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Dani Or and Lynn Dudley

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Title: Dani Or and Lynn Dudley


1
Colloidal and Bacterial Transport (Hydrodynamic
and Interfacial Interactions)
Dani Or and Lynn Dudley Dept. of Plants, Soils
and Biometeorology Utah State University, Logan,
Utah
2
Introduction
  • Transport of colloids and bacteria in porous
    media is dependent on interactions between the
    following properties (1) colloid (bacterium)
    (2) porous medium (3) solution composition and
    (4) flow regime.
  • Electrokinetic phenomena play an important role
    in transport of colloidal particles, bacteria
    viruses in porous media due to interactions
    between charged surfaces and flowing fluid.
  • Position of colloids and microorganisms in a
    stream of liquid in a porous medium is a result
    of a balance between electrostatic, viscous,
    gravitational, and thermal forces.
  • Bacterial motility or motion by flagella adds a
    physiological mechanism to their transport (
    convection and diffusion).

3
Outline
  • Colloids near surfaces in a liquid at rest the
    most probable distance.
  • Colloidal particle in motion implications for
    chromatography
  • Attachment/detachment mechanisms of colloidal
    particles.
  • Bacterial transport in porous media diffusion
    and motility.
  • Combined hydrodynamics and motility effects near
    rough surfaces.
  • Convection and macroscopic filtration theory
    for bacterial transport.

4
Colloidal Particles Flowing Near SurfacesForces
determining the most probable distance
  • Bike and Prieve J. Colloids Intef. Sci. 175
    422-434, 1995 analyzed electrokinetic forces on
    a sphere moving in laminar flow next to a charged
    surface.
  • The electrokinetic force is always repulsive !
    (regardless of the signs of surface charges).
  • Considering the balance between gravity (forcing
    the particle towards the wall) and electrostatic
    repulsion on a spherical particle of radius a
    we want to find the equilibrium distance where
    these two forces are balanced.
  • The gravitation force at distance ? is simply
    ?G(?)G? where
  • The electrostatic force ?E(?)B exp(-??) where

5
Colloidal Particles Near SurfacesForces
determining the most probable distance
  • The total potential energy (neglecting van der
    Waals interactions due to the assumed large
    distance a gtgt ? gtgt ?-1 ) is? (?)B exp(-??)G?
    which has a minimum as separation distance ?m
    ?-1ln(?B/G)
  • The most probable distance for a5 ?m is about
    7?-1 (insensitive to parameter values.
  • Thermal energy (kT) perturbs the distance
    according to Boltzmann distribution
  • In the presence of flow electrokinetic forces
    (positive) will increase the separation distance
    (negligible effect in aqueous solution due to low
    viscosity) ? which means faster streamlines!

6
Detachment of Colloidal Particles -
Hydrodynamics(Sharma et al. , J. Colloid
Interface Sci. 149121-134, 1992)
  • Consider a colloidal particle (sphere) attached
    to a surface in the presence of a flowing
    solution.
  • The tangential force FH1.7(6??RVX) where VX is
    axial fluid velocity at R (particle radius).
  • The force required to detach a particle is
    proportional to the adhesive force FH ?FA
  • ? is dependent on the release mechanism, for
    rolling FAa 1.4RFH
  • How do we determine the adhesive force? Via the
    disjoining pressurewhere Ks and ? are
    structural force parameters, n is number of ions
    per unit volume, A Hamaker constant, ? is inverse
    Debye length, and

7
Detachment of Colloidal Particles -
Hydrodynamics(Sharma et al. , J. Colloid
Interface Sci. 149121-134, 1992)
  • The total force acting on the particle is given
    by
  • The lift force is the minimum force required to
    lift the particle by pulling vertically.
  • The area of contact is coupled with Ftotal
    (stronger adhesion force more deformation at the
    contact Hertz solution)

8
Adhesion and Detachment of Colloidal
ParticlesEffects of Particle Size and Composition
  • Larger particles require more hydrodynamic force?
  • Why more hydrodynamic force for the softer
    colloidal particle?

9
Detachment of Colloidal Particles -
Hydrodynamics(Sharma et al. , J. Colloid
Interface Sci. 149121-134, 1992)
  • Adhesion force and contact area increase with
    particle size (and Hamaker constant with
    composition) ? increase in critical hydrodynamic
    force for dislodging an attached particle.
  • Reasonable agreement with experiments.

10
Applications Chromatography (e.g., Field-Flow
Fractionation)
  • Capitalizing on colloids tendency to congregate
    at typical distances from a wall (based on size
    and charge) to provide a wide range of size
    separation using a flow system.
  • In FFF a field is applied perpendicular to a
    parabolic flow field in a ribbon-shaped channel.
  • The primary difference between FFF and other
    chromatographic techniques is the external field
    that extends to large (cross-flow) distances
    unlike reliance on DDL and VDW relatively
    short-range forces near the wall in other
    chromatography (hence reducing the the need for
    large surface area along the flow path)

11
Field-Flow Fractionation FFF
Examples(Giddings, Science 260, 1456, 1993)
  • Wide range of colloidal size separation using
    separation along a small flow system.
  • The distribution from a wall is given aswhere
    l is characteristic elevation proportional to the
    applied force field F
  • The retention time tr in a channel of width w
    with a parabolic velocity profile relative to
    void time to (non retarded particle)

12
Motility and Diffusion of Bacteria in Saturated
Sand(Barton and Ford, Appl. Env. Microb.
613329-3335)
  • A study aimed at quantifying macroscopic
    transport parameters using chemotactic vs. random
    motility assays.

Bacteria
No Bacteria
  • Chemotaxis was induced by an attractant (3CB)
    placed in top 2 cm of the column.

13
Motility and Diffusion in Saturated Sand - Grain
Size Effects
14
Motility and Diffusion in Saturated Sand - Grain
Size Effects
15
Local Hydrodynamics on Rough Surface and
Bacterial Transport -surface topography and
motility
Scheuerman, T.R., A.K. Camper, and M.A.
Hamilton, Effects of sabstratum topography on
bacterial adhesion J. Colloid Interface Sci.
20823-33,1998.
16
Attachment in Grooves Hydrodynamics and Motility
  • Higher attachment rates for strains with flagella
    and more on the down stream.
  • Only the motile bacteria were found in the bottom
    of the grooves.
  • Motility assists in (1) surmounting energy
    barriers (2) enhancing diffusion rates hence
    bacteria-surface collisions (approach velocity).

17
Bacterial Transport in Porous Media Filtration
Theory (Friedman, 1999 Brown and Jaffe, 2001)
  • Assuming that bacteria are removed at a constant
    rate along a flow path in a porous medium
    yieldswhere ? is the filter coefficient and C
    bacterial concentration.
  • Integration along column length L yields
    where C0 is the inlet
    concentration.
  • The parameter ? is determined experimentally from
    data shown on the right (two strains of bacteria
    in four soils).

Sand
Clay
18
Bacterial Transport in Porous Media Filtration
Theory (Friedman, 1999 Brown and Jaffe, 2001)
  • The filter coefficient ? is dependent on the
    properties of the (1) colloid (bacterium) (2)
    porous medium (3) solution composition and (4)
    flow regime.
  • The determination of these interactions requires
    a microscopic approach that defines
    where dc is the diameter of the
    collectors (grains), n porosity, ? collision
    efficiency, and ? collector efficiency.
  • Flow of bacteria past a spherical collector
    representing a soil particle is shown along with
    primary transport mechanisms.

19
Bacterial Transport in Porous Media Filtration
Theory
  • Various mechanisms contributes to the
    collector-bacterium collisions (and its
    efficiency).
  • An expression for these interactions that aslo
    considers the efficiency of a collector within a
    porous bed (neighboring collectors) was
    developedwhere AS for the bed and its
    porosity, and Npe,NvdW, NR, and NG are
    dimensionless numbers accounting for diffusion,
    van der Waals, interception, and sedimentation.
  • Other aspects must be considered such as
    plugging of a filter by attached bacteria and
    electrostatic repulsion (DLVO) which strongly
    affect the parameter ? (collision efficiency).

20
Bacterial adhesion to solid surfaces disjoining
pressure
  • The interplay between electrostatic forces and
    attractive van der Waals surface forces and the
    charge of the bacterium cell determines the
    minimum approach distance (position of the energy
    barrier/well).
  • Most bacteria in soils are negatively charged
    (otherwise, immobile).

Positively charged net attraction
Negatively charged net repulsion
Jucker, B.A., H. Harms, and A.J.B. Zehnder,
1996, Adhesion of the Positively Charged
Bacterium Stenotrophomonas (Xanthomonas)
maltophilia 70401 to Glass and Teflon, J. Bacter.
1785472-5479.
21
Bacterial Transport in Porous Media Filtration
Theory (Friedman, 1999 Brown and Jaffe, 2001)
  • Calculated separation distances (and energy
    barrier) based on DLVO theory.

22
Breakthrough Curves for Bacterial Transportionic
strength and surfactant (Brown and Jaffe, 2001)
  • The DDL thickness as a function of ionic strength
    (I) is
  • As ionic strength increases bacterial attachment
    increases hence transport decreases.
  • The BTCs also show the effect of the surfactant
    (see 2 mM)

23
DDL and Bacterial Transporteffects of surfactant
on collision efficiency
  • Reduction in (estimated) collision efficiencies
    as a function of Debye length and surfactant
    addition.

Maximum chain length
24
Surfactants and Bacterial TransportPotential
travel distance
  • Two ionic strengths, a range of particle size,
    and experimental resuls (symbols).
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