The combined effects of hydrodynamic interactions and Brownian motion on the orientation of particles flowing through fixed beds

In a previous publication [Phys. Fluids 31, 728 (1988)], the evolution of the orientation distribution in a dilute suspension of axisymmetric ‘‘tracer’’ particles flowing through a bed of fixed fibers or spheres was determined under conditions in which hydrodynamic interactions played a dominant role in determining particle orientation. In this paper, the previous results are extended to account for the effects of Brownian motion on the tracer particles and for different configuration statistics of the force in the fixed bed. In the former case, orientational evolution equations are developed and solutions obtained that are valid for large values of the rotary Peclet number (the parameter regime of greatest interest). In the latter case, it is demonstrated that, when the disturbance flow ceases to have fore–aft symmetry, a small orientational drift and dispersion are introduced into the resulting evolution equations. The latter effects are particularly important since they will occur in all fixed beds because of interactions between bed particles.