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.

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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

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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!

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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

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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)

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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?

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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.

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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)

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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)

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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.

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Motility and Diffusion in Saturated Sand - Grain
Size Effects
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Motility and Diffusion in Saturated Sand - Grain
Size Effects
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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.
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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).

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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
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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.

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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).

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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.
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Bacterial Transport in Porous Media Filtration
Theory (Friedman, 1999 Brown and Jaffe, 2001)

• Calculated separation distances (and energy
  barrier) based on DLVO theory.

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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)

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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
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Surfactants and Bacterial TransportPotential
travel distance

• Two ionic strengths, a range of particle size,
  and experimental resuls (symbols).