Hydrodynamic interaction of rigid fluid particles

Abstract

The hydrodynamic interaction of rigid or fluid particles at small Reynolds numbers is reviewed. The paper focuses on the many instances in which the "microscopic" lenght scale (eg.the average domain size) is much larger than the molecular dimensions (so that the domain possess macroscopic properties) but much smaller than the characteristic lenght of the macroscopic sample. In such circumstances the heterogeneous material can be viewed as a continuum on the macroscopic scale and macroscopic or "effective" properties can be ascribed to it.

A quantitative definition of an ensemble average for particulate systems is discussed. The ensemble average refers to an average over a collection of a large number of systems which are identical in their macroscopic details but are different in their microscopic details. For reasons pf mathematical analogy, the general results given here for the effective viscosity translate into equivalent results for the thermal conductivity, electrical conductivity, dielectric constant and diffusion coefficient. The translational and rotational particle motions are marked to be governed by several intrinsic tensors that depend only upon the size and shape of the particle.

Bipolar coordinates are employed to obtain "exact" solution of the slow, Poisenille flow past two spherical bubbles. The influence of surface active agents on the flow is investigated.