HYDRODYNAMIC AND DISPERSION BEHAVIOUR OF AN
ANALYTICAL SILICA MONOLITH RECONSTRUCTED
FROM SUB-MICROTOMOGRAPHIC SCANS USING
COMPUTATIONAL FLUID DYNAMICS
VIVEK VASUDEVAN

NATIONAL UNIVERSITY OF SINGAPORE
2013 HYDRODYNAMIC AND DISPERSION BEHAVIOUR OF AN
ANALYTICAL SILICA MONOLITH RECONSTRUCTED
FROM SUB-MICROTOMOGRAPHIC SCANS USING
COMPUTATIONAL FLUID DYNAMICS
VIVEK VASUDEVAN
(M.S., West Virginia University, U.S.A.
B. Chem. Eng., University Dept. of Chemical Technology, India)

at Analyze, Ansys and Fluent for helping me figure out several bottlenecks in my
computational efforts.
I am deeply grateful to all the lab officers, namely, Mdm Chow Pek, Mdm
Alyssa Tay, Mdm Novel and Mr. Wee Siong, for their administrative support. I am
thankful to NUS for providing me an opportunity to pursue research on a scholarship.

iii

I am ever thankful to my wife, Dr. Mrs. Karthiga Nagarajan, for being a
source of support and strength and believing in my abilities. I thank my in-laws for
always being there for my wife and helping her provide me with constant
encouragement and support. I would not have been able to purse a higher level of
education if not for my parents‘ encouragement and selflessness to send me away for
higher studies. I dedicate this thesis as a small repayment for all their innumerable
sacrifices for securing my future. I am grateful to the Almighty and to Karthiga for the
most beautiful and precious gift, my son Aaditya, who provided me with the impetus
to complete my doctoral studies and look ahead in life.
class="bi x15 y3c w0 h0"

v

TABLE OF CONTENTS
ACKNOWLEDGEMENTS II
DECLARATION IV
TABLE OF CONTENTS V
SUMMARY IX
LIST OF TABLES XI
LIST OF FIGURES XII
LIST OF ABBREVIATIONS AND SYMBOLS XVII
1. INTRODUCTION 1

POROUS DISPERSION SIMULATIONS 42
5.1. INTRODUCTION 42
5.2. RESEARCH OBJECTIVES 46
5.3. RESEARCH APPROACH 47
5.4. RESULTS AND DISCUSSIONS 48
5.4.1 Inverse Size Exclusion Chromatography (ISEC) 48
5.4.2 Porosity Analysis 52
5.4.3 Pore and Skeleton Size Distributions 56
5.4.4 Hydrodynamic Simulations 60
5.4.5 Peak Parking Simulations 71

vii

5.4.6 Transient Dispersion Simulations 73
5.4.7 Estimation of Transcolumn Dispersion 77
5.4.8 Estimation of Transchannel and Short-Range interchannel eddy
dispersion 84
5.5. CONCLUSIONS 88
6. MODEL VALIDATION FROM NON-RETAINED AND RETAINED
DISPERSION SIMULATIONS 92
6.1. INTRODUCTION 92
6.2. RESEARCH OBJECTIVES 92
6.3. RESEARCH APPROACH 93
6.4. MODEL SETUP 94
5.4.9 Porous Conditions 94
5.4.10 Non-retained conditions 96
5.4.11 Retained conditions 96
6.5. RESULTS AND DISCUSSIONS 97
5.4.12 Peak Parking Simulations 97
5.4.13 Transient Dispersion Simulations 100

BIBLIOGRAPHY 179
LIST OF PUBLICATIONS AND PRESENTATIONS 192
ix

SUMMARY
Downstream separation of mixtures in a variety of fields such as protein
purification, quality control of drugs, pharmacokinetic studies, and determination of
pollutants or food additives has traditionally been carried out using particulate HPLC
columns where the separation efficiency increases with decreasing particle size, at the
cost of higher operating pressures. Monoliths are a class of chromatographic columns
cast in the form of tubes, rods or disks as a single and co-continuous block that is
porous and permeable. A high external porosity resulting from a regular network of
through-macropores and a mesoporous skeleton network provide a combination of
low hydraulic resistance to the mobile phase and enhanced mass transfer rates of
sample molecules through the column, respectively. In this research, an analysis of
the transport properties of the bulk homogeneous core of a silica monolith is
presented via direct numerical simulations in a topological model reconstructed from
3D nanotomographic scans.
A commercially available silica monolith (Chromolith
®
) was scanned at three
isotropic resolutions to investigate the resolution required to adequately capture the
throughpore and skeleton-surface heterogeneity. Hydrodynamic behaviour of the
macropore space in domains representative of the bulk porosity was analysed via
computational fluid dynamics. A 30 m cubic unit cell at 190 nm scanning resolution
was found to be representative of the Darcy permeability, with a ±6% deviation from
experimental and reported literature data. Transcolumn eddy dispersion, reported to
be the single-most dominant contributor of inefficiency in the first generation of silica
monoliths, was estimated from the deviation of axial dispersion simulations under
non-porous, porous/non-retained and retained simulations from experiments using


LIST OF TABLES
Table 2.1: Image analysis of reconstructed volumes of silica monoliths 21
Table 5.1: Hydrodynamic and dispersion simulations in computational mimics of
commercial monoliths 43
Table 5.2: CT Image Reconstruction at Different Resolutions 53
Table 5.3: CT Image Reconstruction from Different Locations 53
Table 5.4: Pore Size Distributions 61
Table 5.5: Skeleton Size Distributions 61
Table 6.1: Parameter estimation for transcolumn dispersion and external film
mass transfer resistance 118
Table 6.2: Parameters associated with short-range interchannel dispersion
estimation 121
Table 6.3: Comparison of parameters in phenomenological approach to estimate
transcolumn dispersion 124
Table 7.1: Manual threshold values for artificial monolith generation 134
Table 7.2: Pore and skeleton size distributions of reconstructed monoliths 135
Table 7.3: Parameters characterizing transchannel dispersion in the reconstructed
monoliths 157
Table 7.4: Parameters characterizing short-range interchannel dispersion under
non-porous conditions. 157
Table 7.5: Parameters characterising short-range interchannel dispersion under
porous/non-retained conditions in the reconstructed monoliths. 159
Table 7.6: Parameters characterising short-range interchannel dispersion under
retained conditions in the reconstructed monoliths. 159
xii

LIST OF FIGURES

Figure 1.1: Publications on monolithic chromatography in recent years 3


Figure 5.13: Scaled transverse velocity frequency distributions at u
sf
= 1.003 mm/s.
68
Figure 5.14: Representative geometry for hydrodynamic and dispersion analysis.
(A) 30m unit cell (B) Steady-state velocity profile at u
sf
= 1mm/s (C)
Steady-state pressure profile at u
sf
= 1mm/s. 70
Figure 5.15: Transient diffusion coefficient D(t) in the axial and transverse
directions normalised by molecular diffusivity (D
m
= 7.5 x 10
-11
m
2
/s)
vs. effective diffusion length. Horizontal lines indicate the respective
asymptotic obstruction factors. 72
Figure 5.16: Time evolution of a pulse of BSA in the non-porous representative
geometry at u
sf
= 1mm/s. 74
Figure 5.17: Transient transverse dispersion coefficients normalized by molecular
diffusion vs. transverse dispersion length at various reduced-linear
velocities. Dotted lines indicate the transient transverse coefficients
simulated in the 40m model. 76

velocities under non-retained conditions. Dotted lines indicate the
transient coefficients simulated for the non-porous case. 101
Figure 6.5: Transient transverse dispersion coefficients normalized by molecular
diffusion vs. transverse dispersion length at various reduced-linear
velocities under retained conditions 103
Figure 6.6: Transient axial dispersion coefficients normalized by molecular
diffusion vs. transverse dispersion length at various reduced-linear
velocities under retained conditions 103
Figure 6.7: Experimental and simulated reduced-plate heights vs. reduced-linear
velocity under non-retained conditions. Dotted line indicates fit after
estimation of transcolumn eddy dispersion and external film mass
transfer from

and, respectively. 107
Figure 6.8: Experimental and simulated reduced-plate heights vs. reduced-linear
velocity under retained conditions. Dotted line indicates fit after
estimation of transcolumn eddy dispersion and external film mass
transfer from

and, respectively. 107
Figure 6.9: Experimental and simulated reduced-plate heights vs. reduced-linear
velocity under non-retained conditions. Dotted line indicates fit after
estimation of transcolumn eddy dispersion from Giddings‘ coupled
theory (and). 111
Figure 6.10: Experimental and simulated reduced-plate heights vs. reduced-linear
velocity under retained conditions. Dotted line indicates fit after
estimation of transcolumn eddy dispersion from Giddings‘ coupled
theory (and). 113
Figure 6.11: Comparison between transcolumn dispersions estimated in (A) this
work and (B) Gritti and Guiochon (2011). 114

porosity. 140
Figure 7.7: Variation of tortuosity factor with model porosity. 142
Figure 7.8: Darcy-Weißbach friction factor-Reynolds number relation for the
reconstructed monoliths using (A) pore, (B) skeleton and (C) domaion
size as the scaling dimension. 143
Figure 7.9: Transient axial diffusion coefficient D
eff
(t) normalised by molecular
diffusivity (D
m
) vs. effective diffusion length for the reconstructed
models. Horizontal lines indicate the respective asymptotic obstruction
factors. 145
Figure 7.10: Transverse dispersion coefficient (D
T
) normalised by molecular
diffusivity (D
m
) vs. reduced superficial velocity (ν
sf
) for the various
reconstructed monoliths under non-porous conditions. 147

xvi

Figure 7.11: Transverse dispersion coefficient (D
T
) normalised by molecular
diffusivity (D
m

) under porous/non-
retained conditions. The linear velocity is reduced by (A) pore
diameter, (B) skeleton diameter and (C) domain size. (D) shows the
graph in (B) rescaled to Figure 7.12B. 152
Figure 7.15: Longitudinal dispersion coefficient (D
L
) normalised by molecular
diffusivity (D
m
) vs. reduced-linear velocity (ν
ave
) under retained
conditions. The linear velocity is reduced by (A) pore diameter, (B)
skeleton diameter and (C) domain size. 154
Figure 7.16: Estimation of transcolumn dispersion to overall dispersion in the
reconstructed monoliths under non-porous conditions. 162
Figure 7.17: Estimation of transcolumn and external film mass transfer dispersion
to overall dispersion in the reconstructed monoliths under porous/non-
retained conditions. 163
Figure 7.18: Estimation of transcolumn and external film mass transfer dispersion
to overall dispersion in the reconstructed monoliths under retained
conditions. 165
xvii

LIST OF ABBREVIATIONS AND SYMBOLS

Macropore tortuosity factor

Mobile phase viscosity



S-R interchannel
Giddings‘ coupled parameter characteristic of short-range
interchannel eddy dispersion

S-R interchannel
Giddings‘ coupled parameter characteristic of short-range
interchannel eddy dispersion

t
Total porosity

xviii


transchannel
Giddings‘ coupled parameter characteristic of transchannel
eddy dispersion

transchannel
Giddings‘ coupled parameter characteristic of transcolumn
eddy dispersion

transcolumn
Giddings‘ coupled parameter characteristic of transcolumn
eddy dispersion



Mean skeleton diameter

Convective interaction media
C
s
Effective volume averaged concentration (in mesopores)
CLSM Confocal Laser Scanning Microscopy
C
m
Bulk mobile phase concentration
cP Centipoise

xix

CSV Comma separated values file
CT Computed Tomography
d
dom
Domain size
DEAE Diethylaminoethyl
D
eff
Effective diffusion coefficient
D
L
Axial dispersion coefficient
D
m
Molecular diffusivity
d
p
Particle diameter

Reduced-HETP due to external film mass transfer resistance
h
Long
Reduced-HETP due to longitudinal / axial molecular diffusion
HPLC High Performance Liquid Chromatography
h
sim
Reduced-simulated HETP
h
Skel
Reduced-HETP due to skeleton mass transfer resistance

xx

h
S-R interchannel
Reduced-HETP due to short-range interchannel eddy dispersion
h
transchannel
Reduced-HETP due to transchannel eddy dispersion
h
transcolumn
Reduced-HETP due to transcolumn eddy dispersion
Hz Hertz
I.D. Internal diameter
ISEC Inverse Size Exclusion Chromatography
K Equilibrium constant
k’ Phase retention factor
k” Zone retention factor under retained conditions
kDa kiloDalton

P
atm
Atmospheric pressure
PEEK Polyetheretherketone
R
2
Regression coefficient
Re Reynolds number
REV Representative Elementary Volume
RP Reversed Phase
RPLC Reversed Phase Liquid Chromatography
RSD Relative Standard Deviation
S Skeleton surface area
SEM Scanning Electron Microscope
STL Stereolithographic file
TEM Transmission Electron Microscope
TFA Trifluoroacetic acid
THF Tetrahydofuran
t
R
Residence time
u
max
Maximum linear velocity
u
min
Minimum linear velocity
u
sf
Superficial velocity

of macropore channels is less constricted and less tortuous than in packed beds.
Another characteristic is that the stationary phase skeleton is made up of a network of
small, thin threads of porous silica or organic polymers. As these thin threads have no
effect on hydraulic resistance, they can be reduced to accelerate the mass transfer of
sample molecules. These two structural characteristics provide a combination of low

2

hydraulic resistance to the mobile phase, and enhanced mass transfer rates of sample
molecules through the column. Silica monolithic columns have found many
applications in diverse fields such as high throughput analysis of drugs and
metabolites, separation of environmentally relevant substances and food additives,
separation of enantiomers and separation of complex biological samples like tryptic
digests (Cabrera, 2004).
A quick search on ScienceDirect reveals the relative interest in silica
monoliths among researchers in recent years. Figure 1.1 shows the number of
publications on silica monoliths in comparison to the total number of papers published
for all monoliths in the last few years. The successful commercialization and reliable
reproducibility of Chromolith
®
has triggered an immense interest in characterizing
silica monoliths (Cabrera, 2004).
Monoliths owe their versatility to the fact that, unlike conventional packed
beds where the flow channel and stationary phase dimensions are closely related to
the average particle diameter, the pore and skeleton dimensions can be controlled
independently during the in-situ polymerization process (Guiochon, 2007). This poses
a challenge in modelling monoliths since there is no single geometrical feature that
can uniquely characterize both their hydrodynamic as well as separation performance.
Several authors have used ‗domain size‘ – sum of the average through macropore
diameter (as deduced from mercury porosimetry) and the average skeleton element