r
QUANTIFYING THE MORPHOLOGY OF COLLOID DEPOSITION IN
GRANULAR MEDIA USING FRACTAL DIMENSION
by
Michael Eugene MontEton
B.S., University of Colorado Denver, 2009
A thesis submitted to the
University of Colorado Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2011
This thesis for the Master of Science
degree by
Michael Eugene MontEton
has been approved
by
David C. Mays
Tim Lei
MontEton, Michael Eugene (M.S., Civil Engineering)
Quantifying the Morphology of Colloid Deposition in Granular Media Using
Fractal Dimension
Thesis directed by Assistant Professor David C. Mays
ABSTRACT
The hydraulic conductivity of a porous medium is usually thought of as
being constant over a given period of time. However, when the medium is
subjected to inflow of fluids carrying colloids, the interconnected pore spaces
become increasingly congested with accumulations of those colloids. It is
difficult, if not impossible with presentday technology, to directly measure the
buildup in the individual pore spaces.
Previous researchers have shown that it is possible to measure the fractal
dimension of accumulation in the pore spaces of a static sample of an index
matched medium in fluid. The purpose of this study is to build an apparatus and
software that can dynamically record the fluid flow rate, the timedependent head
loss across a flow cell containing the medium, the mass balance in the system,
and the fractal dimension of the colloid accumulation. Correlations between the
hydraulic conductivity, the specific deposition of colloids, and the fractal
dimension of the colloids can then be made.
This abstract accurately represents the contents of the candidates thesis.
Signed
David C. Mays
DEDICATION
I dedicate this thesis to the scientists and engineers of our world who
constantly seek to expand our understanding of water. Water itself has taught me
to be flexible in my thinking and adaptable to a wide variety of circumstances.
I also dedicate this thesis to my wife, Melony, who has always been my
inspiration.
ACKNOWLEDGEMENT
I would like to convey my thanks to my advisor, Dr. David C. Mays, for
his guidance and invitation into the world of basic scientific research. I also
thank our collaborators: Dr. Benjamin Gilbert, of Lawrence Berkeley National
Laboratory, and Dr. Tim Lei.
I am very appreciative of the Faculty Development Grant to Dr. Mays
which supported me with a salary in the fall of 2010, and the Program
Development Grant to Dr. Gilbert and Dr. Mays from Lawrence Berkeley
National Laboratories that funded materials and supplies over the lifetime of the
project, starting in 2007.
Id like to especially thank the final member of my committee, Dr. James
C. Y. Guo, who has mentored me throughout my involvement in the study of
water.
My thanks also go to the University of Colorado Denver for the facilities
and the great faculty and staff, including but not limited to:
Larry Scherrer Colorado Advanced Photonics Laboratory
Maria Rase UC Denver, Civil Engineering
Sam Wheeler UC Denver Network Administrator
Randy Ray
UC Denver Machine Shop
TABLE OF CONTENTS
List of Figures............................................................xi
List of Tables.............................................................xv
Chapter
1. Introduction.............................................................1
1.1 Physical Processes....................................................1
1.1.1 Infiltration.......................................................1
1.1.2 Clogging...........................................................2
1.2 Motivation............................................................4
1.2.1 Filter Beds........................................................4
1.2.2 Remediation........................................................4
1.3 Research..............................................................5
1.3.1 Type of Research...................................................5
1.3.2 Research Problem...................................................6
1.4 Scope.................................................................6
1.5 Experimental Framework................................................7
1.5.1 Process Orientation................................................7
vi
1.5.2 Data Management..................................................10
2. Literature Review.....................................................11
2.1 Fluid Flow Through Granular Aggregates.............................11
2.1.1 Darcys Law.....................................................11
2.1.2 Hydraulic Conductivity..........................................12
2.1.3 Head Loss per Length............................................14
2.1.4 Specific Discharge..............................................14
2.2 Modeling Colloid Aggregation.......................................14
2.2.1 Diffusion Limited Cluster Aggregation (DLCA)....................14
2.2.2 Reaction Limited Cluster Aggregation (RLCA).....................16
2.2.3 Ionic Strength..................................................16
2.2.4 Convectionlimited Aggregation..................................18
2.3 Fractal Dimension..................................................19
2.3.1 Definition......................................................19
2.3.2 Application.....................................................22
2.3.3 Typification of Aggregates......................................23
2.4 Electronic Pressure Measurement....................................24
2.4.1 Transducer Theory...............................................24
2.5 Optics.............................................................25
2.5.1 Physical Optics.................................................25
vii
2.5.2 Scattering.......................................................26
2.5.3 Transmittance....................................................27
2.5.4 Absorption.......................................................29
2.5.5 Absorbance.......................................................30
2.5.6 Refraction.......................................................30
2.5.7 Refractive Index.................................................31
2.5.8 Theory of Optical Elastic Scattering.............................33
2.5.9 Static Light Scattering..........................................35
2.5.10 Spectrophotometry................................................40
2.6 Mass Balance........................................................40
2.6.1 Definition.......................................................40
3. Experimental Methods...................................................43
3.1 System Components...................................................43
3.1.1 Fluid Flow System................................................44
3.1.2 Head Data System.................................................46
3.1.3 Static Light Scattering System...................................49
3.1.4 Spectrometer Mass Balance System.................................53
3.1.5 Final Design.....................................................57
3.2 Granular Media......................................................59
3.2.1 Glass Beads......................................................59
viii
3.2.2 Nafion..........................................................59
3.3 Colloids...........................................................62
3.3.1 Carboxylated Polystyrene Nanospheres............................62
3.4 Isopropanol and Deionized Water Solution...........................63
3.4.1 Preparation.....................................................63
3.4.2 Usage...........................................................64
3.4.3 Calcium Nitrate Flocculent......................................64
3.5 Data Analysis......................................................64
3.5.1 Time Scale Coordination.........................................64
3.5.2 Mass Balance Data...............................................65
3.5.3 Graphical Approach..............................................67
4. Summary of Results...................................................69
4.1 Flocculated Colloids...............................................70
4.1.1 lOmM Ca(N03)2, 5.0 mL/min.......................................70
4.1.2 100mMCa(N03)2, 5.0 mL/min.......................................79
5. Conclusions and Discussion...........................................88
5.1 Clogging...........................................................88
5.1.1 Effect of Ionic Strength........................................88
5.1.2 Effect of Flow Rate.............................................89
5.1.3 Effect of Granular Media Size...................................89
IX
5.2 Improvements to System............................................90
5.2.1 Plumbing........................................................90
5.2.2 Spectrometer....................................................90
5.2.3 Static Light Scattering.........................................91
5.2.4 Time Coordination and Data Files................................92
5.3 Granular Media Response to Increased Pressure.....................93
5.4 Future Applications...............................................94
Appendix
A. Effects of Filtering on Transducer Data...........................95
B. Order of Preparation for Study Trial...............................107
C Asbuilt Diagram of Fluid Flow....................................110
D Beam Width in Flow Cell............................................Ill
References.............................................................113
x
LIST OF FIGURES
Figure 1.1 Granular Soil Structure ("Science Buddies.Org," 2007)...........1
Figure 1.2 Possible Locations of Colloid Aggregation (D. Mays, 2010).......3
Figure 1.3: Soil and Groundwater Remediation (Environmental, 2010).........5
Figure 1.4: Clogging Study Flow Cell and Manifold (Cannon, 2009; D. C. Mays
et al., 2009)...........................................................8
Figure 1.5: Preliminary Study Setup..........................................9
Figure 2.1: Darcy's Law Apparatus(Fitts, 2002)............................. 11
Figure 2.2: Deposition and Mobilization of Colloids (Crops.org, 2011)......15
Figure 2.3 Electrostatic Double Layer (ZetaMeter, 2010)...................16
Figure 2.4 Electrostatic Repulsive Potential (Hogg, 2010)..................17
Figure 2.5 Fractal Dragon: a Selfsimilar Construction (en.Wikipedia.org)..21
Figure 2.6 3dimensional Fractal Aggregate from Colloids (Matthews & Hyde,
2011)..................................................................22
Figure 2.7 Fractal Aggregates with Their Fractal Dimensions (Min, 2006)....23
Figure 2.8: Differential Pressure Sensor (Piersen, 2010)...................24
Figure 2.9 Light Ray/Particle Interaction (Webb, 2000)......................26
Figure 2.10: Luminous Transmission (GigahertzOptik.de, 2011)................28
Figure 2.11: Absorption of all Frequencies except Red (Gallagher, 2001)....29
xi
Figure 2.12: Incidence of Refraction via Planar Surface (Hanson, 2006)...31
Figure 2.13: Index Matching of Nafion and Solutions (Kanold, 2008).......33
Figure 2.14: Relative Regimes of Scattering Theory (Webb, 2000)..........35
Figure 2.15: Methods of Depicting Scattering Data (Webb, 2000)...........36
Figure 2.16: Vector Analysis of Scattering Light (Sorensen, 2001)........37
Figure 2.17: Loglog Plot of I(q) Versus q (Sorensen, 2001)..............38
Figure 2.18: Optical Structure Factor Measurement (Sorenson, 2001).......39
Figure 2.19 The BeerLambert Law (wikidoc.org, 2009).....................41
Figure 3.1: Block Diagram of Study Components............................43
Figure 3.2 Glass Flow Column with Pressure Ports.........................45
Figure 3.3: Regression Graph for Transducer Calibration..................48
Figure 3.4: SLS Apparatus Diagram........................................50
Figure 3.5: Intensity Spectrum Graph (0 ppm).............................54
Figure 3.6: Absorbance Spectrum with and without Colloids................55
Figure 3.7: Example of Absorbance Strip Chart............................56
Figure 3.8: Flow Cell with Photon Detector and Spectrometer cell.........57
Figure 3.9: Flow Cell in Maintenance Clamp...............................58
Figure 3.10: WaterChannel Model of Nafion (SchmidtRohr and Chen).......60
Figure 3.11: Nafion in Flow Cell before and after Trial..................62
Figure 3.12: Graphical Approach to Fractal Dimension (Sorensen, 2001)....68
xii
Figure 4.1: Head Loss Data Flocculated Colloids, Sample 2011 04 002........70
Figure 4.2: Concentration of Effluent Sample 2011_04_002...................71
Figure 4.3: Mass Accumulation in Flow Cell for Sample 2011 04 002..........72
Figure 4.4: Regression Fitting for Fractal Dimension at 11 minutes.....74
Figure 4.5: Regression Fitting for Fractal Dimension at 30 minutes.....75
Figure 4.6: Regression Fitting for Fractal Dimension at 44 minutes.....76
Figure 4.7: Regression Fitting for Fractal Dimension at 62 minutes.....77
Figure 4.8: Regression Fitting for Fractal Dimension at 76 minutes.....78
Figure 4.9: Head Loss Data for Sample 2011 04 001.......................... 79
Figure 4.10: Concentration of Effluent, Sample 2011 04 001.................80
Figure 4.11: Mass Accumulation in Flow Cell for Sample 201104 001..........81
Figure 4.12: Regression Fitting for Fractal Dimension at 24 minutes.....83
Figure 4.13: Regression Fitting for Fractal Dimension at 62 minutes.....84
Figure 4.14: Regression Fitting for Fractal Dimension at 73 minutes.....85
Figure 4.15: Regression Fitting for Fractal Dimension at 87 minutes.....86
Figure 4.17: Aggregated Colloids after in situ Rinsing with Blank Solution.87
Figure A. 1: CADD Drawing of Filter Analysis...............................101
Figure A. 2: Graph of Two Filter Performance...............................106
Figure C. 1: AsBuilt Diagram........
Figure D. 1: Flow Cell/ Lens Geometry
110
Figure D. 2: Beam Refraction through Flow Cell
LIST OF TABLES
Table 3.1: Head ranges for Validyne DP 15 series transducers................46
Table 3.2: Calibration spreadsheet for transducer array.....................47
Table 4.1: Fractal dimension of sample 2011 04 002 aggregated colloids.......73
Table 4.2: Fractal dimension of sample 2011 04 001 aggregated colloids.......82
Table A. 1: Results of data with no filter..................................102
Table A. 2: Results of data with filter on positive side....................103
Table A. 3: Results of data with filters on each side of transducer.........104
xv
1. Introduction
1.1 Physical Processes
1.1.1 Infiltration
Water has the capability of transporting particles from one region to
another. It can move large boulders and gravel down river beds, or carry micro
and nanoscale particles down through the interconnected pore spaces of granular
soil, which is called infiltration. These spaces are formed because the grains have
been deposited, thus they do not form an impermeable body like a crystalline
rock structure. Their aggregated structure more resembles a loose skeleton whose
members barely touch at their tangent points, leaving room for water to move
freely between them, as can be seen in Figure 1.1.
Figure 1.1 Granular Soil Structure ("Science Buddies.Org," 2007)
The mechanism that drives water through the spaces is dominated by
head, the amount of energy that each unit of water has. The water always flows
from regions of high head to low head. Bernoullis equation in terms of energy
per unit weight describes the elements contributing to total head H\
p V2
H + z +  (1.1)
Y 2 g
P is pressure, y is the specific weight of the fluid, z is the elevation of the
fluid, V is the velocity of the fluid, and g is the acceleration of gravity. The units
are expressed in terms of length [m]. Normally, the flow in porous media is slow
enough that the velocity has no effect on the measurable amount of head. When
the flow stops, or is static, the head throughout the column is the same, but when
it flows there are losses caused by friction, so that the head at the end of the flow
is less than the head at the beginning.
1.1.2 Clogging
The nature of clogging is well understood on a macroscopic scale:
colloids or pollutants are trapped in the fdter media, flow rate is decreased, and
the efficiency of the filter decreases. As a result of clogging, the mass of trapped
material reaches a limit and the influent either diverts past the media or travels
through preferential pathways in the bed without depositing any more colloids.
On a microscopic scale their aggregated structure can be described in terms of
their fractal dimension (Wiesner, 1999). These colloids usually find it difficult to
2
aggregate unless there is an ionic concentration sufficiently strong enough to
overcome the doublewall electrostatic barrier (D. Mays, 2007).
The clogging behavior in the aggregate matrix may be influenced by
several factors such as the colloid concentration, the specific deposit, and the
location of the clogging in the matrix. According to research by Mays, the model
has four possibilities, per Figure 1.2:
HIGH FRACTAL DIMENSION
(c)
LOW FRACTAL DIMENSION
Figure 1.2 Possible Locations of Colloid Aggregation (D. Mays, 2010)
3
1.2 Motivation
1.2.1 Filter Beds
During the process of water purification, whether for drinking purposes or
to meet minimum specifications for storm water release or wastewater release,
one of the first steps is use granular media to remove colloids in the range of 10
nm to 10 um by adsorption. The filter beds pore spaces soon become choked
with buildup.
It is necessary to understand the deposit morphology in order to design
better methods for cleaning the filters so they may be reused.
1.2.2 Remediation
Cleanup of environmental damage to aquifers or semisaturated soil is
often difficult to accomplish. The colloids adsorb onto soil particles and also clog
the aquifers media in the same manner as the filter beds. New methods of
removing contaminants need to be calibrated in order to return the soil to a more
desirable state. Figure 1.3 is a diagram of a possible scenario involving
remediation of a site that has been polluted.
4
Separate Dilution Anaerobic Aerobic
phase fuel biodegradation biodegradation
Figure 1.3: Soil and Groundwater Remediation (Environmental, 2010)
By developing an understanding of the structure of the clogging, and the
structure after a method is used to clean the aggregate over time, it will be easier
to assess the viability of a particular method of cleanup.
1.3 Research
1.3.1 Type of Research
There are two basic types of research: fundamental and applied.
According to the UNESCO definitions of research types (UNESCO, 1962) this
study is an oriented fundamental study into the background of clogging in soils.
It is hoped that this research will further the understanding of the correlations
between restricted fluid flow in a packed medium (infiltration), the change in
hydraulic conductivity caused by the clogging, and the fractal dimension of the
aggregated clogging colloids.
5
1.3.2 Research Problem
There are many factors involved in understanding infiltration and
clogging. Some of them may have a greater impact than others on the rate of
clogging. One of the most important markers may be the morphology of the
fractal dimension of the aggregation of colloids in the filter matrix (D. Mays,
2010; Wiesner, 1999). It is known that the aggregation has fractal dimension(D.
C. Mays et al., 2009), but the research has not been done to map how the fractal
dimension responds to different factors like flow rate, particle size, and ionic
strength.
In order to understand and accurately document the clogging process, a
physical model needs to be constructed having a constant inflow rate, a column
of aggregates to represent onedimensional flow, and an unrestricted outflow.
The model then needs to have several means to correlate the deposition of
colloids, flow rate, change in head across points in the column, and the size and
shape of the aggregation of colloids in the filter; all of which must be coordinated
simultaneously in order to form a timerelated model of the microscopic process.
1.4 Scope
The scope of the study is to:
Investigate the morphology of colloidal deposition in pore spaces during
fluid flow through granular aggregates
6
Construct a working physical model of infiltration and clogging
Incorporate electronic recording systems for flow rate, head loss, mass
balance, and fractal dimension
Develop the procedures for repeatable experiments including solution
chemistry, calibration, observation, and software utilization
Demonstrate that there is sufficient proof to move to the next phase of
experimentation wherein enough data can be collected to form a
correlational relationship between timerelated hydraulic conductivity
morphology and the fractal dimension of the clogging
1.5 Experimental Framework
1.5.1 Process Orientation
Since a large part of the study involves investigation, the initial phase of
experimentation was directed towards understanding how the experiments should
proceed. The basic element is a small flow cell constructed of optically clear
glass with pressure ports, mounted vertically with the flow direction being
downward. Figure 1.4 features the flow cell, filled with glass beads, mounted in
the manifold, which was designed by Orion Cannon in 2009 for his masters
thesis, and constructed by Randy Ray in the UC Denver machine shop.
7
Figure 1.4: Clogging Study Flow Cell and Manifold (Cannon, 2009; D. C. Mays et al., 2009)
8
All of the measurements and data were directly related to it. The first set
of experiments was designed to see how well the instrumentation would work by
using glass beds to represent the granular aggregates. Several key factors
emerged concerning the nature of the fluid flow from the pump, the operation of
the pressure transducers, and the limits of the flow cells design. These
experiments were performed in the University of Colorado Denvers
Environmental and Hydraulics Laboratory, as shown in Figure 1.5.
Figure 1.5: Preliminary Study Setup
After working out several methods necessary for conducting experiments
with repeatable results, the apparatus and peripheral machinery was moved to the
Colorado Advanced Photonics Technology Center (CAPT) Laboratory. The
apparatus then had to be installed in the static light scanning space. Since the
9
study involved the use of fluids, great care had to be taken involving the delicate
laser and electronic equipment. The four main processes of fluid flow, head loss
measurement, mass balance by spectrometry, and fractal dimension measurement
by static light scattering then had to be coordinated.
1.5.2 Data Management
The main variables in the study were:
Fluid flow rate: from 0.1 meters per day to 10 meters per day
Aggregate size: from 100 mesh to 16 mesh or from 0.149 mm to 1.19 mm
in diameter
Ionic Strength: either 0.1 M Ca(N02)3 or none
Colloid concentration
Each set experiments was conducted at least twice. Data collected from the
SLS instrumentation had two duplicates per measurement, with a minimum of
ten data points throughout the run. The spectrometric data was collected
continuously and at least ten data points coinciding with the SLS measurements
were taken. The pressure transducers operated continuously throughout each run.
10
Equation Chapter 2 Section 2Literature Review
2.1 Fluid Flow Through Granular Aggregates
2.1.1 Darcys Law
In the late 1850s Henry Darcy developed an empirical relationship
between the flow Q [m/s] of water through sand and the hydraulic conductivity K
[m/s] of the sand multiplied by the gradient G [m/m] of the head and the cross
sectional area A of the column (Mullen, 2007):
Q = KGA (2.1)
Figure 2.1: Darcy's Law Apparatus(Fitts, 2002)
A negative sign is given to the right side of the equation to indicate that
flow is in the direction of head loss. For onedimensional vertical flow, the law is
written as:
Q = ~K~j~A (2.2)
dz
2.1.2 Hydraulic Conductivity
The hydraulic conductivity of an aquifer or porous medium is based on
the properties of the aquifer and the properties of the fluid which is described by
the following equation developed by Hubbert (1956):
K = (2.3)
v
2 2
For which k [cm ] is the intrinsic permeability of the aggregate and v [cm /s] is
the kinematic viscosity of the fluid. For spherical objects, the value of k may be
estimated using the KozenyCarman equation :
1 ( d2 } U50
o 00
where n is the porosity and d5o is the median diameter of the aggregate. The
equation takes into account the tortuosity r of the flow path, which is the
effective flow length compared to a straight line (Bear, 1988).
r=i(2'5)
12
Since the Darcy equation is an empirical relationship, there are several
caveats involved. The main restriction is that the flow regime should be well
within the laminar range, in order to be able to treat the specific discharge,
particle diameter void ratio as average quantities. In fact, the Reynolds number
should be kept below 10 and most certainly around 1. The Reynolds number is a
dimensionless number, signifying the ratio between the inertial force and the
viscous force (Elimelech, Gregory, Jia, & R.A., 1995). For pipe flow it is usually
expressed as:
VL
Re = (2.6)
v
Where V is the velocity of the fluid, and L is a characteristic length.
Because the velocity of the fluid is not apparent, and the characteristic length is
sometimes defined in different ways, the Reynolds number in packed beds is
given as (Bird, 1996):
Re =
pqd
p{\s)
Where d is the particle diameter, u is the dynamic viscosity, and e is the
volume of the voids divided by the total volume. Practically speaking, the
diameter of the particles should be at most l/30th of the column diameter. The
effect of raising the Reynolds number is to create lateral flow in the bed or
column. If the flow rate increases drastically, preferential pathways will form.
(2.7)
13
2.1.3 Head Loss per Length
The head loss per length of flow represents how much energy is
transferred during the fluids path through the aggregates. Since the fluid will
adhere to the surfaces of the aggregates, it experiences friction. The energy loss
will shift heat to the aggregates from the fluid. Some heat will also be used to
break some of the hydrogen bonds between the water molecules (Fowler, 2007).
2.1.4 Specific Discharge
Darcys law can also be expressed as the specific discharge q.
q = (2.8)
dz
It is actually the flow per unit area, per time, which is a flux. The area in question
is the area of the column used to measure dh/dz. The actual velocity of the fluid
is
v= (2.9)
n
2.2 Modeling Colloid Aggregation
2.2.1 Diffusion Limited Cluster Aggregation (DLCA)
DLCA is typified by a static process, where Brownian motion is the main
contributor to colloid interaction. The ratelimiting step is diffusion of matter to
the aggregate (Witten, 1983). In this case the colloids will form flocculants,
which have the tendency to fall out of the solution to the bottom of the container
14
when there are no granular aggregates present. When they are present, and the
fluid is flowing, the flocculated clusters may have a large enough diameter to
stick in the throat of the pore space, as in Figure 2.2.
deposition
few ** %\ !W fra. i .: t A If . ; v/'iV*
til OS i \ gfr~ y 'y\ r ^ \ , z \ qSS ^;; p p ~j. ; s> i / oM 1 vv,^ ou ,1. v v.'CVfV'f J >v. ^( ^t' , .(*: ';.2:.TF fi &&  i: 6 s Vl J
grain attachment airwater KWIIIIMR pora attaining attachmawt flhn attaining attachment
mobilization
Figure 2.2: Deposition and Mobilization of Colloids (Crops.org, 2011)
15
2.2.2 Reaction Limited Cluster Aggregation (RLCA)
RLCA occurs between clusters when many collisions need to occur
before they bond (Koutsoukos & European Colloid and Interface Society, 2001).
That is, when the rate limiting step is diffusion over a barrier in the interaction
potential between the colloids. During a dynamic process the rate of collisions
would be greatly increased over a static situation. One would expect to see more
aggregation during flow than during a quiescent state.
2.2.3 Ionic Strength
The barrier between the colloids is caused by the formation of an
electrostatic double layer. This happens when counterions (electrons) are
attracted to the surface of each colloid.
Positive CounterIond
Negative CoIon9
3
3
3
a
o
a
9
9
Figure 2.3 Electrostatic Double Layer (ZetaMeter, 2010)
16
The cloud of electrons around each colloid makes it difficult for the
colloids aggregate because of repulsive forces until the ions are close enough for
Van der Waals attractive forces to dominate (Derjaguin & Landau, 1941).
Figure 2.4 Electrostatic Repulsive Potential (Hogg, 2010)
The strength of the solution in which the colloids are transported plays a
large role in the aggregation of the colloids. As mentioned previously, the barrier
is composed of oppositely charged ions, or coions. When salt is added such as
Ca(N02)3, the ionic strength of the solution is greatly increased. Ionic strength is
related as
The effect of ionic strength
Physiological ionic
strength
(2.10)
17
where /i is the ionic strength in moles, C is the molar concentration [M], and Z is
the charge of the ion (McNaught & Wilson, 2010). The presence of more ions
compresses the shell size of the coions, so that the Van der Waals attractive
forces overcome the electrostatic repulsion of the coions for the colloids.
The Critical Coagulation Concentration (CCC) is the threshold for
flocculation of the colloids (Sposito, 2008), and is expressed in terms of the
counterion valence to the sixth power:
CCC>Z6 (2.11)
2.2.4 Convectionlimited Aggregation
Where external flows are present, such as those that take place in the void
structure of the granular aggregates in the flow cell, the rate limiting step is the
convective transport of the colloids (Warren, Ball, & Boelle, 1995). When there
is no interaction barrier the degree of aggregation is determined by the Peclet
number, Pe, where v is the velocity of the particle, L is the diameter and D is the
mass diffusion constant, signifying the tradeoff between convection and
diffusion.
Pe = (2.12)
D
18
2.3 Fractal Dimension
2.3.1 Definition
The geometric definition of dimension states that a configuration has
dimension n, if n is the least number of realvalued parameters which can be
continuously used to determine the points of the configuration (James & James,
1992). The familiar line, surface and volume would still have dimension 1, 2, and
3 by that definition. It is also relevant for vector spaces, whose basis is the least
number of linearly independent vectors that can generate the space. These ideas
work very well for regularly defined spaces, but what about entities that arent
smooth, or are discontinuous?
Hausdorff dimension
The earliest investigation into a noninteger notion of dimension was
originally published by Felix Hausdorff in 1918 (Hausdorff, 1919), from a
geometric construction of Constantin Caratheodory. Their approach came from
the notion of a measure. It can be defined for any set, and is easily manipulated.
The central idea is that of delta (6), the cover of a set. For any set of points U in
ndimensional space, the diameter of U is the greatest distance apart of any pairs
of points in U. If {Ui} is a finite collection of sets of diameters at most 6 that
19
cover F, then {Ui} is a 8 cover of the set F. The mathematical definition of an s
dimensional Hausdorff measure of F is:
(2.13)
It has the surprising property that there is a one value of s at which SC5 (F)jumps
from infinity to zero (Falconer, 2003), which is the fractal dimension of the set:
Mandelbrot
Benoit Mandelbrot applied the idea of measure and cover to the study of
geometry in nature. There are many objects whose measured length increases as
the size of the yardstick is reduced, such as coastlines. He found that the measure
M of the length 8 follows the formula
By plotting the measured map length of the coastline of Norway as a
function of the size 6x8 squares used to cover the coastline, he found that the
dimension s is approximately 1.52. By taking logarithms of both sides and
rearranging, s can be expressed as
Ms{F) = cS[
(2.14)
s = lim
(2.15)
logÂ£
20
The Mandelbrot Set is a general class of fractal shapes in two dimensions
that are generated by an iterated function
+ C (2lV
with z0 = C,where points in the complex plane for which the orbit of z does not
tend to infinity are in the set(Weisstein, 19992011). Pictured below in Figure 2.5
is a fractal shape generated as a member of the Mandelbrot set. The computed
fractal dimension is important to know, as the shape is very similar to a class of
fractal aggregates.
Figure 2.5 Fractal Dragon: a Selfsimilar Construction (en.Wikipedia.org).
The numerical value of d for the Fractal Dragon is calculated to be
approximately 1.52 (Chang & Zhang, 2009).
21
2.3.2 Application
In order to quantify colloidal deposits, direct measurement is impractical.
By finding the fractal dimension, and knowing the bulk properties, the size and
position of the aggregations can be determined.
N is the number of colloidal particles (proportional the colloidal mass), ko is a
constant of proportionality approximately equal to one, Rg is the radius of
gyration, a is the colloidal radius, and D is the dimension.
As can be seen in Figure 2.6, the aggregate is composed of selfsimilar
shapes, with a large amount of empty space (porosity).
Figure 2.6 3dimensional Fractal Aggregate from Colloids (Matthews & Hyde, 2011).
(2.17)
22
2.3.3 Typification of Aggregates
DLCA has a range of D from 1.75 to 1.8, whereas Rate Limited Cluster
Aggregation has a range from 2.1 to 2.2 (Elimelech, Gregory, Jia, & Williams,
1995). Convectionlimited aggregation produces fractal dimension D of
approximately 2.5 (Warren et al., 1995). Figure 2.7 gives some perspective on
the types and formation of different fractal aggregates.
_______________ft = 2 8__________ft = 2.>_________ft = 1.8
ft = 1.2
y as IJD
y 3.84
r 10L4
23
2.4 Electronic Pressure Measurement
2.4.1 Transducer Theory
Transducers are strainbased instruments: operating by the use of
diaphragms which are connected to small moving coils, exactly like a telephone
microphone. Figure 2.8 shows how they are constructed.
I
ton**
Figure 2.8: Differential Pressure Sensor (Piersen, 2010)
The signal from the transducer is always in reference to something. In the
case of a fluid pressure measurement, the reference is the atmosphere. A
drawback of using the atmosphere is that its pressure varies considerably. By
using the same fluid, but in a different location, the pressure, or in our case, head
loss, is insulated from random atmospheric pressure variations.
Since the information about the head loss is carried by the output of the
transducer, and it is always slightly changing, the signal is than an alternating
current. The way that it is measured is in terms of change of voltage compared to
a very small DC carrier voltage (V/v), or variable reluctance.
24
The sensitivity of the sensor depends on the thickness of the diaphragm.
The sensitivity places a limit on the range of each sensor, because pressures that
exceed the range can cause damage to the diaphragm. At the same time, a high
sensitivity creates a higher amount of noise, so part of the challenge was to
design an array of sensors for a much wider range than any single transducer and
reduce the inherent noise.
2.5 Optics
2.5.1 Physical Optics
Light is an electromagnetic phenomenon whose nature is twofold: it can
be either thought of as particles (photons) or waves. In this study, we are
concerned with how light conducts itself around particles capable of transmitting
it. The study of light in this manner is called physical optics, which deals with the
sum of the photonelectron interactions considered across the boundaries of the
gross physical system. It lies in between geometric optics, which concentrates on
rays, and full wave electromagnetic theory.
25
2.5.2 Scattering
Formally, scattering occurs when the bound electron cloud in the material
interacts with the photon of the incident light beam, and reemits the photon in a
different direction (Webb, 2000). With the optical phenomenon of interference,
optical scattering accounts for other more macroscopic optical phenomena
including transmission, diffraction, reflection and refraction. Absorption,
however, is an electronic excitation in the material which cannot be accounted by
optical scattering.
The following illustration in Figure 2.9 shows how scattered light is
defined in various ways as it encounters matter.
Diffracted ray
Transmitted aftep^
internal reflection
Reflected
Transmitted ray
No interactiarundeviated ray
Figure 2.9 Light Ray/Particle Interaction (Webb, 2000)
26
The total energy for a single photon may be expressed as the sum of the
scattering intensities and the energy absorbed by the individual atom from
photons that do not escape the bound electron cloud. The total effect of the
particle on the light is termed extinction (Wedd, 2003):
Extinction = Scattering + Absorbtion (2.18)
2.5.3 Transmittance
Transmittance is the calculated amount of light that passes through an
object or sample. It equals the number of photons that travel through the object in
a linear fashion, without being absorbed, or scattered diffusely, compared to the
number of photons which were emitted by the source. It is usually expressed as a
percent, by measuring the intensity of the throughput at a receptor and comparing
it to the source intensity("Light Transmission," 2011). Figure 2.11 shows how
transmitted light differs from the incident light.
27
Light Input 100 %
Light Output 70 %
70% Regular Luminous Transmission
v.
Light Output
I
Light Input
> Regular and
Diffuse Transmission
Figure 2.10: Luminous Transmission (GigahertzOptik.de, 2011)
The transmittance is usually measured as a function of a particular
wavelength, since the intensity is frequency dependent, as related by the
following equation, where 1(A) and I0(A) are the intensities of the transmitted
and the incident laser beams at optical frequency A respectively.
(2.19)
28
2.5.4 Absorption
Absorption is the process of a light ray or photon being absorbed to excite
the electronic state of the matter. The absorbed photon energy can be dissipated
as heat or an optically redshifted photon can be reemitted depending on the
molecules. The total energy of the matter is then increased by the energy of the
photon. The visible effect is to perceive the color of an object, which is the
absence of the absorbed wavelength. In Figure 2.11, the eye perceives the apple
as red, since the other wavelengths except red have been absorbed by the apple.
Figure 2.11: Absorption of all Frequencies except Red (Gallagher, 2001)
29
2.5.5 Absorbance
Absorbance is an alternative quantity to describe optical transmission.
Absorbance is unitless, expressed as a logarithm, with the following formula,
where T is transmission:
A= log,
( 1 'A
(2.20)
2.5.6 Refraction
Light changes its propagation direction as light propagates from one
optical medium to another optical medium. There are several factors determining
the amount of optical refraction including: the optical materials, the angle of
incidence, and the wavelength of the light, but the most important factor that
determines optical refraction is, in the static light scattering experiment, the
refractive indices of the optical material. To put it into context, the amount of
refraction from the spherical aggregates needs to be minimized so that the
detector is receiving scattered photons mostly from the aggregating colloids.
30
2.5.7 Refractive Index
The refractive index (n^) is defined as the velocity of light in vacuum (C)
divided by the velocity of light in the material ().
c
n, =
(2.21)
Refractive index can be used to calculate the refractive angle as light propagates
from one medium to another medium following Snells law where nA and nB are
the refractive index of the first and the second optical media and and dt are the
incident and refractive angles. Therefore, according to the Snells law, if the
refractive indices are equal, then the refraction angle is the same of the incident
angle, thus resulting in no contribution to the background of light scattering
nA sin 0A = nB sin 0B (2.22)
The action of Snells Law is depicted in Figure 2.13.
Light moving at speed vA \* Medium A Refractive Index 1 1 1 1 "I sh
Medium B \
Refractive Index nB j\
Light moving
at speed vg
Figure 2.12: Incidence of Refraction via Planar Surface (Hanson, 2006)
31
However, if the refractive indices are different, the refractive angle will
differ from the incident angle, thus resulting in some background signal in the
light scattering measurement.
For planar light waves entering the medium perpendicularly, the incident
angle is 0 degrees, as well as the exiting angle. But for planar waves entering a
curved surface at various angles of incidence, the refractive indices need to be
matched so that the exiting light is still travelling in a planar manner. The curved
surface of the flow cell will act as a lens and redistribute the light rays paths, but
they will still be parallel to the incident rays. Inside the cell, though, the indices
of refraction of the fluid and the granular aggregates must be matched so that the
planar nature of the light is preserved.
Index matching of different substances can be accomplished by finding
two fluids whose indices of refraction are grouped around the target index, then
forming solutions of different concentrations which may be analyzed optically
with a refractometer, or by visual inspection (Kanold, 2008). Seen in Figure 2.13
are samples which were used to find the best concentration of fluids to match the
index of refraction for the granular aggregate on the right.
32
Figure 2.13: Index Matching of Nafion and Solutions (Kanold, 2008)
2.5.8 Theory of Optical Elastic Scattering
When an electromagnetic wave (light) interacts with the material elastic
and inelastic scattering can occur. Optical elastic scattering refers to optical
scattering processes such that the photon energy of the incident photon does not
change during the scattering process, resulting in no change of the optical
frequency after the scattering event (Hecht, 1987b). There are also optical
inelastic scattering processes such as Raman scattering which is not relevant to
our experience so it is not discussed in this thesis. Depending on the size of the
material, optical elastic scattering is divided into two categories: Rayleigh
scattering and Mie scattering (Hering, Lay, & Stry, 2004).
Rayleigh scattering is the optical elastic scattering process (Nave, 2001)
of the scattering material having a radius less than the optical wavelength of the
incident light wave. This includes most atoms and molecules. The scattering
efficiency of the Rayleigh scattering has a A4 dependent on the optical
wavelength (A) and Rayleigh scattering is not sensitive to the surface structure of
the scattering material. Therefore Rayleigh scattering is often used to explain the
33
blue color of a clear sky due to higher scattering efficiency of scattering the blue
frequencies than the red frequencies by the air molecules from sunlight.
Mei scattering theory encompasses all of the prior theories, and was
developed by Gustav Mie around 1908 on the mathematics concerning the color
of gold colloids (Mie, 1908). It is applicable to spheres of all sizes (Hecht,
1987a),but particularly in the Mie range, which is for sizes between
0. 1
x = 2ff(r/A) (2.23).
Specifically, at least two of the following conditions must be met (Webb, 2000):
x1 or x1
n 11 or n 11 (2.24).
x(l)l or x(l)l
The following diagram depicts where different scattering theories are useful. Mie
theory predicts scattering for spherical particles exactly. It is the central tool for
determining the actual size of very small particles such as aerosols and pigment
nanoparticles.
34
Figure 2.14: Relative Regimes of Scattering Theory (Webb, 2000)
Although Mie theory was originally derived based on spherical particles,
Mie theory is also useful for measuring scattering of nonspherical particles in
nonideal cases. Thus Mie theory can be applied to finding the equivalent
spherical radius of aggregated colloids as well as its associated fractal dimension
2.5.9 Static Light Scattering
Based on the Mie scattering theory, the technique of Static Light
Scattering, or SLS, is developed. SLS is the measurement of the intensity of
scattered light at different angles, or equivalently the qvector, around the
suspended colloidal sample. SLS theories do not involve quantum effects which
would come into play during relative motion of particles. Seen below are various
35
ways of describing the position and intensity of the scattered light. The
noticeable peaks in the intensity data are referred to as Mie humps. They
represent the fringe effects from different sphere sizes.
Figure 2.15: Methods of Depicting Scattering Data (Webb, 2000)
36
The diagram in Figure 2.16, below, shows how incident light with wave
vector k, from the left impinges on the particle and scatters at r towards the
detector with scattering vector ks at angle 6 so that
= k:k.
(2.25)
Figure 2.16: Vector Analysis of Scattering Light (Sorensen, 2001)
Using n0 as the index of refraction of the colloid, the scattering vector for
vertically polarized light is then:
47rn0 sin(#/2)
I
(2.26)
37
By applying the scaling concepts from fractal geometry with the above
vector analysis, Sorensen developed the following relations for the intensity of
the scattering compared to the qvector in a lattice of N scatterers:
N is the number of scatterers, R is size of the region, 2a is the separation
between particles (diameter) in region R, Dm is the fractal mass dimension, and
Ds is the surface fractal dimension of the surface of region R. The difference (2
Dm Ds) is the overall fractal dimension D, as shown in Figure 2.17. Sorensen
goes on to show how the equations may be used for either a sphere of diameter d,
where D=d, or for a fractal aggregate where D= D, = Ds
be described as the radius of gyration, Rg, of the aggregated colloid.
N2
I (q) oc j N2(q R)_2Dm+Ds
N2(R/a)"2Dm~Ds
for q < R '
for R'1 < q < a"1 > (2.27)
for q > a'1
2
l(q)
Slope =
 (2Dm Ds)
R
i
l
a
q
Figure 2.17: Loglog Plot of I(q) Versus q (Sorensen, 2001)
38
Sorensen develops the relation between I and q as the optical structure
factor measurement as shown in Figure 2.18. From the optical structure the
following values may be deduced: the aggregate radius of gyration /?Â£,the fractal
dimension D of the aggregated colloids, the polydispersity of the aggregate size
distribution and the monomer size a, if the wavelength of incident light is short
enough. The region to the right of aA is where the Mie humps caused by
spherical scatterers are located.
Rayleigh Guinier
regime regime
~nN2 = NmN
Power Law
regime
Monomer
regime
Slope = 4
R
i
a
g
Figure 2.18: Optical Structure Factor Measurement (Sorenson, 2001).
39
2.5.10 Spectrophotometry
Spectrophotometry is the combination of providing a light source and
recording the intensity of light after it travels through a sample. The instrument
consists of three major sections: a light source, a sample cell and a photometer.
Both the source and the photometer are part of a stack of machines, including a
processor and memory. The processing can be done on board or using a separate
computer.
2.6 Mass Balance
2.6.1 Definition
The mass balance is simply that the accumulated mass equals the mass in
minus the mass out.
Maccused =M,nMou, (228)
The mass of the colloids which enter the flow cell is a function of the
flow rate [mL/min], the concentration of the colloids [ppm] and the total flow
time, since the inflow will be assumed to have a constant concentration.
Mm=QCM (2.29)
Concentration of the influent is set by dilution of a known colloidal
concentration. It follows the law
C,VX=C2V2 (2.30)
40
The effluent concentration can be measured through spectroanalysis. The
concentration C of the outflow is directly related to the absorption A by the Beer
Lambert Law, as illustrated in Figure 2.19:
Figure 2.19 The BeerLambert Law (wikidoc.org, 2009)
A = elC
(2.31)
Where Â£ is the molar absorbtivity with units of [L mol'1 cm'1], / is the
path length of the sample that is, the length of the spectrometer cell in which the
sample is contained, and C is the concentration of the compound in solution,
expressed in [ mol L'1].
The absorbance of the sample is calculated by
A= log
10
f I / ^
1 s 1 dark
V A) I dark J
(2.32)
41
/ is the intensity registered as photons per second received by the
spectrometer, transmitted through the sample in the solvent. Io is the intensity of
the signal transmitted through the pure solvent. Since there is always background
energy present in both samples, it must be subtracted before computing the
absorbance.
In order to graph the absorbance as a timedependent variable, software used
in the spectrometer must first have an intensity spectrum of the blank sample
with an integration time.
42
Equation Chapter 3 Section 3 Experimental Methods
3.1 System Components
In order to understand the relative subsystems in the study, an overview is
offered which should clarify the overall functioning of the analysis. Seen below
is a block diagram of the fluid flow system, the head data collection system, the
SLS data collection system and the spectrographic mass balance data collection
system.
Figure 3.1: Block Diagram of Study Components
43
3.1.1 Fluid Flow System
The supply consists of two vessels with a switching valve, so that the
flow may be uninterrupted. The supply vessels are oneliter Erlenmeyer flasks
with stoppers to minimize evaporation of the solvent. A stirrer keeps the sample
with colloids thoroughly mixed. A low speed is used to keep air bubbles from
being introduced.
The pump is a Masterflex L/S model peristaltic, twin roller head pump,
manufactured in the United States. Masterflex is a subsidiary of ColeParmer ,
located in Vernon Hills, Illinois. The pump is easily calibrated using Masterflex
specifications and the proper size tubing for the flow value. It provides very
accurate flow from 0.1 ml/minute to 20 ml/minute. In our case the heads were
installed antisymmetrically so that the output was not pulsed.
The flow cell is constructed of high grade optical borosilicate glass. It has
an inner diameter of 1.2 cm, and is 10 cm long. Four ports are arranged as shown
in the following diagram (Figure 3.2).
44
Material:
Pyre* Glass
Wall Thickness
1.3 1.5mm
n/428 THREAD
Figure 3.2 Glass Flow Column with Pressure Ports
The manifold was designed to be able to support the cell, and to provide
an inflow and outflow port. The plate is bored through with a recess for accepting
the cell. A screen mesh is placed in the recess at the outflow to prevent the
aggregates from escaping. The cutaway plates also have an additional port facing
out which is convenient for head measurements and air bubble bleeding.
The manifold can be either secured to a clamp for maintenance or directly
onto a mount that fits into the SLS space. It can also accommodate a separate
motordriven vertical displacement device.
After leaving the manifold drain, the effluent is directed to the
spectrometer SMAZ cell, and then goes directly to a receiving flask.
45
3.1.2 Head Data System
The head loss is measured across a length of the flow column using
Validynes DP 15 series transducers. Validyne Engineering Corporation is located
in Northridge, California. Three transducers were installed in parallel between
port 3 and port 4. The ranges and sensitivity of each transducer is listed in Table
3.1, seen below. The output from the transducers is recorded using Validynes
EasySense software, at specified intervals averaging up to a thousand
measurements per second.
Table 3.1: Head ranges for Validyne DP15 series transducers
MODEL Low Range (cm) High Range (cm)
DP 1520 5.60 8.80
DP 1526 14.0 22.5
DP1532 140 225
Because of the highly sensitive nature of the transducers, it was necessary
to buffer the data physically by using flow filters in the pressure lines from the
flow cell. The filters also served to prevent granular aggregates from migrating
into the transducers. A separate report on the use of the filters is in Appendix 1.
Typically, the signals from the transducers were calibrated from V/v to
centimeters of head through a regression process using three data points from a
pair of static columns. The significant figure for calibrating the transducers is one
decimal place, since the columns accuracy is limited to 0.1 cm. The three data
46
points were the result of one minute of recorded static pressure per data point, as
demonstrated in the Table 3.2.
The transducers have separate ratings, so they are placed in parallel
across the third and fourth ports. An average of their readings can be made to
assure quality, or if the rating is exceeded on one, it can be switched out of the
loop.
Table 3.2: Calibration spreadsheet for transducer array
Calibration for positive delta H reading
Transducer dh (cm) v/V (oneminute average)
DP 1520 0 0.0607
5 0.1219
10 0.1732
DP1526 0 0.0072
5 0.0013
10 0.0056
DP 1532 0 0.0083
5 0.0110
10 0.0140
The spreadsheet generated the following regression graph (Figure 3.3),
which was used to calibrate the transducers so that they recorded head loss over
the cell length versus time. The transducer array was susceptible to drift, so a
check for accuracy was performed before every trial.
47
Figure 3.3: Regression Graph for Transducer Calibration
48
3.1.3 Static Light Scattering System
The SLS system was originally designed by Dr. Tim Lei, professor of
Electrical Engineering at UC Denver for the CAPT lab. The core of the system is
a travelling photon detector which describes an arc of 151 degrees from the line
of direct transmission. The systems other components consist of:
A HeliumNeon laser
A signal chopper
A vertical polarizer
Waveguides to direct the laser beam to the cell
A collimating (reverse Fourier) lens placed before the flow cell
An auxiliary laser used to align the cell/stanchion with the photon
detector
A radial control computer to precisely move the detector along the arc to
specified points
A second photodetector and power meter to record incident beam signal
strength before and after trials
A shield to reduce the incident beam at the direct transmission point to
protect the main photodetector at small scattering angles
A LabView controlled computer to record the data and control the
amplification of the detector signal.
49
Seen here in Figure 3.4 is a diagram of the studys systems:
Figure 3.4: SLS Apparatus Diagram
The heliumneon laser produces an intensity controlled beam at a
wavelength of 633 nm. The light is then processed with a signal chopper that
turns it into an AC waveform (O'Haver, 2000), before being vertically polarized.
The light must be vertically polarized to conform to the requirements of static
light scattering analysis(Sorensen, 2001). The beam is reflected three times
before passing through the first alignment aperture. The beam then enters a
reverse Fourier lens (Lehar, 2010; Webb, 2000), that counteracts the spreading
50
caused by the flow cell. After leaving the flow cell, the scattered light is received
slightly outofplane by the detector as it travels. At small angles the detector is
protected from the high intensity present at the beginning of the trial by a semi
circular mirror. It is positioned so that only 10 percent of the straight beam would
impinge the detector at zero degrees.
The movement of the detector is controlled by a three axis driver,
programmed to stop for milliseconds at various positions, where the detector
opens its aperture to take a picture of the scattered light.
The secondary detector is used to record the signal strength before and
after the trial in order to document any drift in the output of the laser. It is also
part of the alignment process, giving a peak value at proper positioning of the
cell and the lens.
The data which is recorded in the computer includes the angular
description as qvector, and the intensity of the scattered light, after being
processed by an amplifier. The amplification can be optimally selected to keep
the signal from oversaturating the input, and high enough to register faint signals
at large angles. The data is then ready for postprocessing to determine the fractal
dimension of the colloids at that particular time.
During the previous SLS study by Cannon (2009), which used samples in
cuvettes that did not have flow involved, the scattering from the cuvette, the
51
fluid, and the granular medium were subtracted from the total scattering, leaving
the scattering caused by the colloids. A similar approach was taken in this study,
using a scan of the sample before colloidal flow was initiated, but after the flow
had stabilized the head loss and the slight compression of the sample. Since two
scans were made for each record, the data was averaged for each value of the q
vector.
52
3.1.4 Spectrometer Mass Balance System
An OceanOptics, Dunedin, Florida, JAZ compact spectrometer was used for
the study. It could be operated as a selfcontained unit or in conjunction with a
separate computer using SpectraSuite software. The components consist of:
A tungsten lamp light source
Fiber optic cables to route the source light to the sample cell and return
the transmitted light to the photometer
An FIALab, Belleview, Washington, SMAZ flow cell to allow
continuous realtime absorbance data.
Following the directions in the SpectraSuite manual were generally sufficient
to operate the machine correctly, but knowledge of the trick of using subtraction
of dark pixels to graph absorbance helped. The spectrometer uses reference
measurements of the intensity of the transmitted light spectrum through a blank
sample (.omniref files), and a measurement of the background noise (.omnidark
files). The spectrum of light from the tungsten lamp covered from 469 to
llOOnm.
By storing a reference, the absorbance can be calculated by the software. It is
important to note that the measurement should take place on either a single pixel
or over a small range where the absorbance is highest. It is also a good idea to
53
use the stored references as a reference monitor to minimize drift. The range for
the monitor should coincide with the range of absorbance measurement.
The following screenshot (Figure 3.5) of one of the intensity graphs shows
the saturation amplitude and the spread of the emission spectrum from the lamp:
Figure 3.5: Intensity Spectrum Graph (0 ppm)
The electric dark option removes information from dark pixels which are
not being triggered by a photon that would distort the absorbance calculation.
Care must be taken to do it in the proper order, or the data can be misconstrued.
Figure 3.6 shows a sidebyside comparison of the absorbance spectrum of a
54
blank sample, and a sample with 100 ppm carboxylated polystyrene. Both have
lOmM concentration of Ca(N03)2, and are in flow conditions in the SMAZ cell.
Notice the green line in the center of each graph: it signifies the
wavelength used to create the absorbance strip charts. It was chosen because it is
where the absorbance for a blank sample was practically zero.
Figure 3.6: Absorbance Spectrum with and without Colloids
. In order to be able to calculate the concentration from the absorbance, a
regression should be done using a ten minute average of the absorbance at 0 ppm
and 100 ppm. The software does this by running a strip chart. The parameters can
be set using the wizard. The record of the trial is also on a userdefined strip
chart, as seen next in Figure 3.7.
55
Figure 3.7: Example of Absorbance Strip Chart
The calculated concentration values for the effluent can then be smoothed
over a range of values in order to determine the specific deposit of colloids in the
flow cell.
56
3.1.5 Final Design
One of the main restraints for the system was to be compact, as the space
allotted for the SLS components, the flow cell and the spectrometer cell was only
three feet high, four feet deep and five feet long. Figure 3.8 shows the completed
setup for the SLS portion of the study.
Figure 3.8: Flow Cell with Photon Detector and Spectrometer cell
A separate platform for the main computer and SLS rotation driver was
already in place, but two more platforms were necessary. The first one had to be
57
adjacent to the SLS space, so that the flow cell stanchion could be removed and
mounted for maintenance, and replacement of the clogged granular media. Seen
below in Figure 3.9 is a picture of the manifold and cell being held in a clamp,
after the cell had become fully clogged.
Figure 3.9: Flow Cell in Maintenance Clamp
58
3.2 Granular Media
3.2.1 Glass Beads
During the preliminary investigation, manufactured glass beads were used
in the flow cell. They had a sphericity of nearly unity and a median diameter of 2
mm. When the flow rate was kept at or below 5 mL/min, the Reynolds number
was in the range of 1.0 to 2.0, which made them a good test subject for fine
tuning the flow cell and transducer operation. They were not suitable for
operation in the SLS system, though, since they could not be indexmatched.
3.2.2 Nafion
Nafion is a product made from Teflon by E. I DuPont (Lehar, 2010;
Webb, 2000). It is usually prepared in sheets, but for the studys use it was a
shredded granular material resembling abraded vinyl from C. G. Processing,
Rockland, Delaware. The product was graded by diameter from 1635 mesh; 35
60 mesh and460100 mesh. It is hydrophilic, so that when exposed to water it
expands slightly and assumes a softened, spherical shape resembling tapioca
pudding. The amount of fluid each grain absorbs comes into equilibrium after 24
48 hours.
One theory of its structure is that of having water channels ("Ion Power 
Products," 2011), so that fluids are transported deep inside each grain, as shown
in Figure 3.8. It will, however, rapidly dehydrate when exposed to air.
59
Water Channel Model
H2O channel crystallite
Figure 3.10: WaterChannel Model ofNafion (SchmidtRohr and Chen).
During former studies (Kanold, 2008 and Cannon, 2009), guided by Dr.
Mays, Nafion was determined to have a very close index of refraction to water
and isopropanol as was shown in Figure 2.13. The refractive index is reported to
be 1.379 (SchmidtRohr & Chen, 2008) at 20C, but it will vary according to
manufacturer and fluid content. Both Kanold and Cannon found that the solution
of 42% isopropanol and 58% deionized water produced the best results. The
same concentration amounts came as a result of this studys efforts.
One of the main concerns in the study was the removal of air bubbles
from the system, especially in the Nafion. After soaking in the solution while
being gently stirred, most of the air bubbles were removed. The solution had to
60
be decanted once to help diminish the brownish appearance of some of the
grains. When the Nafion was placed in the cell, it had to be inserted using a bulb
and 'A inch tube, so that new air bubbles were minimized. Gentle backwashing
using a pump rate of 1.0 ml/minute lifted the mass of Nafion up in the cell about
a centimeter, and then the air bubbles could rise up through the softened granular
aggregates. Looking closely at the Nafion, the individual grains could be seen to
drop back down in the cell.
61
Shown in Figure 3.10 is a picture of the cell with Nafion in it, prior to a
trial. Next to it is the same cell after the trial, showing how the colloids have
coated the aggregates. The ionic strength of the solution was low, so there was
almost no coating of the Nafion compared to later trials.
Figure 3.11: Nafion in Flow Cell before and after Trial
3.3 Colloids
3.3.1 Carboxylated Polystyrene Nanospheres
The colloids used in the study were 99 nm and 106 nm diameter
monodisperse carboxylated polystyrene spheres, manufactured under strict
quality controls and suspended in latex beads, 10% by mass. The latex beads are
comprised of approximately 69% water. A small amount of surfactant
(carboxylate) is added by the manufacturer to keep the nanospheres
62
monodisperse. The polystyrenes refractive index (dry) is 1.55 to 1.59 (Sigma
Aldrich, 2011).
The target concentration of the colloids was 100 parts per million (ppm).
The standard dilution equation was used to calculate the volume of solution
needed to arrive at 1000 mL of solution.
CxVi = C2V2 (2.1)
The exact volume of colloids needed was then calculated to be 1 ml for
every 999 ml of solution. Essentially, since 1000 ml graduated cylinders were
being used; the volume of solution was rounded to 1 liter.
3.4 Isopropanol and Deionized Water Solution
3.4.1 Preparation
Isopropanol (C3H8O) has molecular weight 60.08 grams per mole. It
completely mixes with water, which makes preparing a solution fairly
straightforward. Both the isopropanol and deionized water are each filtered
twice through 2.0 um filter paper using vacuum pressure. The fluids are allowed
to settle overnight and degas. The next day 420 ml of the isopropanol is gently
poured into a 1000 ml graduated cylinder.
Enough water is added to bring the total volume to 1000 ml, which makes
a 42% C3H8O in 58% H2O solution. Stirring, using a stir plate with magnetic stir
63
bar overnight at low speeds, in a stoppered flask mixes the solution and removes
the air bubbles.
3.4.2 Usage
The solution was then used to saturate the flow cell and the transducer
pressure lines. It also served as the baseline for the absorbance calculations in the
spectrometer. The refractive index of 40% isopropanol solution is 1.36 at 20 C
(Hyperphysics, 2011).
3.4.3 Calcium Nitrate Flocculent
According to the empirical SchulzeHardy rule (Haynes, 2011), by
increasing the ionic strength of the solution, the colloids will flocculate easier.
Compared to a solution containing NaCl, the critical coagulation concentration of
calcium nitrate would be at least 16 mM. The hypothesis is that the mass of
accumulated colloids should increase by adding the calcium nitrate. Too much in
relation to the concentration of colloids may produce a gel instead of fractal
structures, so the ionic strength may have to be adjusted.
3.5 Data Analysis
3.5.1 Time Scale Coordination
Since the study involved the use of three data recording systems which
had time stamps, an appropriate method of analyzing the data needed to be
64
developed. The head data and mass data were continuously recorded, but the SLS
data was gathered at rough intervals of every 15 to 30 minutes.
Each data file of SLS data also was spread out over a 2 to5 minute
window; since the detector had to traverse the arc twice each way for every
record (each file contains two scans), but since the colloidal accumulation
doesnt change much in five to ten minutes the time stamp on the SLS data file
can be used as the marker. As a result, it seems logical to analyze the data in
subsections or sampling periods defined by the time when each SLS scan was
made.
In order to keep the scan of the intensity from over saturating the
amplifier, the SLS signal processing has a user controlled value for the value of
the amplification of each scan. In preliminary tests the saturation level was noted,
and a value of 0.2 was found to be conservative enough to prevent saturation
during any part of the trial. A value of 0.3 gave clearer results, though, for the
latter part of the scan. Since it is possible to scale and overlay the data later
during processing, it was deemed necessary to take scans over both values of
amplification.
3.5.2 Mass Balance Data
The JAZ spectrometer recorded absorbance data concerning the effluent
from the flow cell over the full range of each trial. Each value was averaged with
65
twenty values before and after it to create a higher reliance. Using the SLS
defined time stamp as the end of one section of the data analysis and the
beginning of the next one, the outflow mass could be calculated for each
sampling period over time.
Using a similar process to the one concerning intensity and system drift
for the SLS laser, the JAZ spectrometer also had reference values for intensity
taken before and after each trial, because the calculated concentration of the
effluent depended on calibration from intensity. Usually, calibration for a
spectrometer is done once using a regression over several concentration values in
a quiescent sample in a cuvette, but since an SMAZ flow cell was used to take
real time measurements, the spectrometer had to be calibrated using a flowing
sample over a range of time. Since the conditions in the cell could change from
buildup of colloids or relative drift in the lamp output, before and after
calibrations were made so that they could be normalized in the same manner as
the SLS scans.
66
3.5.3 Graphical Approach
In order to find the fractal dimension of the aggregated colloids in the
flow cell, one way is to graphically scale the slope of the powerlaw regime
(Figure 2.17) data from the SLS scans. The basic steps are:
1. Record intensity in // W of the uninterrupted laser beam, I0
2. Using the blank sample data from the initial record for each trial, find the
average intensity from the duplicate scans for each 0value. Use these
3. For each time stamped record, average the intensities from the two scans,
values as l(to, 9), normalize by
record as I(tt, 9), normalize by
4. Subtract I(t0, 9) from I(t, 9). Record as I(ti,9).
5. Normalize the adjusted value by dividing by the scattering area
6. Convert angles to ^vectors using q = Ann A. 1 sin [0 / 2)
7. Plot a loglog graph of q versus the adjusted, normalized intensity
8. The slope of the power law region (Dm) is the fractal dimension of the
aggregated colloids as shown in Figure 3.11 below.
Figure 3.12: Graphical Approach to Fractal Dimension (Sorensen, 2001)
68
4. Summary of Results
The results of the trials are can only be judged as preliminary. Most of the
experimental work involved designing the equipment so that it could function as
desired. The relevant trials are grouped as follows:
Flocculated colloids at flow rate 5.0 mL/min, using 10 mM concentration
of calcium nitrate
Flocculated colloids at flow rate 5.0 mL/min, using 100 mM
concentration of calcium nitrate
69
4.1 Flocculated Colloids
4.1.1 lOmM Ca(NOa)2, 5.0 mL/min
Head Loss Data
The head loss data for the trial with 10 mM flocculent at 5.0 ml/minute
generated the graph as seen in Figure 4.1 below:
Head Loss Sample 2011 04 002
100 ppm, 5.0 mL/min, lOmM
t [min]
Figure 4.1: Head Loss Data Flocculated Colloids, Sample 2011_04_002
70
Mass Balance Data
The concentration and mass balance of the effluent as calculated from the
absorbance is shown in Figures 4.2 and 4.3:
Outflow Concentration: Sample 2011_04_002
100 ppm, 5.0 mL/min, lOmM
t (min)
Figure 4.2: Concentration of Effluent Sample 2011 04 002
71
Mass (mg)
Mass Deposit of Sample 2011 04 002
100 ppm, 5.0 mL/min, 10 mM
0.0 50.0 100.0 150.0 200.
t [min]
Figure 4.3: Mass Accumulation in Flow Cell for Sample 201104 002
72
Fractal dimension data
Table 4.1 shows the fractal dimension of the sample and the elapsed time
from start that it represents.
Table 4.1: Fractal dimension of sample 201104 002 aggregated colloids
SCAN Elapsed Time (min) D []
1 0 Reference scan
3 11 1.9
5 30 2.0
7 44 2.0
9 62 2.0
11 76 2.0
Figures 4.4 to 4.8 show the qvector vs intensity plots for scans 1 through
11. Scan number 1 is a reference scan which allows correction for the
background information in the granular media. The fractal dimension is
computed as a regression fitting of a power function on the relatively straight
power law region.
73
Intensity (O.D.)
Intensity I v. Scattering Vector q:
Sample 2011_04_002_A_3
100 ppm, 5.0 mL/min, lOOmM
q (A1)
Figure 4.4: Regression Fitting for Fractal Dimension at 11 minutes
Full Range
Fractal
Dimension
Power (Fractal
Dimension)
74
Intensity (O.D.)
Intensity I v. Scattering Vector q:
Sample 2011_04_001_A_8
100 ppm, 5.0 mL/min, lOOmM
q (A1)
Figure 4.5: Regression Fitting for Fractal Dimension at 30 minutes
Full Range
Fractal Region
Power (Fractal
Region)
75
Intensity (O.D.)
Intensity I v. Scattering Vector q:
Sample 2011_04_002_A_5
100 ppm, 5.0 mL/min, lOOmM
1.00E07
1.00E08
1.00E09
1.00E10
"''S e #\ * f / > \ 7= 31 16x2019
V : 0.996
\ j .***
1.00E05 1.00E04 1.00E03
q (A1)
I.00E02
Figure 4.6: Regression Fitting for Fractal Dimension at 44 minutes
Full Range
Fractal
Dimension
Power (Fractal
Dimension)
76
Intensity (O.D.)
Intensity I v. Scattering Vector q:
Sample 2011_04_002_A_9
100 ppm, 5.0 mL/min, lOOmM
1.00E07
1.00E08
1.00E09
1.00E10
1.00E05 1.00E04 E00E03 1.00E02
q (A1)
rV'v > Â£ Ti ll / i16x1978
\ = 0.993
\ jT **
Figure 4.7: Regression Fitting for Fractal Dimension at 62 minutes
Full Range
Fractal
Dimension
Power (Fractal
Dimension)
77
Intensity (O.D.)
Intensity I v. Scattering Vector q:
Sample 2011_04_002_A_11
100 ppm, 5.0 mL/min, lOOmM
1.00E07
1.00E08
1.00E09
1.00E10
r V t > y = 3 il 6x2009
* ... a = 0.9955
A* *
1.00E05
1.00E04
1.00E03
1.00E02
Full Range
Fractal
Dimension
Power (Fractal
Dimension)
q (A1)
Figure 4.8: Regression Fitting for Fractal Dimension at 76 minutes
78
4.1.2 1 OOmM Ca(N03)2, 5.0 mL/min
Head Loss Data
The head loss data for the trial at 5.0 ml/minute, using 100 mM
concentration of calcium nitrate generated the graph as seen below in Figure 4.9.
Transducer DP 1520 was turned off when pressure exceeded its tolerance range.
Head Loss Sample 2011 04 001
100 ppm, 5.0 mL/min, lOOmM
t [min]
Figure 4.9: Head Loss Data for Sample 2011 _04_001
79
Mass Balance Data
The concentration and mass balance of the effluent as calculated from the
absorbance is shown in Figures 4.10 and 4.11:
Outflow Concentration of Sample 2011 04 001
100 ppm, 5.0 mL/min, lOOmM
Figure 4.2: Concentration of Effluent, Sample 2011_04_001
80
Mass (mg)
Mass Deposit of Sample 2011 04 001
100 ppm, 5.0 mL/min, lOOmM
0.0 20.0 40.0 60.0 80.0 100.0
t [min]
Figure 4.3: Mass Accumulation in Flow Cell for Sample 2011 04 001
81
Fractal dimension data
Table 4.2 shows the fractal dimension of the sample for each scan and the
elapsed time when it was taken.
Table 4.2: Fractal dimension of sample 2011 04 001 aggregated colloids
SCAN Elapsed Time (min) D []
1 0 Reference scan.
6 24 1.5
8 62 1.8
10 73 1.4
12 87 1.0
Figures 4.12 through 4.15 show the qvector vs intensity plots for scans 1
through 12 of sample 2011_04_001.
82
Intensity (O.D.)
Intensity I v. Scattering Vector q:
Sample 2011_04_001_A_6
100 ppm, 5.0 mL/min, lOOmM
q (A1)
Figure 4.4: Regression Fitting for Fractal Dimension at 24 minutes
Full Range
Fractal Region
Power (Fractal
Region)
83
Intensity (O.D.)
Intensity I v. Scattering Vector q:
Sample 2011_04_001_A_8
100 ppm, 5.0 mL/min, lOOmM
q (A1)
Figure 4.5: Regression Fitting for Fractal Dimension at 62 minutes
Full Range
Fractal Region
Power (Fractal
Region)
84
Intensity (O.D.)
Intensity I v. Scattering Vector q:
Sample 2011_04_001_A_10
100 ppm, 5.0 mL/min, lOOmM
1.00E07 I
1.00E08
1.00E09
1.00E10 4
1.00E05 1.00E04 1.00E03 1.00E02
WVv % y = 5ED ^ R2 = 0.< "V x1.406 784
V
V <
Full Range
Fractal Region
Power (Fractal
Region)
q (A1)
Figure 4.6: Regression Fitting for Fractal Dimension at 73 minutes
85
