Colloidal dispersions
When particles in a suspension are smaller than a micron,
one must include the effects of Brownian motion, electrical double
layers and van der Waals' forces in addition to hydrodynamics.
In some early work, I calculated the effect of Brownian rotations on
the rheology of a suspension of nonspherical particles, concentrating on the
singular limit of weak Brownian rotations in which small effects
accumulate over a long time.
While the inertia of particles and fluid plays an essential role
during each random Brownian step, the diffusion process is slow and
density does not enter the expression for the diffusivity.
Inertia however does give rise to longtime tails in the velocity
correlation function.
Further, small nonlinear effects of fluid inertia can have a cumulative
effect on the equilibrium distribution of the particles.
Another paradox in Brownian motion is that very stiff constraints
in complex configurationchanging particles cannot be idealised in
thermodynamics by rigid bonds as they can in mechanics.
With two postdocs, I have recently constructed efficient
numerical algorithms which circumvent this.
I am currently interested in migration of Brownian particles across
sheargradients in pipe flow, in a direction counter to that
suggested by thermodynamics.
Electrical double layers have a large effect on the interactions
between colloidal particles.
Traditional theories linearise some exponential expressions for small
potentials, without justification.
By adopting the ideas of boundary layers from fluid mechanics, a
rigorous theory for large potentials has been developed.
Van der Waals' forces join together two particles if they come close.
In dilute suspensions large fractal aggregates can form.
Such aggregates have been much studied in the case in which
Brownian motion brings the particles together.
However, once the aggregates are larger than one micron, sedimentation
and shear flow are more important.
By calculating the strength of such aggregates, I was able to
explain why mud at a volume concentration of 10^{4} in
water, i.e. just murky water, produces an initial sediment occupying
over 30% of the volume, and how this weak fluffy sediment then
compacts under its own weight over 24 hours.
