (Re=4xVxRHA)) was 50 to 500 
where Rh is the hydraulic radius of the rectangular flow channel. Therefore, 
results and conclusions reported here are only applicable to these flow 
conditions.
Horizontal distributions presented in Fig. 11 show that bulk flow velocity 
does not just influence the average mass transfer coefficient, as shown in Fig.
12, but also influences the fluctuation of the local mass transfer coefficient. By 
performing a simple statistical analysis on all four distributions, we can see that
the standard deviation of local mass transfer coefficients (numbers labeled next
'
to average data points in Fig. 12), decreased as the flow velocity increased.
In the bulk flow, convective transport is the dominant process of mass 
transport. From the results presented in Curve (I) of Fig. 13, the contribution of 
convective transport to the overall mass transfer coefficient was estimated. The
49
mass transfer coefficient and the bulk flow velocity in the reactor were linearly 
related;
k(m / s) = 7.10 x IO"3 x  V(m /  s) + 6.83 XlO"3 (14)
From the slope of Curve (I), = 7.10 x IO"3, we can estimate the
variation of convective flow velocity, AV, for the change of mass transfer 
coefficient, Ak, in channel flow.
The linear relationship between average mass transfer coefficient and 
bulk flow velocity also holds reasonably well inside the biofilm, as shown in 
Curve (2) & (3) of Fig. 13. The linear regressions for both curves reveal that the 
slopes and intercepts decrease as depth into the biofilm changes from 100 pm to 
10 pm. The decreasing slope means that the influence of bulk flow velocity on 
the average mass transfer coefficient decreases toward the bottom of reactor, as 
expected. It also implies that bulk fluid nutrients are more accessible in the top 
portion of biofilms than in the bottom, even though the liquid flows inside the 
entire biofilm. The intercepts of the curves are the mass transfer coefficients at 
zero flow velocity.
Analysis of horizontal distribution of local mass transfer coefficient
The results presented in Fig. 10 show that the local mass transfer 
coefficient across a horizontal plane in a biofilm is not constant and its value is.
50
site specific. Calculated arithmetic average values and the standard deviations of 
the distributions in Fig. 10 are given in Table 2. Significant fluctuations of mass 
transfer coefficient occurred just above the top of the solid biofilm matrix, z=200 
Jim, and inside the biofilm, but not above a water channel.
Table 2. analysis of horizontal distributions in Fig. 10
Horizontal
distributions
z, vertical 
position 
(pm)
k, average 
mass transfer 
coefficient 
(m/s)
Ak,
standard 
variation of k 
(m/s)
Ak/k,
percentage of 
variation
(%)
(a) 1000 1.38e-4 9.72e-7 0.8
(b) 500 1.45e-4 3.21 e-6 2.2
(c) 300 1.79e-4 2.1 Oe-S 11.7
(d) 200 1.40e-4 2.66e-5, 19.0
(e) 100 1.28e-4 2.56e-5 20.0
(f) 50 1.00e-4 2.93e-5 29.3
For the flow velocity of 1.58 cm/s, in the bulk flow at z=1000 p.m, the 
variation of mass transfer coefficient was 0.8 %. The small variability is due to 
the stable bulk flow provided by the gravitational flow system. Just above the top 
of the biofilm solid matrix, from z=200 to 500 pm, both the average mass transfer 
coefficient and the standard variations of mass transfer coefficient increase 
considerably. The magnitude of the change can be seen more clearly by plotting 
k vs. z in Fig. 15. A separate experimental result, presented in Fig. 16, shows 
that what happened above the top of biofilm clusters was not an isolated 
phenomenon. These changes suggest the existence of increased mixing in this 
region. Turbulence could be the result of the interaction between structure of the
51
biofilm matrix and fluid hydrodynamics. Bioturbation 28,36 (active movement of 
biofilm surface) could contribute to the increase in mass transfer rate.
Secondary structural heterogeneity of biofilms
If mass transfer inside the biofilm matrix was dominated by molecular 
diffusion, as is commonly believed, the local mass transfer coefficient should be 
relatively constant. However, the horizontal distributions presented in Fig. IOe 
and 10f show that local mass transfer coefficient inside the biofilm was not 
constant and significant variations were observed. Results suggest a more 
complex mass transport mechanism than simple molecular diffusion inside 
biofilm clusters.
The vertical variation of mass transfer coefficient can be seen from the 
vertical profiles presented in Fig. 8 and 9. The sudden increases of the mass 
transfer coefficient in Curve (b) of Fig. 8 and Curve (a) of Fig. 9 show that local 
mass transfer coefficient can be unexpectedly high at some locations inside 
biofilm clusters. Similar measurements were carried out in uniform 3% calcium 
alginate layers as presented in Fig. 6 and 7. No such abrupt change in mass 
transfer coefficient was observed. Therefore, the possibility of transport of 
reacting species along the shaft of the microelectrode due to the movement of 
the microelectrode was considered insignificant. We suggest that the existence
52
of channels facilitating convective flow within biofilm clusters is the major cause 
of the fluctuation in local mass transfer coefficient.
By using the relation established earlier for mass transfer coefficient and 
convective flow velocity, the change in convective flow velocity was estimated for 
the observed fluctuation of local mass transfer coefficient. The difference of 
mass transfer coefficients, Ak, between point CD and ®  in Curve (a) of Fig. 9 is 
8x10 5 m/sec. According to the slope of Eqn, 14, the change in flow velocity, AV, 
is calculated to be 1.13 cm/sec. Such a change in convective flow velocity could 
be caused by a significant difference in physical structure between these two 
points in the biofilm cluster.
It is, therefore, hypothesized that the internal structure of the biofilm matrix 
is not uniform. A conceptual model of the biofilm matrix accounting for such a 
possibility is shown in Fig. 17. The model assumes existence of flow channels 
with variable cross sectional areas and irregular orientations inside biofilm 
clusters. Also, the irregular flow just above the top of the biofilm cluster is 
depicted to show the existence of turbulence in this region.
The possibility of flow channels inside biofilm clusters adds an additional 
dimension of heterogeneity to the existing biofilm model. This extended model 
contributes to our understanding of biofilm heterogeneity and may also help 
explain some puzzling experimental results, such as the one reported by Jansen 
and Kristensen15 who measured a higher diffusivity in biofilm than that in pure
53
water. The results are not surprising if convective transport inside biofilm is 
considered.
Local shear rate on microelectrode surface
As discussed in the Theory chapter, the effect of the local shear rate on the 
microelectrode surface can be calculated from the local mass transfer coefficient 
according to Eqn. (13). The equation is only valid when a circular-disk 
microelectrode is physically present in a liquid flow field. Since results presented 
in Curve (1) of Fig. 12 were taken in bulk flow, corresponding local shear rates 
were calculated according to Eqn. (13) and are shown in Fig. 18. By curve fitting, 
the relation between local shear rate on the circular-disk microelectrode and bulk 
flow velocity can be expressed in a simple exponential formula
S = -1.006 + 0.3522 X Z159xy (15)
The relation indicates that local shear rate on a rigid microeiectrode surface 
increases exponentially with the increase of bulk flow velocity in the studied 
velocity range. Although it is unknown whether the conclusion can be applied to 
viscoelastic biofilm surfaces, the technique enables us for the first time to study 
spatial changes in local shear stress.
To correlate biofilm detachment with the flow rate and shear rate in specific 
biofilm reactors, further study is suggested that microelectrodes can be
54
introduced into the biofilm from below in order to substitute biofilm surface with 
microelectrode surface.
Correlation of local flow velocity and local mass transfer coefficient
It has been demonstrated that LCT can be combined with other techniques, 
such as CSLM1 to obtain additional information. Fig. 14 shows the quantitative 
relation between local mass transfer coefficient and local flow velocity measured 
at the same location in a biofilm void. By plotting local mass transfer coefficient 
vs. local flow velocities as shown in Fig. 19, a simple logarithmic relationship is 
revealed except for the last data point which was taken at the bottom of the
X '
reactor.
It should to be pointed out that only the horizontal component of flow 
velocities is measured by PIV; three dimensional flow velocities cannot yet be 
measured with this technique. Above biofilm clusters, the possible turbulent flow 
as discussed earlier makes it impossible to use PIV to measure local flow 
velocity and correlate it with local mass transfer coefficients.
H
or
iz
on
ta
lly
 A
ve
ra
ge
d 
M
as
s 
Tr
an
sf
er
 
C
oe
ffi
ci
en
t (
m
/s
)
55
2.00E-04
1.50E-04 --
1.00E-04 ■ ■
the top of 
the cluster
5.00E-05 * *
0.00E+00
Vertical Position (|im)
Fig. 15 Vertical profile of horizontally averaged mass transfer coefficient 
calculated from Fig. 10
H
or
iz
on
ta
lly
 A
ve
ra
ge
d 
M
as
s 
Tr
an
sf
er
 
C
oe
ffi
ci
en
t (
m
/s
)
56
1.40E-04
1.20E-04
1.00E-04
8.00E-05
6.00E-05
4.00E-05
the top of 
the cluster2.00E-05
0.00E+00
Vertical Position (jim)
Fig. 16 Vertical profile of horizontally averaged mass transfer coefficient 
for a 200 pm thick biofilm cluster. Flow velocity=©.75 cm/sec
57
Bulk flow
◄----------------------------------------------------
◄---------------------------------------
◄---------------------------------
4--------------------
Fig. 17 The proposed structural model of biofilm cell cluster
58
Bulk Flow Velocity (cm/s)
Fig. 18 The relationship between local shear rate on circular disk 
microelectrode and bulk flow velocity
59
0.01 ---------------------------------------------------------------------- ----------------------------------- ----------------------------------- — — -----------------------
0.00E+00 5.00E-05 1.00E-04 1.50E-04 2.00E-04 2.50E-04
Local Mass Transfer Coefficient (cm/s)
Fig. 19 Correlation between local mass transfer coefficient and local 
flow velocity in a biofilm void
60
SUMMARY
Technique development and applications
An experimental technique has been developed for measuring local mass 
transfer coefficients in biofilms. The technique was adapted from a conventional 
limiting current technique. The electrode used was mobile and its diameter was 
reduced to a few micrometers to prevent damaging the biofilm structure and 
disturbing the hydrodynamics. The tip of the microelectrode formed a microsink 
for an electroactive species purposely added to the reactor. The local mass 
transfer coefficient calculated from the measured limiting current to the 
microelectrode is related to the local effective diffusivity which is a function of 
local hydrodynamics which in turn depends on local biofilm structure. Viable 
plate counts and time-lapse microscopy showed that biofilm structure remained 
intact and biofilm remained viable during limiting current measurements. The 
overall measurement error for local mass transfer coefficient was estimated to be 
between +7% to -5%.
This thesis also explored the possible application of using LCT to measure 
local shear stress in biofilm reactor. A flow field model was developed for the
61
circular-disk microelectrodes. Analytical relationships between mass transfer 
coefficient and shear rate were established. The calculated local shear rate data 
showed the exponential increase with the increase of bulk flow velocity.
Mass transfer process in aerobic biofilms
By applying LCT to biofilm systems, vertical profiles and horizontal 
distributions of the local mass transfer coefficient in biofilms were obtained. The 
following conclusions can be drawn from these results:
1. The influence of hydrodynamics on the average mass transfer coefficient 
decreases into the biofilm away from the bulk fluid.
2. The mass transfer coefficient increases just above the biofilm surface. 
This suggests the existence of turbulence in the immediate region just above the 
biofilm.
3. Vertical profiles of the local mass transfer coefficient measured across 
interstitial voids are similar to those measured in the absence of biofilm.
4. Vertical profiles of the local mass transfer coefficient measured across 
biofilm matrixes demonstrated unexplained variability. This variability was 
attributed to the heterogeneous structure of biofilm matrix.
I
62
RECOMMENDATIONS FOR FUTURE RESEARCH
1. The technique presented in this thesis should be further applied for the 
quantification of local mass transfer rates in other biofilm systems to gain a 
broader and more general understanding of the mass transfer process in 
heterogeneous biofilms.
2. The technique has shown its potential application for study of local shear 
rate in biofilm system. More investigation is needed to understand local shear 
rate information and relationships between biofilm detachment into biofilm or 
sloughing and local shear stress. It is suggested that a microelectrode be 
introduced from bottom of reactor so that microelectrode surface can experience 
the same flow condition that the biofilm surface does.
3. The technique also has potential for investigating local turbulent intensity 
and frequency in biofilms due to its rapid response characteristics.
4. In order to use the measured local mass transfer coefficients in existing 
biofilm models, the theoretical relationship between apparent diffusivity and local 
mass transfer coefficient to the microelectrode has to be established.
5. For the case of no flow, LCT may be modified to perform Potential Step 
Chronoamperometry to directly measure effective diffusivity inside biofilm.
63
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69
NOMENCLATURE
[ Units: M--mass, !--length, T-time]
A is the sensing area of microelectrode, ( L2).
C is the concentration of substrate, ( ML3).
C0 is the concentration of reacting electrolyte in the bulk, ( M L3 )>
Cf is the concentration of substrate on biofilm surface, ( ML'3) ;
Cs is the concentration of reacting electrolyte on electrode surface^ ML'3) 
Cx is the concentration of biomass, ( ML'3).
D is the diffusivity of substrate, ( L2T 1)
F is the Faraday’s constant, =96485 C/mole(
I is the electrical current, ( Ampere )
J is the flux of reactant, ( MT'1 L 2)
k is the mass transfer coefficient, ( LT1)
Kc is the saturation constant, ( ML'3).
n is the number of mole of electron transferred, (M )
Fe is Peclet number (=Sxr2ZD)
Rh is the hydraulic radius of the reactor, ( ! )
Re is Reynolds number, (=VxrZ v) 
r is the radius of microelectrode, ( L )
S is the shear rate, ( T 1)
Sh is Sherwood number, (=kxrZD)
70
V is the flow velocity, ( LT1) 
x is the direction of liquid flow, ( L )
z is the vertical position perpendicular to bottom of biofilm reactor, ( L ) 
AC is the concentration difference, ( ML3).
8 is the thickness of external mass transfer boundary layer, ( L )
r| = z/r
0 = CZC0
 ^= x/r
(|> = (x= + y=r
T is the shear stress, (=jjxS)
| i is the viscosity of electrolyte solution, ( c p ) .
p is the density of electrolyte solution, ( ML3) 
v is the kinematic viscosity, (=pZ p)
71
APPENDIX
Experimental Raw Data
Raw data of Fig. 5
72
Fe(CN)63" cone. (mM) Limiting current (x107A) Mass transfer coefficient 
(m/s)
3.15 0.13 2.42x10"
6.3 0.25 2.33x10"
12.5 0.47 2.21x10"
25 0.86 2.02x10"
50 1.67 1.96x10"
Diameter of microelectrode: 15 gm 
Flow velocity: 1.83 cm/sec
Raw data of Fig. 6
Verical limiting k (m/s) Verical limiting k (m/s) Verical limiting k (m/s)
Position current (x l O7 Position current (x l O7 Position current (xIO7
(pm) A) (pm) A) (pm) A)
0 0.49624 0.00012 620 0.49116 0.00012 1240 0.43096 0.00011
20 0.50093 0.00013 640 0.48814 0.00012 1260 0.42505 0.00011
40 0.49815 0.00013 660 0.48667 0.00012 1280 0.41948 0.00011
60 0.50025 0.00013 680 0.48584 0.00012 1300 0.41441 0.0001
80 0.50293 0.00013 700 0.48853 0.00012 1320 0.41006 0.0001
100 0.51255 0.00013 720 0.48496 0.00012 1340 0.40606 0.0001
120 0.50943 0.00013 740 0.48184 0.00012 1360 0.40225 0.0001
140 0.50049 0.00013 760 0.4811 0.00012 1380 0.39849 0.0001
160 0.49668 0.00012 780 0.48262 0.00012 1400 0.39741 1E-04
180 0.50181 0.00013 800 0.48306 0.00012 1420 0.39775 0.0001
200 0.50337 0.00013 820 0.48115 0.00012 1440 0.39717 1E-04
220 0.50474 0.00013 840 0.47935 0.00012 1460 0.39409 9.9E-05
240 0.51123 0.00013 860 0.48071 0.00012 1480 0.39121 9.8E-05
260 0.5086 0.00013 880 0.47774 0.00012 1500 0.39009 9.8E-05
280 0.50918 0.00013 900 0.47598 0.00012 1520 0.39033 9.8E-05
300 0.50513 0.00013 920 0.4729 0.00012 1540 0.38623 9.7E-05
320 0.51314 0.00013 940 0.47329 0.00012 1560 0.38399 9.7E-05
340 0.50943 0.00013 960 0.47124 0.00012 1580 0.38071 9.6E-05
360 0.50103 0.00013 980 0.47129 0.00012 1600 0.37861 9.5E-05
380 0.49561 0.00012 1000 0.46978 0.00012 1610 0.375 9.4E-05
400 0.49585 0.00012 1020 0.46812 0.00012 1640 0.3709 9.3E-05
420 0.49614 0.00012 1040 0.46504 0.00012 1650 0.3687 9.3E-05
440 0.4981 0.00013 1060 0.46245 0.00012 1660 0.3646 9.2E-05
460 0.49619 0.00012 1080 0.46016 0.00012 1670 0.35234 8.9E-05
480 0.50567 0.00013 1100 0.45864 0.00012 1680 0.10537 2.6E-05
500 0.49717 0.00013 1120 0.4564 0.00011 1685 0.08335 2.1E-05
520 0.49185 0.00012 1140 0.45396 0.00011 1690 0.07803 2E-05
540 0.49087 0.00012 1160 0.45015 0.00011
560 0.49326 0.00012 1180 0.44668 0.00011
580 0.49863 0.00013 1200 0.44512 0.00011
600 0.49673 0.00012 1220 0.44243 0.00011
Diameter of the microelectrode: 5 gm 
Flow velocity: 1.15 cm/sec 
Fe(CN)63' cone.: 21 mM
73
Raw data of Fig. 7
Verical limiting k (m/s) Verical limiting k (m/s) Verical limiting k (m/s)
Position current Position current Position current
(nm) (x107A) (um) (x107A) (um) (x107A)
0 0.50278 0.00013 580 0.49019 0.00012 1180 0.41543 0.0001
20 0.50703 0.00013 600 0.49248 0.00012 1200 0.41104 0.0001
40 0.50567 0.00013 620 0.49292 0.00012 1220 0.4085 0.0001
60 0.50425 0.00013 640 0.49077 0.00012 1240 0.40532 0.0001
80 0.50205 0.00013 660 0.49282 0.00012 1260 0.40225 0.0001
100 0.50254 0.00013 680 0.49317 0.00012 1280 0.40225 0.0001
120 0.50532 0.00013 700 0.48745 0.00012 1300 0.4021 0.0001
140 0.50552 0.00013 720 0.4855 0.00012 1320 0.40571 0.0001
160 0.50957 0.00013 740 0.4855 0.00012 1340 0.40108 0.0001
180 0.51563 0.00013 760 0.48203 0.00012 1360 0.39775 0.0001
200 0.51235 0.00013 780 0.48223 0.00012 1380 0.39561 9.9E-05
220 0.5061 0.00013 800 0.47984 0.00012 1400 0.3915 9.8E-05
240 0.50845 0.00013 820 0.47891 0.00012 1420 0.39053 9.8E-05
260 0.50249 0.00013 840 0.47691 0.00012 1440 0.39556 9.9E-05
280 0.50684 0.00013 860 0.47324 0.00012 1460 0.39331 9.9E-05
300 0.50606 0.00013 880 0.47427 0.00012 1480 0.39165 9.8E-05
320 0.50567 0.00013 900 0.47207 0.00012 1500 0.38906 9.8E-05
340 0.50718 0.00013 920 0.47012 0.00012 1520 0.39024 9.8E-05
360 0.50625 0.00013 940 0.46812 0.00012 1540 0.38696 9.7E-05
380 0.50064 0.00013 960 0.46548 0.00012 1560 0.38535 9.7E-05
400 0.502 0.00013 980 0.46094 0.00012 1580 0.3833 9.6E-05
420 0.50205 0.00013 1000 0.45986 0.00012 1600 0.38047 9.6E-05
440 0.49902 0.00013 1020 0.45596 0.00011 1620 0.3773 9.5E-05
460 0.50093 0.00013 1040 0.45225 0.00011 1640 0.37632 9.5E-05
480 0.49927 0.00013 1060 0.45361 0.00011 1660 0.37691 9.5E-05
500 0.49468 0.00012 1080 0.4436 0.00011 1670 0.36856 9.3E-05
520 0.49644 0.00012 1100 0.43672 0.00011 1680 0.35293 8.9E-05
540 0.49365 0.00012 1120 0.43247 0.00011 1690 0.10669 2.7E-05
560 0.49053 0.00012 1140 0.42691 0.00011 1695 0.08525 2.1E-05
1160 0.42124 0.00011 1700 0.07959 2E-05
Diameter of the microelectrode: 5 
Flow velocity: 1.15 cm/sec 
Fe(CN)63' cone.: 21 mM
74
Raw data of Fig. 8
Curve (a) Curve (b)
Verical limiting k (m/s) Verical limiting k (m/s)
Position current Position (|im) current
(Iim ) (x107A) (XlO7A)
0 0.0008 9.62E-07 2 0.0016 1.92E-06
2 0.002 2.41 E-06 6 0.0098 1.18E-05
4 0.009 1.08E-05 8 0.013 1.56E-05
6 0.0164 1.97E-05 10 0.0176 2.12E-05
8 0.0192 2.31 E-05 12 0.0184 2.21 E-05
10 0.0218 2.62E-05 14 0.0178 2.14E-05
12 0.0228 2.74E-05 16 0.0172 2.07E-05
14 0.0232 2.79E-05 18 0.017 2.04E-05
16 0.0232 2.79E-05 20 0.0166 2E-05
18 0.0246 2.96E-05 22 0.0164 1.97E-05
20 0.0248 2.98E-05 24 0.0162 1.95E-05
30 0.026 3.13E-05 26 0.0158 1.9E-05
70 0.0306 3.68E-05 28 0.0156 1.88E-05
100 0.0306 3.68E-05 30 0.0154 1.85E-05
200 0.0306 3.68E-05 40 0.019 2.29E-05
900 0.031 3.73E-05 50 0.0154 1.85E-05
1000 0.0312 3.75E-05 60 0.012 1.44E-05
1500 0.0314 3.78E-05 70 0.0108 1.3E-05
2000 0.0316 3.8E-05 80 0.012 1.44E-05
90 0.01 1.2E-05
100 0.009 1.08E-05
110 0.0076 9.14E-06
120 0.0186 2.24E-05
130 0.0206 2.48E-05
140 0.0264 3.18E-05
150 0.0162 1.95E-05
160 0.0288 3.46E-05
170 0.029 3.49E-05
180 0.029 3.49E-05
190 0.0292 3.51 E-05
200 0.0292 3.51 E-05
300 0.0298 3.58E-05
400 0.0286 3.44E-05
500 0.0292 3.51 E-05
600 0.0298 3.58E-05
700 0.0308 3.7E-05
800 0.0312 3.75E-05
900 0.0314 3.78E-05
1000 0.0316 3.8E-05
Diameter of the microelectrode: 7 gm 
Flow velocity: 0.41 cm/sec 
Fe(CN)63 cone.: 22.4 mM
75
Raw data of Fig. 9
Curve (a) _____ Curve (b)
Verical Position 
(nm)
limiting current 
(XlO7A)
k (m/s) limiting current 
(XlO7A)
k (m/s)
1000 0.346 0.000184 0.345 0.000184
900 0.344 0.000183 0.34 0.000181
800 0.328 0.000175 0.33 0.000176
700 0.312 0.000166 0.319 0.00017
600 0.286 0.000152 0.302 0.000161
500 0.235 0.000125 0.282 0.00015
450 0.221 0.000118 0.183 9.74E-05
400 0.183 9.74E-05 0.146 7.77E-05
350 0.168 8.94E-05 0.129 6.87E-05
300 0.152 8.09E-05 0.114 6.07E-05
280 0.143 7.61 E-05 0.105 5.59E-05
260 0.135 7.19E-05 0.095 5.06E-05
240 0.127 6.76E-05 0.095 5.06E-05
220 0.12 6.39E-05 0.09 4.79E-05
200 0.113 6.01 E-05 0.086 4.58E-05
180 0.106 5.64E-05 0.082 4.36E-05
160 0.098 5.22E-05 0.077 4.1 E-05
140 0.088 4.68E-05 0.073 3.89E-05
120 0.078 4.15E-05 0.071 3.78E-05
100 0.066 3.51 E-05 0.083 4.42E-05
80 0.052 2.77E-05 0.166 8.84E-05
60 0.047 2.5E-05 0.008 4.26E-06
40 0.034 1.81 E-05 0.061 3.25E-05
20 0.025 1.33E-05 0.01 5.32E-06
0 0.008 4.26E-06 0.007 3.73E-06
Diameter of the microelectrode: 10 |im 
Flow velocity: 1.58 cm/sec 
Fe(CN)63 cone.: 24.8 mM
Raw data of Fig. 10
76
Diameter of the microelectrode: 10 jam 
Flow velocity: 1.58 cm/sec 
Fe(CN)63 cone.: 24.8 mM
(a) z=1000 |im
k(m/s) y (um)
x (nm) 0 25 50 75 100 125 150 175 200 225 250
0 I 4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1 4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1 4E-04
25 1.4E-04 1.4E-04 1.4E-04 1.4E-04 I 4E-04 1.4E-04 I 4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
50 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
75 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
100 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1 4E-04 1.4E-04
125 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1 4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
150 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
175 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
200 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
225 1.4E-04 1.4E-04 1.4E-04 1 4E-04 1.4E-04 I 4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
250 1.4E-04 1.4E-04 1.4E-04 1.4E-04 I 4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
(b) z=500 (im
k(m/s) y (um)
x (um) 0 25 50 75 100 125 150 175 200 225 250
0 1.3E-04 1.4E-04 1.5E-04 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04
25 1.3E-04 1.4E-04 1.4E-04 1.4E-04 1.5E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04
50 1.4E-04 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04 1.4E-04
75 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1 4E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04
100 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.4E-04 1.5E-04 1.4E-04 I 4E-04 1.5E-04 1.5E-04 1.4E-04
125 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04
150 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04 1.4E-04
175 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.4E-04
200 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04 1.4E-04
225 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04 1.4E-04 1.4E-04
250 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.4E-04 1.4E-04 1.5E-04 1.4E-04 1.4E-04
77
Raw data of Fig. 10 (continued)
(c) z=300 (im
k(m/s) y (Hm)
x (nm) 0 25 50 75 100 125 150 175 200 225 250
0 8.2E-05 1.4E-04 1.7E-04 1.6E-04 1.7E-04 1.9E-04 1.9E-04 1.9E-04 2.0E-04 1.9E-04 2.0E-04
25 8.2E-05 1.6E-04 1.8E-04 1.9E-04 1.9E-04 1.9E-04 2.1E-04 2.1E-04 2.1E-04 2.0E-04 2.0E-04
50 1.7E-04 1.8E-04 1.9E-04 1.7E-04 1.9E-04 1.9E-04 1.9E-04 1.8E-04 2.0E-04 1.9E-04 1.7E-04
75 1.7E-04 1.9E-04 1.9E-04 1.7E-04 1.8E-04 1.9E-04 1.8E-04 1.7E-04 1.7E-04 1.9E-04 1.7E-04
100 1.8E-04 1.8E-04 1.8E-04 1.4E-04 1.7E-04 1.7E-04 1.7E-04 1.9E-04 1.7E-04 1.9E-04 1.8E-04
125 1.6E-04 1.8E-04 1.9E-04 1.7E-04 1.6E-04 1.8E-04 1.8E-04 1.8E-04 1.8E-04 2.0E-04 1.9E-04
150 1.6E-04 1.8E-04 1.8E-04 1.8E-04 1.5E-04 1.7E-04 1.9E-04 1.8E-04 1.8E-04 1.9E-04 1.9E-04
175 1.6E-04 1.8E-04 1.9E-04 1.9E-04 1.8E-04 1.7E-04 1.9E-04 1.8E-04 1.9E-04 1.8E-04 1.9E-04
200 1.7E-04 1.8E-04 1.9E-04 1.8E-04 1.8E-04 1.7E-04 1.7E-04 1.7E-04 1.9E-04 2.0E-04 1.9E-04
225 1.7E-04 1.8E-04 1.9E-04 1.7E-04 2.0E-04 2.0E-04 1.9E-04 1.9E-04 1.9E-04 8.3E-05 1.9E-04
250 1.6E-04 1.8E-04 1.8E-04 1.9E-04 1.9E-04 1.8E-04 1.9E-04 2.0E-04 1.2E-04 2.1E-04 1.9E-04
(d) z=200 |im
k(m/s) Y (Hm)
X (H m ) 0 25 50 75 100 125 150 175 200 225 250
0 3.2E-05 1.2E-04 1.2E-04 1.1E-04 1 4E-04 1.3E-04 1.5E-04 1.6E-04 1.4E-04 1.5E-04 1.7E-04
25 3.2E-05 1.3E-04 1.6E-04 I 7E-04 1.3E-04 1.5E-04 1.4E-04 1.6E-04 1.5E-04 1.7E-04 1.4E-04
50 1.5E-04 1.7E-04 1.7E-04 1.4E-04 1.7E-04 1.4E-04 1.6E-04 1.4E-04 1.4E-04 1.2E-04 1.4E-04
75 1.5E-04 1.6E-04 1.7E-04 1.2E-04 1.3E-04 1.3E-04 1.4E-04 1.2E-04 1.4E-04 1.3E-04 1.5E-04
100 1.5E-04 1.8E-04 1 3E-04 1.4E-04 1.0E-04 1.5E-04 1.5E-04 1.3E-04 1.5E-04 1.3E-04 1.7E-04
125 1.4E-04 1.4E-04 1.3E-04 1.5E-04 1.1E-04 1.5E-04 1.4E-04 1.6E-04 1.7E-04 1.6E-04 1.7E-04
150 1.4E-04 1.2E-04 1.6E-04 1.5E-04 I . IE-04 1.4E-04 1.3E-04 1.7E-04 1.6E-04 1.7E-04 1.4E-04
175 1.5E-04 1.4E-04 1.6E-04 1.4E-04 1.4E-04 1.4E-04 1.5E-04 1.5E-04 1.5E-04 1.5E-04 1.3E-04
200 1.3E-04 1.5E-04 1.6E-04 1.3E-04 1.4E-04 1.3E-04 2.6E-05 1.5E-04 1.5E-04 1.6E-04 1.3E-04
225 1.3E-04 1.6E-04 1.4E-04 1.5E-04 1.3E-04 2.8E-05 1.5E-04 1.5E-04 1.6E-04 1 4E-04 1.5E-04
250 1.2E-04 1.5E-04 1.3E-04 1.3E-04 6.3E-05 1.3E-04 1.5E-04 1.2E-04 1.7E-04 1.4E-04 1.5E-04
78
Raw data of Fig. 10 (continued)
(e) z= 100 gm
k(m/s) y (|im)
x (nm) 0 25 50 75 100 125 150 175 200 225 250
0 1.5E-05 7.9E-05 1.1E-04 1.0E-04 1.2E-04 1.1E-04 1.4E-04 1.1E-04 1.4E-04 I 4E-04 1 4E-04
25 1.6E-05 9.9E-05 1.3E-04 1.2E-04 1.3E-04 1.1E-04 1.5E-04 1.3E-04 1.7E-04 1.4E-04 1.6E-04
50 1.5E-04 1.5E-04 1.6E-04 1.6E-04 1.3E-04 1.1E-04 1.3E-04 1.3E-04 8.6E-05 1.3E-04 1.4E-04
75 1.4E-04 1.5E-04 1.4E-04 1.5E-04 1.1E-04 1.3E-04 1.2E-04 1.3E-04 1.4E-04 1.1E-04 9.1E-05
100 1.3E-04 1.3E-04 1.2E-04 1.2E-04 1.0E-04 1.3E-04 1.5E-04 1.3E-04 1 3E-04 1.8E-04 1.IE-04
125 9.4E-05 1.2E-04 I. IE-04 1.2E-04 1.2E-04 1.3E-04 1.3E-04 1.5E-04 1.3E-04 1.8E-04 1.5E-04
150 9.3E-05 1.1E-04 1.1E-04 1.1E-04 1.1E-04 1.2E-04 1.2E-04 1.5E-04 1.5E-04 1.6E-04 1.7E-04
175 1.0E-04 1.1E-04 1.4E-04 1.1E-04 1.4E-04 1.1E-04 1.3E-04 1.6E-04 1.5E-04 1.3E-04 1.6E-04
200 1.1E-04 1.5E-04 1.5E-04 1.2E-04 1.3E-04 I.  IE-04 1.4E-04 1 4E-04 1.6E-04 1.4E-04 1.5E-04
225 6.4E-05 1.3E-04 1.3E-04 1.5E-04 1.5E-04 1.2E-04 1.7E-04 1.2E-04 1.3E-04 1.6E-04 1.2E-04
250 9.1E-05 1.3E-04 I. IE-04 1 4E-04 1.1E-04 1.5E-04 1.3E-04 1.5E-04 1.2E-04 1.5E-04 1.3E-04
(f) z=50 fim
k(m/s) y (|im)
x (|im) 0 25 50 75 100 125 150 175 200 225 250
0 2.5E-05 4.1 E-05 1.2E-04 1.1E-04 5.9E-05 6.5E-05 9.3E-05 5.1 E-05 1.3E-04 1.0E-04 1.5E-04
25 2.5E-05 1.1E-04 8.7E-05 1.1E-04 1.0E-04 1.1E-04 1.3E-04 8.1 E-05 8.5E-05 8.6E-05 8.0E-05
50 8.8E-05 1.2E-04 6.1 E-05 1.3E-04 1.4E-04 1.3E-04 9.9E-05 9.5E-05 8.5E-05 9.0E-05 7.6E-05
75 7.6E-05 1.3E-04 6.3E-05 1.2E-04 1.2E-04 8.9E-05 1.2E-04 7.0E-05 8.2 E-05 8.1 E-05 7.4E-05
100 7.3E-05 8.6E-05 1.3E-04 1.2E-04 1.1E-04 1.3E-04 I.  IE-04 8.5E-05 9.5E-05 9.3E-05 7.2 E-05
125 6.7E-05 8.5E-05 1.5E-04 I.  IE-04 1. IE-04 8.8E-05 1.2E-04 9.0E-05 8.8E-05 9.3E-05 1.2E-04
150 1.1E-04 7.1 E-05 1.0E-04 I 3E-04 1.2E-04 6.8E-05 8.2E-05 7.9E-05 1.5E-04 1.7E-04 I 6E-04
175 6.9E-05 9.3E-05 1.3E-04 1.3E-04 7.3E-05 7.1 E-05 7.8E-05 1.3E-04 1 4E-04 1.4E-04 I 2E-04
200 8.5E-05 5.1 E-05 1.1E-04 1.2E-04 8.9E-05 6.9E-05 7.7E-05 1.3E-04 1.4E-04 1.4E-04 1.4E-04
225 8.9E-05 9.9 E-05 1.1E-04 6.3E-05 8.7E-05 8.0E-05 8.5 E-05 1.2E-04 1.3E-04 I. IE-04 I 2E-04
250 7.1E-05 1.1E-04 8.5E-05 8.5E-05 6.4E-05 7.1 E-05 7.2E-05 1.2E-04 1 3E-04 1.1E-04 1 9E-04
Raw data of Fig. 11
79
Diameter of the microelectrode: 9 jim 
Fe(CN)63 cone.: 22.0 mM
(a) V=1.40 cm/sec
K (m/s) y (Mm)
x (|im) 0 25 50 75 100 125 150 175 200 225 250
0 9.7E-05 9.8E-05 1.0E-04 9.8E-05 1.0E-04 1.0E-04 1.0E-04 9.8E-05 9.7E-05 1.0E-04 1.0E-04
25 9.7E-05 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04
50 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04
75 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04
100 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04
125 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 9.9E-05 I 0E-04 1.0E-04 1.0E-04
150 1 0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 9.5E-05 1.0E-04 1.0E-04 1.0E-04
175 1.0E-04 9.8E-05 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 9.5E-05 1.0E-04 1.0E-04 1.0E-04
200 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 9.8E-05 1.0E-04 1.0E-04 1.0E-04 1.0E-04
225 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04 1.0E-04
250 1.0E-04 1.0E-04 1.0E-04 1.0E-04 9.8E-05 1.0E-04 9.7E-05 9.8E-05 9.8E-05 1.0E-04 1.0E-04
(b) V=0.88 cm/sec
k(m/s) Y (Lim)
x (urn) 0 25 50 75 100 125 150 175 200 225 250
0 9.5E-05 9.0E-05 8.7E-05 8.5E-05 7.2E-05 8.9E-05 8.8E-05 9.0E-05 9.4E-05 8.1 E-05 9.0E-05
25 9.5E-05 9.8E-05 1.0E-04 9.8 E-05 9.8E-05 1.0E-04 9.8E-05 1.0E-04 1 0E-04 1.0E-04 1.0E-04
50 1.0E-04 1.0E-04 9.8E-05 9.8E-05 9.6E-05 9.8E-05 9.8E-05 9.8E-05 9.7E-05 1.0E-04 1.0E-04
75 9.8E-05 9.5E-05 9.0E-05 9.7E-05 9.7E-05 9.8E-05 9.5E-05 9.7E-05 9.8E-05 9.4E-05 9.8E-05
100 9.4E-05 9.4E-05 8.8E-05 9.5E-05 9.5E-05 9.8E-05 9.8E-05 9.8 E-05 9.8E-05 9.7E-05 9.7E-05
125 9.3E-05 9.1E-05 8.7E-05 8.8E-05 9.4E-05 1.0E-04 1 0E-04 9.8 E-05 9.8 E-05 9.3E-05 9.4E-05
150 9.3E-05 8.0E-05 8.7E-05 8.8E-05 8.8 E-05 9.3E-05 9.5E-05 9.3E-05 9.2E-05 9.5E-05 9.8E-05
175 9.0E-05 9.4E-05 9.0E-05 9.0E-05 8.5 E-05 9.3E-05 9.2E-05 9.4E-05 9.5E-05 9.7E-05 9.7 E-05
200 8.5E-05 9.1E-05 9.1 E-05 9.1 E-05 8.8E-05 8.7E-05 8.8E-05 8.8 E-05 8.7E-05 8.8E-05 9.3E-05
225 8.6E-05 9.1 E-05 8.8E-05 8.5E-05 8.6E-05 9.1 E-05 8.9E-05 8.9E-05 9.4E-05 9.3E-05 9.0E-05
250 7.8E-05 8.5E-05 8.5E-05 5.4E-05 9.0E-05 9.1 E-05 8.6E-05 9.0E-05 9.3E-05 9.1 E-05 8.8E-05
(c) V=0.76 cm/sec
80
Raw data of Fig. 11 (continued)
k(m/s) y (Hm)
x (nm) 0 25 50 75 100 125 150 175 200 225 250
0 9.4E-05 8.2E-05 9.0E-05 8.5E-05 6.6E-05 8.2E-05 7.5E-05 9.0E-05 9.0E-05 8.4E-05 7.1 E-05
25 9.4E-05 9.7E-05 9.7E-05 9.7E-05 9.8E-05 9.7E-05 9.7E-05 9.7E-05 9.8E-05 9.8E-05 9.7E-05
50 9.8E-05 9.8E-05 9.7E-05 9.7E-05 9.5E-05 9.5E-05 9.5E-05 9.7E-05 9.5E-05 9.8E-05 9.8E-05
75 9.8E-05 9.4E-05 9.3E-05 9.6E-05 9.5E-05 8.8E-05 9.3E-05 9.4E-05 9.5E-05 8.8E-05 9.5E-05
100 9.5E-05 9.5E-05 9.1E-05 9.4E-05 9.0E-05 8.8E-05 9.5E-05 9.8E-05 9.4E-05 9.5E-05 9.5E-05
125 9.3E-05 9.1E-05 9.1E-05 9.4E-05 9.3E-05 8.8E-05 9.5E-05 9.7E-05 9.5E-05 8.5E-05 8.8E-05
150 9.4E-05 9.2E-05 9.0E-05 9.4E-05 8.2E-05 7.9E-05 9.1 E-05 9.0E-05 9.0E-05 9.4E-05 9.4E-05
175 7.8E-05 9.3E-05 9.0E-05 8.8E-05 8.1E-05 8.8E-05 8.7E-05 8.8E-05 9.4E-05 9.3E-05 9.4E-05
200 8.8E-05 8.8E-05 8.8E-05 8.4E-05 7.8E-05 8.3E-05 8.7E-05 7.8E-05 8.3E-05 8.0E-05 8.0E-05
225 8.5E-05 8.8E-05 8.7E-05 9.1E-05 8.5E-05 8.5E-05 8.0E-05 8.2E-05 8.0E-05 8.7E-05 9.3E-05
250 7.2E-05 8.3E-05 8.7E-05 8.4E-05 8.2E-05 8.5E-05 8.0 E-05 8.1 E-05 7.7E-05 7.4E-05 8.1 E-05
(d) V=0.41 cm/sec
k(m/s) y (pm)
x (pm) 0 25 50 75 100 125 150 175 200 225 250
0 9.4E-05 7.4E-05 7.7E-05 7.4E-05 7.5E-05 8.2E-05 8.4E-05 8.2 E-05 8.7E-05 6.7E-05 7.2E-05
25 9.4E-05 9.8E-05 9.7E-05 9.8E-05 9.7E-05 9.7E-05 9.8E-05 9.8E-05 9.8E-05 9.8E-05 9.7E-05
50 9.8E-05 9.8E-05 9.7E-05 9.7E-05 9.1 E-05 9.3E-05 9.7E-05 9.1 E-05 9.1 E-05 9.7E-05 9.7 E-05
75 1.0E-04 9.4E-05 9.3E-05 9.4E-05 8.8E-05 9.4 E-05 9.5E-05 8.9E-05 9.4E-05 9.4E-05 9.7E-05
100 9.0E-05 9.4E-05 8.5E-05 9.3E-05 9.4E-05 9.0E-05 9.3E-05 9.5E-05 9.4E-05 9.4E-05 9.1 E-05
125 8.8E-05 8.8E-05 9.1 E-05 8.5E-05 8.1 E-05 8.1 E-05 8.7E-05 9.3E-05 9.5E-05 9.0E-05 9.4E-05
150 8.6E-05 9.1 E-05 8.8E-05 8.2 E-05 8.8E-05 8.2E-05 9.1 E-05 9.0E-05 8.6E-05 9.4E-05 9.5E-05
175 8.1 E-05 8.8E-05 8.8E-05 8.5 E-05 7.8E-05 8.4E-05 8.8E-05 8.8E-05 9.3E-05 9.0E-05 8.2E-05
200 8.5E-05 8.5E-05 8.4 E-05 8.2E-05 8.7E-05 8.2E-05 8.5E-05 8.7E-05 8.4E-05 8.4E-05 8.1 E-05
225 7.8E-05 8.5E-05 8.1 E-05 8.7E-05 8.4E-05 8.6E-05 8.6 E-05 9.0 E-05 8.2E-05 7.5E-05 8.4 E-05
250 8.2E-05 7.8E-05 8.2E-05 8.2E-05 8.2E-05 8.3E-05 8.7E-05 8.6E-05 7.3E-05 9.0E-05 7.8E-05
81
Raw data of Fig. 14
Vertical
position
(pm)
k (m/s) Velocity (cm/s) Vertical
position
(pm)
k (m/s) Velocity (cm/s) Vertical
position
(pm)
k (m/s) Velocity
(cm/s)
0 4.00E-05 0.012 670 1.91E-04 1.092 1340 2.00E-04 1.932
10 1.34E-04 0.032 680 1.91E-04 1.102 1350 2.00E-04 1.942
20 1.49E-04 0.052 690 1.91E04 1.122 1360 1.99E-04 1.952
30 1.53E-04 0.062 700 1.91 E-04 1.132 1370 2.00E-04 1.962
40 1.54E-04 0.082 710 1.91 E-04 1.152 1380 1.99E-04 1.972
50 1.55E-04 0.092 720 I 92E-04 1.162 1390 2.00E-04 1.982
60 1.58E-04 0.112 730 1.91 E-04 1.182 1400 1.99E-04 1.992
70 1.58E-04 0.132 740 1.91 E-04 1.192 1410 2.01 E-04 2.002
80 1.60E-04 0.142 750 1.93E-04 1.202 1420 2.01 E-04 2.012
90 1.60E-04 0.162 760 1.93E-04 1.222 1430 2.00E-04 2.022
100 1 63E-04 0.182 770 1.92E-04 1.232 1440 2.01 E-04 2.032
110 1.64E-04 0.192 780 1.93E-04 1.252 1450 2.01 E-04 2.042
120 1.64E-04 0.212 790 1.92E-04 1.262 1460 2.01 E-04 2.052
130 1.66E-04 0.232 800 1.93E-04 1.282 1470 2.01 E-04 2.062
140 1.67E-04 0.242 810 1 94E-04 1.292 1480 2.02E-04 2.072
150 1.69E-04 0.262 820 1.94E-04 1.302 1490 2.00E-04 2.082
160 1.69E-04 0.282 830 1.95E-04 1.322 1500 2.01 E-04 2.092
170 1.70E-04 0.292 840 I 95E-04 1.332 1510 2.00E-04 2.102
180 1.70E-04 0.312 850 1.94E-04 1.342 1520 2.00E-04 2.112
190 1.71E-04 0.332 860 1 94E-04 1.362 1530 1.99E-04 2.122
200 1.72E-04 0.342 870 1.95E-04 1.372 1540 2.01 E-04 2.132
210 1 73E-04 0.362 880 1.95E-04 1.382 1550 2.00E-04 2.142
220 1.73E-04 0.382 890 1 93E-04 1.402 1560 2.01 E-04 2.152
230 1.74E-04 0.392 900 1.94E-04 1.412 1570 2.01 E-04 2.152
240 1.74E-04 0.412 910 1 94E-04 1.422 1580 2.01 E-04 2.162
250 1.75E-04 0.432 920 1 93E-04 1.442 1590 2.02E-04 2.172
260 1.76E-04 0.442 930 1.93E-04 1.452 1600 2.01 E-04 2.182
270 1.77E-04 0.462 940 1.93E-04 1.462 1610 2.02E-04 2.192
280 I 77E-04 0.482 950 I 94E-04 1.482 1620 2.02E-04 2.202
290 1.76E-04 0.492 960 1.95E-04 1.492 1630 2.02E-04 2.212
300 1.78E-04 0.512 970 1.94E-04 1.502 1640 2.02E-04 2.222
310 1.78E-04 0.532 980 1.95E-04 1.512 1650 2.02E-04 2.232
320 1.79E-04 0.542 990 1.95E-04 1.532 1660 2.02 E-04 2.232
330 1.80E-04 0.562 1000 1.95E-04 1.542 1670 2.02E-04 2.242
340 1.80E-04 0.572 1010 1.95 E-04 1.552 1680 2.01 E-04 2.252
350 1.79E-04 0.592 1020 1.96E-04 1.572 1690 2.01 E-04 2.262
360 1.81E-04 0.612 1030 1.97 E-04 1.582 1700 2.02E-04 2.272
370 1.81E-04 0.622 1040 1.95E-04 1.592 1710 2.02E-04 2.282
380 1.81E-04 0.642 1050 1.96E-04 1.602 1720 2.02E-04 2.282
390 1.80E-04 0.662 1060 1.97E-04 1.612 1730 2.01 E-04 2.292
Raw data of Fig. 14 (continued)
82
Vertical
position
(pm)
k (m/s) Velocity (cm/s) Vertical
position
(pm)
k (m/s) Velocity (cm/s) Vertical
position
(pm)
k (m/s) Velocity
(cm/s)
400 1.79E-04 0.672 1070 1.96E-04 1.632 1740 2.02E-04 2.302
410 1.83E-04 0.692 1080 1.96E-04 1.642 1750 2.02E-04 2.312
420 1.84E-04 0.702 1090 1.96E-04 1.652 1760 2.00E-04 2.322
430 1.84E-04 0.722 1100 1.97E-04 1.662 1770 2.00E-04 2.322
440 1.84E-04 0.742 1110 1.97E-04 1.682 1780 2.01 E-04 2.332
450 1.85E-04 0.752 1120 1.98E-04 1.692 1790 2.01 E-04 2.342
460 1.85E-04 0.772 1130 1.98E-04 1.702 1800 2.01E-04 2.352
470 1.84E-04 0.782 1140 1.97E-04 1.712 1810 2.02E-04 2.362
480 1.84E-04 0.802 1150 I 97E-04 1.722 1820 2.03E-04 2.362
490 1.86E-04 0.822 1160 I 98E-04 1.732 1830 2.03E-04 2.372
500 1.86E-04 0.832 1170 1.97E-04 1.752 1840 2.03E-04 2.382
510 1.86E-04 0.852 1180 1.99E-04 1.762 1850 2.03E-04 2.392
520 1.87E-04 0.862 1190 1.98E-04 1.772 1860 2.03E-04 2.392
530 1.87E-04 0.882 1200 1.98E-04 1.782 1870 2.03E-04 2.402
540 1.88E-04 0.892 1210 1.98E-04 1.792 1880 2.03E-04 2.412
550 1.88E-04 0.912 1220 I 99E-04 1.802 1890 2.00E-04 2.422
560 1.89E-04 0.922 1230 1.98E-04 1.812 1900 2.03E-04 2.422
570 1 89E-04 0.942 1240 1.98E-04 1.822 1910 2.04E-04 2.432
580 1.88E-04 0.952 1250 1.98E-04 1.842 1920 2.03E-04 2.442
590 1.89E-04 0.972 1260 1 98E-04 1.852 1930 2.03E-04 2.442
600 1.89E-04 0.982 1270 1.98E-04 1.862 1940 2.03E-04 2.452
610 1.91E-04 1.002 1280 1.99E-04 1.872 1950 2.04E-04 2.462
620 1.90E-04 1.012 1290 2.00E-04 1.882 1960 2.03E-04 2.472
630 1.89E-04 1.032 1300 1.99E-04 1.892 1970 2.03E-04 2.472
640 1.91E-04 1.042 1310 2.00E-04 1.902 1980 2.03E-04 2.482
650 1.9 IE-04 1.062 1320 1.99E-04 1.912 1990 2.04E-04 2.492
660 1.90E-04 1.072 1330 2.00E-04 1.922 2000 2.03E-04 2.492
1H O U C H E N  B IN D E R Y  L T D  
UTICA/OMAHA  
NE.