Transcript Models & Experiments Investigating the Role of EPS in Bacterial

Notes on Colloid transport and
filtration in saturated porous
media
Tim Ginn, Patricia Culligan, Kirk Nelson
Purdue Summerschool in Geophysics 2006
But first, we start with
 Brief review of general reactive transport
formalism
Outline
 General reactive transport intro



Multicomponent/two-phase/multireaction
colloid filtration “Miller lite”
Stop and smell the characteristic plane - mcad
 Colloid Filtration “Guiness”




Overview
Processes catwalk
Classical approach
Blocking
 Issues
 Return to macroscale: multisite/population
Gone to mathcad





Some analytical solutions - hope it runs
Just transport
Irreversible filtration no dispersion
Reversible filtration no dispersion
(Dispersion included by superposition.)
Outline
 General reactive transport intro



Multicomponent/two-phase/multireaction
colloid filtration “Miller lite”
Stop and smell the characteristic plane - mcad
 Colloid Filtration “Guiness”




Overview of colloids in hydrogeology
Processes catwalk
Classical approach
Blocking
 Issues
 Return to macroscale: multisite/population
1. Introduction - Background
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
Problems Involving Particle Transport
through Porous Media in Environmental
and Health Systems
 Water treatment system


Deep Bed Filtration (DBF)
Membrane-based filtration
 Transport of pollutants in aquifers


Colloidal particle transport1
Colloid-facilitated contaminant transport2
 Transport of microorganisms



1.
2.
Pathogen transport in groundwater
Bioremediation of aquifers
…
Ryan, J.N., and M. Elimelech. 1996. Colloids Surf. A, 107:1–56.
de Jonge, Kjaergaard, Moldrup. 2004. Vadose Zone Journal, 3:321–325
…and some more
 In situ bioremediation


transport of bacteria to contaminants1
excessive attachment to aquifer grains – biofouling
 Bacteria-facilitated contaminant transport
(e.g.,DDT2)
 Clinical settings


1.
2.
Blood cell filtration
Bacteria and viruses filtration
Ginn et al., Advances in Water Resources, 2002, 25, 1017-1042.
Lindqvist & Enfield. 1992. Appl. Environ. Microbiol, 58: 2211-2218.
Outline
 General reactive transport intro



Multicomponent/two-phase/multireaction
colloid filtration “Miller lite”
Stop and smell the characteristic plane - mcad
 Colloid Filtration “Guiness”




Overview
Processes catwalk
Classical approach
Blocking
 Issues
 Return to macroscale: multisite/population
Processes in colloid-surface
interaction





Actual colloid,
Inertia in (arbitrary) velocity field
Torque, drag due to nonuniform flow
Diffusion,
hydrodynamic retardation/lubrication

Effective increase in viscosity near surface
 Electrostatic (dynamic) interaction

DLVO (=LvdW + doublelayer model
electrostatics)
 Buoyancy/gravitational force
Overview
 General reactive transport intro



Multicomponent/two-phase/multireaction
colloid filtration “Miller lite”
Stop and smell the characteristic plane - mcad
 Colloid Filtration “Guiness”




Overview
Processes catwalk
Classical approach – “Colloid filtration theory”
and some Details
Blocking
 Issues
 Return to macroscale: multisite/population
Classical take on Processes in
colloid-surface interaction
 Inert, Spherical colloid to Sphere (flat)
 Inertia in (Stokes) velocity field
 Torque, drag due to nonuniform flow

approximated
 Diffusion (superposed)

hydrodynamic retardation/lubrication
 Electrostatic (dynamic) interaction

DLVO (=LvdW + doublelayer model
electrostatics )
 Buoyancy/gravitational force added

So flow must be downward
Forces And Torques – RT model
Trajectory Analysis
Smoluchowski-Levich Solution
(particle has finite
diameter)
(particle diameter = 0)
TD
TD
FG
h
+
=
FB
FI = inertial force due to Stokes flow*
FD = drag force due to Stokes flow*
TD = drag torque due to Stokes flow*
FG = gravitational force
FB = buoyancy force
FvdW = van der Waals force
*with corrections near surface
FI = inertial force due to Stokes flow
FD = drag force due to Stokes flow
TD = drag torque due to Stokes flow
FBR = random Brownian force
Classical CFT :Happel spherein-cell
 Clean-bed “Filtration Theory”
• Single “collector” represents a solid
phase grain. A fraction h 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 (electrostatic and ionic strength)
• 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.
h0  h D  h I  hG
Single collector efficiency
h
Filtration coefficient

First-order deposition rate


3(1 n)
h
2dc
katt  u
Bulk “kf” by classical filtration theory
nC
  f c  kC
t
 3 1  n U
k  h
 n
2
d

c 
First-order removal
Rate = filter coefficient * porewater velocity
=> two-step process
n porosity
C aqueous phase concentration of colloid suspension
fc flux of C
U groundwater (Darcy) specific flux
 fraction of colloids encountering solid surface that stick (empirical2,3)
h fraction of aqueous colloids that encounter solid surface (modeled1,3-6)
1. Rajagoplan & Tien. 1976. AIChE J. 22: 523-533.
2. Harvey & Garabedian. 1991. ES&T 25: 178-185.
3. Logan et al. 1995. J. Environ. Eng. 121: 869-873.
3. Nelson & Ginn. 2001 Langmuir 17: 5636-5645
4. Tufenkji & Elimelech. 2004 ES&T 38: 529-536.
5. Nelson & Ginn. 2005 Langmuir 21: 2173-2184
Details1:Happel sphere-in-cell model2
 Happel sphere-in-cell is
porous medium
 Stokes’ flow field
 h calculated via trajectory
analysis1
 Additive decomposition

h=hI+hG+hD
 Initial point of limiting
trajectory
 h = A1/A2 = sin2qs
1.
Rajagoplan & Tien. 1976. AIChE J.
22: 523-533.
2.
Happel. 1958. AIChE J. 4: 197-201.
A1
A2
Detail: Basic solution (analytical)
due to Rajagopalan & Tien (1976)
 Hydrodynamic retardation effect = the increased drag
force a particle experiences as it approaches a surface.
Interception by boundary
 a deviation from Stokes’ law
condition
 Hydrodynamic correction factors
Sedimentation group
 Particle velocity expressions gives:




1 
U


uq r, q  
B s2  D 1  s3  NG sinq
s1
r

1  
ur r, q   t  A 1   
fr 



2
frm
 NG cosq 
London van der
Waals group
 rtd N LO

2

U
2 

2    

where frt, frm, s1, s2, and s3 are the drag correction factors.
Detail: h vs. 
 irreversible adsorption constant, kirr = f(,h)
 h = fraction of colloids contacting solid phase,
calculated a priori from RT model
  = fraction of colloids contacting solid phase
that stick, treated as a calibration parameter
accounting for all forces and mechanisms
not considered incalculation of h
Role of electrostatic forces : aside
Detail: Surface Forces in CFT –
DLVO
 RT model uses DLVO theory for surface
interaction forces:
attractive
repulsive for like charges
potential = van der Waals + double layer
 Theory predicts negligible collection when
repulsive surface interaction exists  RT
model neglects double layer force.
Detail: Surface Forces in CFT –
DLVO
 RT model uses DLVO theory for surface
interaction forces:
attractive
repulsive for like charges
potential = van der Waals + double layer
 Theory predicts negligible collection when
repulsive surface interaction exists  RT
model neglects double layer force.
 Thus, double layer force implicit in .
Highlights of Formulae for h
 Yao (1971)

hydrodynamic retardation and van der Waals force not included
 Rajagopalan and Tien (1976)



deterministic trajectory analysis
torque correction factors
Brownian h added on separately from Eulerian analysis
 Tufenkji and Elimelech (2004)


convective-diffusion equation solution
influence of van der Waals force and hydrodynamic retardation on
diffusion
  fc   UC   D C   

D f 
kT
Diffusion, interception, & sedimentation considered additive
 Nelson and Ginn (2005)

C
Particle tracking in Happel cell – all forces together
Outline
 General reactive transport intro



Multicomponent/two-phase/multireaction
colloid filtration “Miller lite”
Stop and smell the characteristic plane - mcad
 Colloid Filtration “Guiness”




Overview
Processes catwalk
Classical approach – “Colloid filtration theory”
and some Details
Blocking
 Issues
 Return to macroscale: multisite/population
Dynamic surface blocking (ME)
 initial deposition rate (kinetics)
rate  a kc
2
p
 later, when deposition rate drops due to
surface coverage (dynamics)
rate  a kB(s)c
2
p
 retained particles block sites, B is the
dynamic blocking function (misnomer).
B's
 B = fraction of particle-surface collisions that
involve open seats (cake walk).
 Random Sequential Adsorption
 40
176 
3
Bs  1  4ss 
ss    2 s s

 3 3 
6 3

2
Power series in S, for spherical geometry
 Langmuirian Dynamic Blocking
Bs  1   s
  1/ s
Outline
 General reactive transport intro



Multicomponent/two-phase/multireaction
colloid filtration “Miller lite”
Stop and smell the characteristic plane - mcad
 Colloid Filtration “Guiness”




Overview
Processes catwalk
Classical approach – “Colloid filtration theory”
and some Details
Blocking
 Issues
 Return to macroscale: multisite/population
Issues
 CFT coarse idealized model



Chem/env. Engineering, not natural p.m.
Biofilms, organic matter, asperities,
heterogeneity (gsd, psd, surface area,
electrostatic (dynamic), transience, flow
reversal, temperature, etc.
Reversibility ???
 CFT good for trend prediction

Attachment goes up with colloid size, gw
velocity, ionic strength, etc.
 Ultimately need equs for bulk media


Lab
field
Outline
 General reactive transport intro



Multicomponent/two-phase/multireaction
colloid filtration “Miller lite”
Stop and smell the characteristic plane - mcad
 Colloid Filtration “Guiness”




Overview
Processes catwalk
Classical approach – “Colloid filtration theory”
and some Details
Blocking
 Issues
 Return to macroscale: See the data !
Field/Lab observations
 Microbes 1,2,3 and viruses 4,5 first showed
apparent multipopulation rates due to
decreased attachment with scale



Sticky bugs leave early
Readily explained by subpopulations
Some suggest geochemical “heterogeneity”
 Recent surprize is that inert monotype,
monosize and polysize colloids exhibit same6
1.
2.
3.
4.
5.
6.
Albinger et al., FEMS Microbio Ltr., 124:321 (1994)
Ginn et al., Advances in Water Resources, 25:1017 (2002).
DeFlaun et al., FEMS Microbio Ltr., 20:473 (1997)
Redman et al., EST 35:1798 (2001); Schijven et al., WRR 35:1101 (1999)
Bales et al., WRR 33:639 (1997)
Li et al., EST 38:5616 (2004); Tufenkji and Elim. Langmuir 21:841 (2005)Yoon et al., WRR June 2006
Ability-based modeling (because
we can)
 BTCs (first) exhibit long flat tails



Two-site, multisite model1 (google “patchwise”)
Two-population, multipop’n model2 (UAz,
Arnold/Baygents)
Can’t tell the difference
 Profiles (recently) are steeper than expected




1.
2.
3.
Multipopulation works, not multisite (Li et al in 2), 3
This is the location of the front in practice
Upscaling
Alternative explanations
E.g., Sun et al., WRR 37:209 (2001); “patchwise heterogeneity”, CXTFIT ease of use (sorta)
E.g., Redman et al., EST 35:1798 (2001); Li et al. EST 38:5616 (2004)
Johnson and Li, Langmuir 21:10895 (2005); Comment/Reply
Research Needs (at least)
 Formal upscaling



Forces complex but well understood
Approximations tested
Analytical results (Smoluchowski-Levitch1)
 Alternative explanations

C<-> S -> S’ surface transformations 2
Mainly bacteria; need RTD for attachment events



Physical straining of larger sizes (a pop’n model)3
Reentrainment4
Contact (CFT) and surface (multipopn) filtration5
1.
For CFT/Happel cell without interception or sfc forces (LvdW =-hyd. Retardation)
2.
Davros & van de Ven JCIS 93:576 (1983); Meinders et al. JCIS 152:265 (1992); Johnson et al. WRR
31: 2649 (1995); Ginn WRR 36:2895 (2000)
3.
Bradford et al WRR 38:1327 (2002); Bradford et al. EST 37:2242 (2003)
4.
Grolimund et al WRR 37:571 (2001)
5. Yoon et al. WRR June 2006
Appendix: DNS Approach
 Langevin equation of motion


Happel sphere-in-cell
Contemporaneous accounting of all forces
 Solution per colloid
 Calculating h



Monte carlo colloidal release per qs =>
P(qs) frequency of attachment per qs
h as an expectation over P(qs)
Langevin Equation
 Deterministic and Brownian displacements are
combined per time step:
du
mp
 Fh  Fe  Fb
dt
 mp is the particle mass, u is the particle velocity
vector, Fh is the hydrodynamic force vector, Fe is
the external force vector, and Fb is the random
Brownian force vector.
 All three components of random displacement
must be modeled in the axisymmetric (3D  2D)
flow field.
Solution
R  udet Dt  ns R
 R = 3D displacement,
 udet = deterministic velocity vector
 n =3 N(0,1),
 sR = standard deviations of Brownian displacements.
 negligible particle inertia assumed
Dt >> tB (Kanaoka et al., 1983)
tB particle’s momentum relaxation time (=mp/6map).
Thus, tB << Dt < tu
tu is the time increment at which udet is considered con
Highlights of numerical solution
 Stokes’ flow in two-dimensions
 R&T (1976) hydrodynamic drag correction
factors1
 Brownian diffusion algorithm of Kanaoka et
al. (1983)2 for diffusive aerosols
 Coordinate transformation to 2D model
1. Brenner, H., Chem. Eng. Sci. 1961, 16, 242-251; Dahneke, B.E., J. Colloid Interface
Sci., 1974, 48, 520-522.
2. Kanaoka, C.; Emi, H.; Tanthapanichakoon, W., AIChE J., 1983, 29, 895-902.
Coordinates for diffusion
 The Happel model: 3-D -> 2-D polar coordinates
 convert 3-D Brownian Cartesian displacement to spherical, to
polar ˜
˜ y  ny 2DB MDt
˜ z  nz 2 DBM Dt
Rx  nx 2DBM Dt
R
R
y,z, contribute to angular displacements
And thus to r
R˜ y 
˜ q  arcsin 
R
 r 
 
R˜ z 
˜   arcsin 
R
 r 
2 ˜
2 ˜ 
˜R  R
˜  r
 1 sin Rq  1 sin R  2r
r
x


Calculating h
/ 2
h2

Pcollect qS sin qS cosqS dqS
0
 qS starting angle of a colloid
 Pc(qS) frequency of contact with the collector.
 reduces to classical equation when
deterministic (e.g., when Pc(qS) equals one for
all qS < qLT and zero for all qS > qLT).
 task of stochastic trajectory analysis for h is to
find Pc(qS).




Colloid transport and Colloid Filtration Theory
Classical approach
Issues
Direct numerical simulation:


Approach
Examples, Convergence, Testing
 Results
 Blocking - pages from Elimelech's site
 Conclusions
Example Brownian Trajectory
1.6429E-04
1.6428E-04
1.6427E-04
1.6426E-04
r [m]
1.6425E-04
1.6424E-04
1.6423E-04
1.6422E-04
1.6421E-04
1.6420E-04
1.6419E-04
1.1838
1.184
1.1842
1.1844
1.1846
q [rad]
1.1848
1.185
1.1852
1.1854
1.1856
164.44
164.39
164.34
r [ m m]
164.29
164.24
164.19
1.132
1.134
1.136
1.138
1.14
q [rad]
1.142
1.144
1.146
P(qs)
Num ber of bacteria collected w ith (Brow nian m otion included) as function of theta-start
0.025
Bacteria collected
ran1 300 rlzns
ran1 1000 rlzns
MT 12K rlzns
ran1 12K rlzns
0.020
0.015
0.010
0.005
0.000
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
theta-start
0.08
0.09
0.1
0.11
0.12
Convergence of a trajectory - 50K
realizations
Convergence of Collection Freq from ts=.0418 (Case 1, ap = .695 microns, dt = 0.5 msec)
1
0.9
0.8
Frequency of collection
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
10
100
1000
number of realizations
10000
100000
Convergence to deterministic trajectory analysis of
Rajagopalan and Tien (when diffusion is neglected),
Parameters: e = 0.2, as = 50 mm, ap = 0.1 mm, and U = 3.4375 * 10-4 m/s.
The approximate analytical solution is h = 1.5 NR2g2AS (Rajagopalan and Tien, 1976).
Convergence of stochastic simulations for
Smoluchowski-Levich approximation.
Parameters: ap = 0.1 mm, as = 163.5 mm, e = 0.372,
U = 3.4375*10-4 m/sec, m = 8.9*10-4 kg*m/sec, T = 298 K.
8.4E-03
8.3E-03
Dt = 10 ms
8.2E-03
analytical result
D t = 1 ms
8.1E-03
Dt = 100
8.0E-03
h 7.9E-03
7.8E-03
7.7E-03
7.6E-03
7.5E-03
7.4E-03
0
2000
4000
6000
number_of_realizations
8000
10000
12000




Colloid transport and Colloid Filtration Theory
Classical approach
Issues
Direct numerical simulation:


Approach
Convergence
 Results


Smoluchowski-Levitch approximation
General case
 Blocking - pages from Elimelech's site
 Conclusions
Testing comparison to the Smoluchowski-Levich
approximation (external forces, interception neglected).
Parameters: as = 163.5 mm, e = 0.372, U = 3.4375*10-4 m/sec, m = 8.9*10-4 kg*m/sec,
T = 298 K, Dt = 1 ms, N = 6000.
1.E-02
NG04

analytical
h
1.E-03
0
0.2
0.4
0.6
 m)
ap (m
0.8
1
1.2
Comparison of h calculations
R&T (1976) X N&G
- - - T&E (2004)
o N&G Additive
RT_76
NG_04
TE_04
NG_04 additive
RT_76 deterministic
NG_04 deterministic
R&T (1976)
deterministic
N&G deterministic
1E-02
h

1E-03
1E-04
0.2
0.3
0.4
0.5
0.6
0.7
ap (mm)
0.8
0.9
1
1.1
Conclusions
 Lagrangean analysis is viable tool with modern
computers
 Stochastic trajectory analysis suggests diffusion
and sedimentation may not be additive
 More realistic “unit cell” models could be used
 Lagrangean approach allows for arbitrary
interaction potentials



Chemical (mineralogical, patchwise) heterogeneity
Exocellular polymeric substances in bacteria
Polymer bridging, hysteretic force potentials
Parameters
used in
stochastic
trajectory
simulations.
Parameter
Value
Collector radius, as
163.5 mm
Porosity, e
0.372
Approach velocity, U
3.4375 * 10-4 sec
Fluid viscosity, m
8.9 * 10-4 kg·m / sec
Hamaker constant, H
10-20 J
Bacterial density, rp
1070 kg / m3
Fluid density, rf
997 kg / m3
Absolute temperature, T
298 K
Time step, Dt
1 ms
Number of realizations, N
6000
Modification of CFT to Account for EPS
 Distribution of polymer lengths
on the cell surface
 Repulsion modeled by steric
force, Fst(h)1,2
Hypothetical cell (drawn to scale)
O
L
depends on polymer density
and brush length
KT2442
L
E
0.695 mm
 If sufficient polymers contact
collector, cell attaches
depends on polymer density,
length, and adhesion forces
C
h
C
T
O
R
mean polymer length = 160 nm
1. de Gennes. 1987. Adv. Colloid Interface Sci. 27: 189-209.
2. Camesano & Logan. 2000. Environ. Sci. Technol. 34: 3354-3362.
Theoretical Sticking Efficiency
Numerical Calculation of Trajectories
 Steric repulsive force
 Polymer bridging
 Interception
 Sedimentation
 Brownian motion
 London van der Waals
attractive force
 Hydrodynamic retardation
effect
Incorporation of Brownian motion and polymer interactions into
trajectory analysis allows for computation of a theoretical sticking
efficiency.
Theoretical Sticking Coefficient
 Incorporation of polymer interactions and Brownian
motion + assumption that polymers control adhesion 
Trajectory analysis yields the product [h]theo = A1/A2 =sin2 qs
 Then we can define a theoretical value for the sticking
efficiency :
theo = [h]theo / h
where h is the model result without polymer interactions.
 Comparison of theo with experimental  can serve as a
validation tool for the polymer interaction modeling.
Pseudomonas putida KT2442
 Considered for
bioremediation use1,2
 Congo Red stain
image  heavy EPS
coverage on cells
 EPS characteristics
being studied by
Camesano et al.
(WPI)3
KT2442 cells with Congo Red
White areas
indicate EPS
1. Nublein et al. 1992. Appl. Environ. Microbiol. 58: 3380-3386.
2. Dobler et al. 1992. Appl. Environ. Microbiol. 58: 1249-1258.
3. Camesano & Abu-Lail. 2002. Biomacromolecules. 3: 661-667.
Photo credit: Stephanie Smith
Dept. of Land, Air, & Water Resources
Summary
 CFT trajectory analysis modified for explicit
inclusion of Brownian motion and bacterial EPS
interactions
 Brownian trajectory analysis results suggest that
sedimentation and diffusion may not be additive
as previously assumed
 Future work
 comparison of h calculations with
experimental data in the literature
 more realistic modeling of EPS interactions
(e.g., hysteresis)