Evaluation of instability criterion for bidisperse sedimentation

The instability criterion for bidisperse sedimentation derived by Batchelor and Janse van Rensburg was combined with two empirical models for the particle velocities that are consistent with conservation of momentum and used to construct theoretical stability diagrams. The stability boundaries were fully determined by the particle volume fractions, the particle-size ratio, and the ratio of the density differences with the liquid. The results showed that on increasing the particle-size ratio sufficiently, stability, always is attained. For particles of similar size, instabilities occur mainly if the liquid density is intermediate between the particle densities. The stability diagrams agree well with the limited experimental data, if so-called vertical columns are excluded. This seems reasonable since similar structures observed in monodisperse suspensions are not captured by the bidisperse instability criterion either.