Migration of rigid particles in non-Brownian viscous suspensions

There is an obvious need for obtaining a closed set of equations describing multiphase flows and the complexity of their configurations. Despite their “frozen” interfaces, suspensions of rigid particles are also concerned by this issue. The description of the relative motion between the two phases is still controversial, in particular, concerning the forces acting on the particles and involving their concentration gradient or a shear rate gradient. It is our purpose here (a) to develop a two-fluid model especially designed for particles dispersed in a viscous liquid and (b) to close the model for rigid particles with the help of low-Reynolds-number hydrodynamics. Besides the obvious role of gravity forces, the migration of particles relative to the fluid is shown to result from two different physical phenomena: (a) the inhomogeneity of the stress resulting from direct interparticle forces and (b) Fick-like terms in the hydrodynamic force acting on the particles.