A local coupling between sedimentation and convection: Application to the Beenakker-Mazur effect

It is argued that the hydrodynamic behaviour of suspensions may be described by a set of local coupled equations for the convective flow pattern V(r) and for the sedimentation velocity w(r). Due to the cross terms, inhomogeneities in either w or in the particle concentratiob φ may give rise to intrinsic convection, as termed by Beenakker and Mazur. In the low φ limit, coefficients of these phenomenological coarse grained equations can be estimated either via an Onsager reciprocity argument, or by a direct analysis of the stress tensor. Similar ideas may be qualitatively extended to either sharp discontinuities of φ or to the vicinity of a wall: sedimentation parallel to the wall generates a finite tangential convection velocity at the wall, which acts as a source of bulk convection. The results obtained by Beenakker and Mazur in a spherical vessel are thus confirmed. Quite generally, this approach supports the concept of screening in an hydrodynamic suspension - in close analogy with screening of electric field fluctuations in a dielectric.