Colloid Transport Project
Project Advisors:
Timothy R. Ginn, Professor, Department of Civil and
Environmental Engineering, University of California Davis,
Daniel M. Tartakovsky, Professor, Department of Mechanical
and Aerospace Engineering University of
Patricia J. Culligan, Professor, Department of Civil
Engineering and Engineering Mechanics, Columbia
Basic Goal
Examine the transport of a dilute suspension (of micron
sized particles) in a saturated, rigid porous medium under
uniform flow
C
S
 .uc  D 2C 
t
t
Advection

Dispersion
Filtration (sorption,
deposition, or attachment)
Challenge ∂S/∂t….
Classic mathematical models used to describe ∂S/∂t are
inadequate in many cases - even in very simple systems
Problems Involving Particle Transport through
Porous Media
• Water treatment system
– Deep Bed Filtration (DBF)
– Membrane-based filtration
• Transport of contaminants in aquifers
– Colloidal particle transport
• Transport of microorganisms
– Pathogen transport in groundwater
– Bioremediation of aquifers
• Clinical settings
– Blood cell filtration
– Bacteria and viruses filtration
Particle Sizes
-10
(diameter, m) 10
1Å
10-9
10-8
10-7
10-6
1 nm
10-5
10-4
1 mm
Soils
Clay
10-3
10-2
1 mm
1 cm
Sand
Silt
Gravel
Microorganisms
Viruses
Protozoa
Red blood cell
Blood cells
Atoms,
molecules
Bacteria
White blood cell
Atoms
Molecules Macromolecules
Colloids
Suspended particles
Depth-filtration range
Electron
microscope
Light microscope
Human eye
Particle Filtration through a Porous
Medium
Particle suspension injection at C0
Breakthrough concentration
C/Co < 1
C/Co
L
Porous
Medium
Time
Particle breakthrough
Fraction of
particle mass
is permanently
removed by
filtration
Idealized Description of Particle Filtration
• Clean-bed “Filtration Theory”
0   D   I  G
Single collector efficiency
• Single “collector” represents a solid
phase grain. A fraction  of the particles
are brought to surface of the collector
by the mechanisms of Brownian
diffusion, Interception and/or
Gravitational sedimentation.
•A fraction  of the particles that reach
the collector surface attach to the
surface
• The single collector efficiency is then
scaled up to a macroscopic filtration
coefficient, which can be related to
first-order attachment rate of the
particles to the solid phase of the
medium.


Filtration coefficient
First-order deposition rate


3(1 n)

2dc
katt  u
Particle Filtration through a Porous Medium
Particle suspension injection at C0
Breakthrough concentration
C/Co < 1
C/Co
L
Porous
Medium
C
 exp(L)
Co
katt  u


S
 kattC
t
Time
Particle breakthrough

katt (and ) is assumed to be spatially constant and dependent upon particle-solid
interaction energies (DLVO theory) and system physics
Motivation for Work
• Growing body of literature that indicates that katt decreases
with transport distance - points to inadequacies in the
filtration-theory
• Various solutions to fixing these inadequacies
– More complex macroscopic models?
– Modeling at the micro-scale?
• Examine solutions in context of a unique data set that has
resolved particle concentrations in the interior of a porous
medium in real time
Generation of Data Set
• Translucent porous medium – glass beads saturated with water
• Laser induced fluorescent particles
– Micro-size Fluorescent Particles: Excitation wavelength 511532nm, Emission wavelength 570-595nm.
– Laser : 6W Argon-ion Laser
• Digital image processing
– Captured images in real-time with CCD camera
– Image processing software
Particles
 Acrylic particles with organic
fluorescent dyes (fluorecein,
rhodamine) embedded.
 Specific gravity = 1.1
 Particle size

Range: 1-25 mm, d50=7mm
 Surface potential

zeta-potential = -109.97mV.
Unlikely to attach to the glass
bead surface due to the
repulsive electrostatic force
Experimental Set Up
Particle Fluorescence is related to
Particle Concentration
1.2
Without beads
With beads
1.0
1.0
Normalized intensity
Normalized light intensity, I/Imax
1.2
0.8
0.6
y = (1+0.0225)x + (0+0.0043)
0.4
0.2
0.8
0.6
0.4
y = (0.3319+0.0138)x + (0+0.0095)
0.0
0.2
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Nomalized concentration, C/Cmax
• Particle concentration had a linear
relationship with fluorescent light intensity.
1.2
0
200
400
600
800
1000
Pixel (0 - 1024)
• Pixel by pixel calibration eliminated the
optical distortion caused by the camera and
the lens.
Basic Experiment
Inject 10 Pore Volumes (PVs) of particle
suspension at C = 50 mg/l
Follow with injection of 10 Pore Volumes (PVs)
of non-particle suspension at C = 0 mg/l
Series of data for tests in similar porous media at
difference values of uf
Data Available: Particle Breakthrough Curve
at Column Base
S Sirr Sr


 kirr,attC  kr,attC  kr,det Sr
t
t
t
C S
 2C
C

D 2 u
t t
z
z


Normalized concentration, C/C0
1.0
Fast
Medium
Slow
0.8
0.6
0.4
0.2
0.0
0
5
10
Pore volumes
15
20
Particle
density versus
time in fluid
phase at base C versus t at a
fixed z
Particle Concentration Inside the Medium
(C + S) versus time
at various locations
within the medium
Microscopic Observations: Physical
Insight
(a) to (c) Particle injection
(d) to (e) Particle flushing
Particles are irreversibly attached at the
solid-solid contact points (contact filtration)
and at the top surface of the beads (surface
filtration).
The particles are also reversibly attached at
the surface of the beads and possibly at the
contact points.
Flow
direction
Contact Filtration
• Particles moving near beadbead contact points were
physically strained.
Flow direction
Beadglass plate
contacts
Bead-bead
contacts
Surface Filtration
Flow direction
• Some of the particles that
approached the surface of the
beads became “irreversibly”
attached.
Considering the highly negative zeta-potentials of the particles and beads,
surface filtration must be “physical”
- hypothesized that surface roughness held the particles against the drag
force.
Project Tasks
Understand the data set
Model data using traditional filtration-theory
Understand the inadequacies of this theory
Model data set using “more-complex” macroscopic balance
equation
Can any of the coefficients in this balance equation
be given a physical meaning?
Can micro-scale modeling techniques be applied and used
to capture some of the observed behavior
What you will be given
Data sets for three experiments - each at different average
fluid velocity
Experimental information - set-up plus parameters etc.
A library of background literature
Guidance, encouragement, hints (?)
What you will Deliver?
Project report = technical article that discusses
the shortcomings of existing modeling
approaches and explores avenues for
improvements based on (a) macroscopic
modeling approaches and (b) microscopic
approaches