notes on colloid transport and filtration in saturated porous media tim ginn, patricia culligan,...

Notes on Colloid transport and Notes on Colloid transport and filtration in saturated porous filtration in saturated porous

mediamedia

Tim Ginn, Patricia Culligan, Kirk NelsonTim Ginn, Patricia Culligan, Kirk Nelson

Purdue Summerschool in Geophysics 2006Purdue Summerschool in Geophysics 2006

But first, we start withBut first, we start with

Brief review of general reactive transport Brief review of general reactive transport formalismformalism

OutlineOutline

General reactive transport introGeneral reactive transport intro Multicomponent/two-phase/multireactionMulticomponent/two-phase/multireaction colloid filtration “Miller lite”colloid filtration “Miller lite” Stop and smell the characteristic planeStop and smell the characteristic plane - mcad - mcad

Colloid Filtration “Guiness”Colloid Filtration “Guiness” OverviewOverview Processes catwalkProcesses catwalk Classical approachClassical approach Blocking Blocking

IssuesIssues Return to macroscale: multisite/populationReturn to macroscale: multisite/population

Gone to mathcadGone to mathcad

Some analytical solutions - hope it runsSome analytical solutions - hope it runs Just transportJust transport Irreversible filtration no dispersionIrreversible filtration no dispersion Reversible filtration no dispersionReversible filtration no dispersion (Dispersion included by superposition.)(Dispersion included by superposition.)

OutlineOutline


Colloid Filtration “Guiness”Colloid Filtration “Guiness” Overview of colloids in hydrogeologyOverview of colloids in hydrogeology Processes catwalkProcesses catwalk Classical approachClassical approach BlockingBlocking


Particle SizesParticle Sizes1. Introduction - Background1. Introduction - Background

10-2 10-310-410-510-610-710-810-910-10(diameter, m)

1 Å 1 nm 1 m 1 mm 1 cm

Soils

Atoms,molecules

Microorganisms

Blood cells

Electronmicroscope

Light microscope Human eye

Depth-filtration range

Red blood cell

White blood cell

BacteriaViruses Protozoa

GravelSandSiltClay

Atoms MoleculesMacromolecules

Colloids Suspended particles

Problems Involving Particle Transport Problems Involving Particle Transport through Porous Media in Environmental through Porous Media in Environmental

and Health Systemsand Health Systems Water treatment systemWater treatment system

Deep Bed Filtration (DBF)Deep Bed Filtration (DBF) Membrane-based filtrationMembrane-based filtration

Transport of pollutants in aquifersTransport of pollutants in aquifers Colloidal particle transportColloidal particle transport11

Colloid-facilitated contaminant transportColloid-facilitated contaminant transport22

Transport of microorganismsTransport of microorganisms Pathogen transport in groundwaterPathogen transport in groundwater Bioremediation of aquifersBioremediation of aquifers ……

1. Ryan, J.N., and M. Elimelech. 1996. Colloids Surf. A, 107:1–56.

2. de Jonge, Kjaergaard, Moldrup. 2004. Vadose Zone Journal, 3:321–325

1. Ginn et al., Advances in Water Resources, 2002, 25, 1017-1042.

2. Lindqvist & Enfield. 1992. Appl. Environ. Microbiol, 58: 2211-2218.

In situIn situ bioremediation bioremediation transporttransport of bacteria to contaminants of bacteria to contaminants11

excessive excessive attachmentattachment to aquifer grains – biofouling to aquifer grains – biofouling

Bacteria-facilitated contaminant transport Bacteria-facilitated contaminant transport (e.g.,DDT(e.g.,DDT22))

Clinical settingsClinical settings Blood cell filtrationBlood cell filtration Bacteria and viruses filtrationBacteria and viruses filtration

……and some moreand some more

OutlineOutline


Colloid Filtration “Guiness”Colloid Filtration “Guiness” OverviewOverview Processes catwalk Processes catwalk Classical approachClassical approach Blocking Blocking


Processes in colloid-surface Processes in colloid-surface interactioninteraction

Actual colloid,Actual colloid, Inertia in (arbitrary) velocity fieldInertia in (arbitrary) velocity field Torque, drag due to nonuniform flowTorque, drag due to nonuniform flow Diffusion, Diffusion, hydrodynamic retardation/lubricationhydrodynamic retardation/lubrication

Effective increase in viscosity near surfaceEffective increase in viscosity near surface

Electrostatic (dynamic) interactionElectrostatic (dynamic) interaction DLVO (=LvdW + doublelayer model DLVO (=LvdW + doublelayer model

electrostatics) electrostatics)

Buoyancy/gravitational forceBuoyancy/gravitational force

OverviewOverview


Colloid Filtration “Guiness”Colloid Filtration “Guiness” OverviewOverview Processes catwalkProcesses catwalk Classical approach – “Colloid filtration theory” Classical approach – “Colloid filtration theory”

and some Detailsand some Details BlockingBlocking


Classical take on Processes in Classical take on Processes in colloid-surface interactioncolloid-surface interaction

Inert, Spherical colloid to Sphere (flat)Inert, Spherical colloid to Sphere (flat) Inertia in (Inertia in (StokesStokes) velocity field) velocity field Torque, drag due to nonuniform flowTorque, drag due to nonuniform flow

approximatedapproximated

Diffusion (Diffusion (superposedsuperposed)) hydrodynamic retardation/lubricationhydrodynamic retardation/lubrication

Electrostatic (dynamic) interactionElectrostatic (dynamic) interaction DLVODLVO (= (=LvdWLvdW + + doublelayer model doublelayer model

electrostatics electrostatics ) )

Buoyancy/gravitational force Buoyancy/gravitational force addedadded So flow must be downwardSo flow must be downward

Forces And Torques – Forces And Torques – RT modelRT model

F I

FG

FB

F vdW

Trajectory Analysis

FI = inertial force due to Stokes flow*FD = drag force due to Stokes flow*TD = drag torque due to Stokes flow*FG = gravitational forceFB = buoyancy forceFvdW = van der Waals force

*with corrections near surface

F IF BR

Smoluchowski-Levich Solution

FI = inertial force due to Stokes flowFD = drag force due to Stokes flowTD = drag torque due to Stokes flowFBR = random Brownian force

(particle diameter = 0)

= +

SURFACE

TD

F D

(particle has finite diameter)

F D

TD

Classical CFT :Happel sphere-Classical CFT :Happel sphere-in-cellin-cell

GID 0

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 (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.

katt u

Filtration coefficient

First-order deposition rate

3(1 n)

2dc

Clean-bed Clean-bed “Filtration Theory”“Filtration Theory”

Bulk “kf” by classical filtration theory

n porosityC aqueous phase concentration of colloid suspension

fc flux of CU groundwater (Darcy) specific flux fraction of colloids encountering solid surface that stick (empirical2,3) fraction of aqueous colloids that encounter solid surface (modeled1,3-6)

nC

t fc kC

k 3

2

1 n dc

U

n

First-order removal

Rate = filter coefficient * porewater velocity => two-step process

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

DetailsDetails11:Happel sphere-in-cell model:Happel sphere-in-cell model22

Happel sphere-in-cell is Happel sphere-in-cell is porous mediumporous medium

Stokes’ flow fieldStokes’ flow field calculated calculated via via trajectory trajectory

analysisanalysis11

Additive decomposition ==II++GG++DD

Initial point of limiting Initial point of limiting trajectorytrajectory

= A= A11/A/A22 = sin = sin22ss

1. Rajagoplan & Tien. 1976. AIChE J. 22: 523-533.

2. Happel. 1958. AIChE J. 4: 197-201.

AA11 AA22

Hydrodynamic retardation effect = the increased drag force a particle experiences as it approaches a surface. a deviation from Stokes’ law Hydrodynamic correction factors Particle velocity expressions gives:

where fr

t, frm, s1, s2, and s3 are the drag correction factors.

u r, 1

s1

Bs2 D 1 s3 NG sin Urur r, 1

frt A 1 2 fr

m NG cos rtdN LO

22 2

U

Detail: Basic solution (analytical) Detail: Basic solution (analytical) due to Rajagopalan & Tien (1976)due to Rajagopalan & Tien (1976)

Sedimentation group

London van der Waals group

Interception by boundarycondition

Detail: Detail: vs. vs.

irreversible adsorption constant, kirreversible adsorption constant, k irrirr = f( = f(,,)) = fraction of colloids contacting solid phase,= fraction of colloids contacting solid phase,

calculated calculated a prioria priori from RT model from RT model = fraction of colloids contacting solid phase= fraction of colloids contacting solid phase

that stick, treated as a calibration parameter that stick, treated as a calibration parameter accounting for all forces and mechanisms accounting for all forces and mechanisms not not considered inconsidered in calculation of calculation of

Role of electrostatic forces : Role of electrostatic forces : asideaside

Detail: Surface Forces in CFT – Detail: Surface Forces in CFT – DLVODLVO RT model uses DLVO theory for surface RT model uses DLVO theory for surface

interaction forces:interaction forces:

potential = van der Waals + double layerpotential = van der Waals + double layer

Theory predicts negligible collection when Theory predicts negligible collection when repulsive surface interaction exists repulsive surface interaction exists RT RT model neglects double layer force.model neglects double layer force.

attractive repulsive for like charges

Detail: Surface Forces in CFT – Detail: Surface Forces in CFT – DLVODLVO RT model uses DLVO theory for surface RT model uses DLVO theory for surface

interaction forces:interaction forces:

potential = van der Waals + double layerpotential = van der Waals + double layer

Theory predicts negligible collection when Theory predicts negligible collection when repulsive surface interaction exists repulsive surface interaction exists RT RT model neglects double layer force. model neglects double layer force.

Thus, double layer force implicit in Thus, double layer force implicit in ..

attractive repulsive for like charges

Highlights of Formulae for Highlights of Formulae for Yao (1971)Yao (1971)

hydrodynamic retardation and van der Waals force not includedhydrodynamic retardation and van der Waals force not included

Rajagopalan and Tien (1976)Rajagopalan and Tien (1976) deterministic trajectory analysisdeterministic trajectory analysis torque correction factorstorque correction factors Brownian Brownian added on separately from Eulerian analysis added on separately from Eulerian analysis

Tufenkji and Elimelech (2004)Tufenkji and Elimelech (2004) convective-diffusion equation solutionconvective-diffusion equation solution influence of van der Waals force and hydrodynamic retardation on influence of van der Waals force and hydrodynamic retardation on

diffusiondiffusion

Diffusion, interception, & sedimentation considered additiveDiffusion, interception, & sedimentation considered additive

Nelson and Ginn (2005)Nelson and Ginn (2005) Particle tracking in Happel cell – all forces together Particle tracking in Happel cell – all forces together

fc UC DC Df kT

C

OutlineOutline





Dynamic surface blocking (ME)Dynamic surface blocking (ME) initial deposition rate (kinetics)initial deposition rate (kinetics)

later, when deposition rate drops due to surface later, when deposition rate drops due to surface coverage (dynamics)coverage (dynamics)

retained particles block sites, B is the dynamic retained particles block sites, B is the dynamic blocking function (misnomer).blocking function (misnomer).

kcarate p2

cskBarate p )(2

B'sB's B = fraction of particle-surface collisions that B = fraction of particle-surface collisions that

involve open seats (cake walk).involve open seats (cake walk). Random Sequential Adsorption Random Sequential Adsorption

Power series in Power series in SS, for spherical geometry, for spherical geometry

Langmuirian Dynamic BlockingLangmuirian Dynamic Blocking

B s 1 4ss 6 3

ss 2 40

3

176

3 2

ss 3

B s 1 s

1/ s

OutlineOutline





IssuesIssues CFT coarse idealized modelCFT coarse idealized model

Chem/env. Engineering, not natural p.m.Chem/env. Engineering, not natural p.m. Biofilms, organic matter, asperities, heterogeneity Biofilms, organic matter, asperities, heterogeneity

(gsd, psd, surface area, electrostatic (dynamic), (gsd, psd, surface area, electrostatic (dynamic), transience, flow reversal, temperature, etc.transience, flow reversal, temperature, etc.

Reversibility ???Reversibility ???

CFT good for trend predictionCFT good for trend prediction Attachment goes up with colloid size, gw velocity, Attachment goes up with colloid size, gw velocity,

ionic strength, etc.ionic strength, etc.

Ultimately need equs for bulk mediaUltimately need equs for bulk media LabLab fieldfield

OutlineOutline




IssuesIssues Return to macroscale: See the data !Return to macroscale: See the data !

Field/Lab observationsField/Lab observations Microbes Microbes 1,2,31,2,3 and viruses and viruses 4,54,5 first showed apparent first showed apparent

multipopulation rates due to decreased attachment with scale multipopulation rates due to decreased attachment with scale Sticky bugs leave earlySticky bugs leave early Readily explained by subpopulationsReadily explained by subpopulations Some suggest geochemical “heterogeneity” Some suggest geochemical “heterogeneity”

Recent surprize is that inert monotype, monosize and Recent surprize is that inert monotype, monosize and polysize colloids exhibit samepolysize colloids exhibit same66

1. Albinger et al., FEMS Microbio Ltr., 124:321 (1994)

2. Ginn et al., Advances in Water Resources, 25:1017 (2002).

3. DeFlaun et al., FEMS Microbio Ltr., 20:473 (1997)

4. Redman et al., EST 35:1798 (2001); Schijven et al., WRR 35:1101 (1999)

5. Bales et al., WRR 33:639 (1997)

6. Li et al., EST 38:5616 (2004); Tufenkji and Elim. Langmuir 21:841 (2005)Yoon et al., WRR June 2006

Ability-based modeling (because Ability-based modeling (because we can)we can)

BTCs (first) exhibit long flat tails BTCs (first) exhibit long flat tails Two-site, multisite modelTwo-site, multisite model1 1 (google “patchwise”)(google “patchwise”) Two-population, multipop’n modelTwo-population, multipop’n model2 2 (UAz, Arnold/Baygents)(UAz, Arnold/Baygents) Can’t tell the differenceCan’t tell the difference

Profiles (recently) are steeper than expectedProfiles (recently) are steeper than expected Multipopulation works, not multisite Multipopulation works, not multisite (Li et al in 2), 3(Li et al in 2), 3

This is the location of the front in practiceThis is the location of the front in practice UpscalingUpscaling Alternative explanationsAlternative explanations

1. E.g., Sun et al., WRR 37:209 (2001); “patchwise heterogeneity”, CXTFIT ease of use (sorta)

2. E.g., Redman et al., EST 35:1798 (2001); Li et al. EST 38:5616 (2004)

3. Johnson and Li, Langmuir 21:10895 (2005); Comment/Reply

Research Needs (at least)Research Needs (at least) Formal upscaling Formal upscaling

Forces complex but well understoodForces complex but well understood Approximations testedApproximations tested Analytical results (Smoluchowski-LevitchAnalytical results (Smoluchowski-Levitch11))

Alternative explanations Alternative explanations C<-> S -> S’ surface transformations C<-> S -> S’ surface transformations 22

Mainly bacteria; need RTD for attachment eventsMainly bacteria; need RTD for attachment events Physical straining of larger sizes (a pop’n model)Physical straining of larger sizes (a pop’n model)33

ReentrainmentReentrainment44

Contact (CFT) and surface (multipopn) filtrationContact (CFT) and surface (multipopn) filtration55

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 ApproachAppendix: DNS Approach

Langevin equation of motionLangevin equation of motion Happel sphere-in-cellHappel sphere-in-cell Contemporaneous accounting of all forcesContemporaneous accounting of all forces

Solution per colloidSolution per colloid Calculating Calculating

Monte carlo colloidal release per Monte carlo colloidal release per ss => =>

P(P(ss) frequency of attachment per ) frequency of attachment per ss

as an expectation over P(as an expectation over P(ss))

Langevin EquationLangevin Equation Deterministic and Brownian displacements are Deterministic and Brownian displacements are

combined per time step:combined per time step:

mmpp is the particle mass, is the particle mass, uu is the particle velocity is the particle velocity vector, vector, FFhh is the hydrodynamic force vector, is the hydrodynamic force vector, FFee is is the external force vector, and the external force vector, and FFbb is the random is the random Brownian force vector. Brownian force vector.

All three components of random displacement All three components of random displacement must be modeled in the axisymmetric (3D must be modeled in the axisymmetric (3D 2D) 2D) flow field.flow field.

mpdu

dtFh Fe Fb

R = 3D displacement, udet = deterministic velocity vector n =3 N(0,1),R = standard deviations of Brownian displacements. negligible particle inertia assumed

t >> B (Kanaoka et al., 1983) B particle’s momentum relaxation time (=mp/6ap).

Thus, B << t < u u is the time increment at which udet is considered constant.

R udet t nR

SolutionSolution

Highlights of numerical solutionHighlights of numerical solution

Stokes’ flow in two-dimensionsStokes’ flow in two-dimensions R&T (1976) hydrodynamic drag correction R&T (1976) hydrodynamic drag correction

factorsfactors11

Brownian diffusion algorithm of Kanaoka et Brownian diffusion algorithm of Kanaoka et al. (1983)al. (1983)22 for diffusive aerosols for diffusive aerosols

Coordinate transformation to 2D modelCoordinate 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.

The Happel model: 3-D -> 2-D polar coordinates convert 3-D Brownian Cartesian displacement to spherical, to polar

y,z, contribute to angular displacements

And thus to r

˜ R x nx 2DBM t ˜ R y ny 2DBMt ˜ R z nz 2DBMt

Coordinates for diffusionCoordinates for diffusion

˜ R arcsin˜ R yr

˜ R arcsin˜ R zr

˜ R r ˜ R x r 1 sin2 ˜ R 1 sin2 ˜ R

2r

Calculating Calculating

S starting angle of a colloid

Pc(S) frequency of contact with the collector.

reduces to classical equation when deterministic (e.g., when Pc(S) equals one for

all S < LT and zero for all S > LT).

task of stochastic trajectory analysis for is to find Pc(S).

SSSScollect dP 2/

0

cossin2

Colloid transport and Colloid Filtration TheoryColloid transport and Colloid Filtration Theory Classical approachClassical approach IssuesIssues Direct numerical simulation:Direct numerical simulation:

ApproachApproach Examples, Convergence, TestingExamples, Convergence, Testing

ResultsResults Blocking - pages from Elimelech's siteBlocking - pages from Elimelech's site ConclusionsConclusions

Example Brownian TrajectoryExample Brownian Trajectory

1.6419E-04

1.6420E-04

1.6421E-04

1.6422E-04

1.6423E-04

1.6424E-04

1.6425E-04

1.6426E-04

1.6427E-04

1.6428E-04

1.6429E-04

1.1838 1.184 1.1842 1.1844 1.1846 1.1848 1.185 1.1852 1.1854 1.1856

[rad]

r [m

]

164.19

164.24

164.29

164.34

164.39

164.44

1.132 1.134 1.136 1.138 1.14 1.142 1.144 1.146

[rad]

r [m]

P(P(ss))

Number of bacteria collected with (Brownian motion included) as function of theta-start

0.000

0.005

0.010

0.015

0.020

0.025

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12

theta-start

Ba

cte

ria

co

llec

ted

ran1 300 rlzns ran1 1000 rlzns MT 12K rlzns ran1 12K rlzns

Convergence of a trajectory - 50K Convergence of a trajectory - 50K realizationsrealizations

Convergence of Collection Freq from ts=.0418 (Case 1, ap = .695 microns, dt = 0.5 sec)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 10 100 1000 10000 100000

number of realizations

Fre

qu

ency

of

colle

ctio

n

Convergence to deterministic trajectory analysis of Rajagopalan and Tien (when diffusion is neglected), Parameters: = 0.2, as = 50 m, ap = 0.1 m, and U = 3.4375 * 10-4 m/s.

The approximate analytical solution is = 1.5 NR22AS (Rajagopalan and Tien, 1976).

7.4E-03

7.5E-03

7.6E-03

7.7E-03

7.8E-03

7.9E-03

8.0E-03

8.1E-03

8.2E-03

8.3E-03

8.4E-03

0 2000 4000 6000 8000 10000 12000

number_of_realizations

t = 100

t = 10 s

t = 1 s

analytical result

Convergence of stochastic simulations forSmoluchowski-Levich approximation.

Parameters: ap = 0.1 m, as = 163.5 mm, = 0.372,

U = 3.4375*10-4 m/sec, = 8.9*10-4 kg*m/sec, T = 298 K.

Colloid transport and Colloid Filtration TheoryColloid transport and Colloid Filtration Theory Classical approachClassical approach IssuesIssues Direct numerical simulation: Direct numerical simulation:

ApproachApproach ConvergenceConvergence

ResultsResults Smoluchowski-Levitch approximationSmoluchowski-Levitch approximation General caseGeneral case

Blocking - pages from Elimelech's siteBlocking - pages from Elimelech's site ConclusionsConclusions

1.E-03

1.E-02

0 0.2 0.4 0.6 0.8 1 1.2

ap (m)

NG04 analytical

Testing comparison to the Smoluchowski-Levich approximation (external forces, interception neglected). Parameters: as = 163.5 mm, = 0.372, U = 3.4375*10-4 m/sec, = 8.9*10-4 kg*m/sec,

T = 298 K, t = 1 s, N = 6000.

Comparison of Comparison of calculations calculations

1E-04

1E-03

1E-02

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

ap (mm)

RT_76 NG_04 TE_04 NG_04 additive RT_76 deterministic NG_04 deterministic

R&T (1976) X N&G - - - T&E (2004) o N&G AdditiveR&T (1976) deterministic N&G deterministic

Lagrangean analysis is viable tool with modern Lagrangean analysis is viable tool with modern computerscomputers

Stochastic trajectory analysis suggests diffusion Stochastic trajectory analysis suggests diffusion and sedimentation may not be additiveand sedimentation may not be additive

More realistic “unit cell” models could be usedMore realistic “unit cell” models could be used

Lagrangean approach allows for arbitrary Lagrangean approach allows for arbitrary interaction potentialsinteraction potentials Chemical (mineralogical, patchwise) heterogeneityChemical (mineralogical, patchwise) heterogeneity Exocellular polymeric substances in bacteriaExocellular polymeric substances in bacteria Polymer bridging, hysteretic force potentialsPolymer bridging, hysteretic force potentials

ConclusionsConclusions

Parameter Value

Collector radius, as 163.5 m

Porosity, 0.372

Approach velocity, U 3.4375 * 10-4 sec

Fluid viscosity, 8.9 * 10-4 kg·m / sec

Hamaker constant, H 10-20 J

Bacterial density, p 1070 kg / m3

Fluid density, f 997 kg / m3

Absolute temperature, T 298 K

Time step, t 1 s

Number of realizations, N 6000

Parameters used in stochastic trajectory simulations.

Modification of CFT to Account for EPSModification of CFT to Account for EPS

Distribution of polymer lengths Distribution of polymer lengths on the cell surfaceon the cell surface

Repulsion modeled by steric Repulsion modeled by steric force, Fforce, Fstst(h)(h)1,21,2

depends on polymer density depends on polymer density and brush lengthand brush length

If sufficient polymers contact If sufficient polymers contact collector, cell attachescollector, cell attaches

depends on polymer density, depends on polymer density, length, and adhesion forceslength, and adhesion forces

KT2442

C

O

L

L

E

C

T

O

R

h0.695 m

mean polymer length = 160 nm

Hypothetical cell (drawn to scale)

1. de Gennes. 1987. Adv. Colloid Interface Sci. 27: 189-209.

2. Camesano & Logan. 2000. Environ. Sci. Technol. 34: 3354-3362.

Theoretical Sticking EfficiencyTheoretical Sticking EfficiencyNumerical Calculation of TrajectoriesNumerical Calculation of Trajectories

Steric repulsive forceSteric repulsive force Polymer bridgingPolymer bridging InterceptionInterception SedimentationSedimentation Brownian motionBrownian motion London van der Waals London van der Waals attractive forceattractive force Hydrodynamic retardationHydrodynamic retardation effecteffect

Incorporation of Brownian motion and polymer interactions into trajectory analysis allows for computation of a theoretical sticking efficiency.

Theoretical Sticking CoefficientTheoretical Sticking Coefficient

Incorporation of polymer interactions and Brownian motion + assumption that polymers control adhesion

Trajectory analysis yields the product []theo= A1/A2 =sin2s

Then we can define a theoretical value for the sticking efficiency :

theo= []theo /

where 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 Pseudomonas putida KT2442KT2442

Considered for Considered for bioremediation usebioremediation use1,21,2

Congo Red stain Congo Red stain image image heavy EPS heavy EPS coverage on cellscoverage on cells

EPS characteristics EPS characteristics being studied by being studied by Camesano et al. Camesano et al. (WPI)(WPI)33

Photo credit: Stephanie Smith Dept. of Land, Air, & Water Resources

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.

SummarySummary

CFT trajectory analysis modified for explicit CFT trajectory analysis modified for explicit inclusion of Brownian motion and bacterial EPS inclusion of Brownian motion and bacterial EPS interactionsinteractions

Brownian trajectory analysis results suggest that Brownian trajectory analysis results suggest that sedimentation and diffusion may not be additive sedimentation and diffusion may not be additive as previously assumedas previously assumed

Future workFuture work comparison of comparison of calculations with calculations with experimental data in the literatureexperimental data in the literature more realistic modeling of EPS interactions more realistic modeling of EPS interactions (e.g., hysteresis)(e.g., hysteresis)

notes on colloid transport and filtration in saturated porous media tim ginn, patricia culligan,...

Documents

colloid transport

contaminant transport

irreversible filtration

viruses filtration bacteria

groundwater pathogen

multisitepopulation

dispersion dispersion

particle sizes