Microhydrodynamics
When small particles move through a viscous fluid, the fluid motion is
governed by the Stokes equations.
The hydrodynamic interactions are then long ranged,
and a naive pairwise summation leads to
divergent integrals, reflecting genuine multiparticle cooperative
effects.
A 1977 paper sets out my `averagedequation' approach for a
rigorous calculation of these cooperative effects.
The paper gave independent derivations of the then recent results for
the hindered settling of sedimenting particles, the effective viscosity
of a suspension and the permeability of a porous medium.
Later I used the method to calculate heat transfer in porous media,
and also cooperative hydrodynamic effects on dynamic light
scattering.
Since then groups in Princeton, Stanford, Cornell and elsewhere have
adopted the method for calculating the rheology of suspensions,
stretching of particles as they flow through a porous medium, random
reorientation of rods as they pass one another and clustering of
rising bubbles.
As small particles sediment, hydrodynamic interactions
continuously change the relative configurations of the particles,
producing fluctuations in individual fall speeds.
These fluctuations lead to a diffusionlike mixing process which
has been measured recently in Paris.
I am currently interested in `intrinsic' convection in sedimentation,
theoretically and experimentally.
Emulsions are small drops of a viscous fluid suspended in a different
fluid.
Under shearing flows the drops deform and break into smaller drops.
If the internal viscosity of the drop is relatively small, as in air
bubbles in glass or water added to fat in modern `lite' foods, the
drops are effectively very slippery and consequently become long and thin
and so difficult to break.
In 1980 I developed a theory for these long thin drops,
explaining the new mechanism by which they eventually break.
Some recent numerical work has shown
that the effects of concentration are much smaller than for rigid
particles, owing to geometrical blockages being resolved
by small deformations and eased by slippery surfaces.
Further, large deformations in a shear flow reduce the collisional
crosssection.
