The effective conductivity of dilute suspensions

The effective conductivity is shown to depend not only on the physical properties and concentration of the particles, but also critically on both the type and strength of any bulk flow which is present. Two distinct types of flow effects are distinguished; the flow dependence of the suspension microstructure (i.e., the statistical distributions of orientation and shape for the particles), and the flow dependence of the local temperature distributions at the microscale of the individual particles. Specific calculations are reported for suspensions of spherical drops, slightly deformed drops, and rigid prolate spheroidal particles, all in the limit of small particle Peclet number. In the latter case, the influence of Brownian rotations is included.