Effect of convection on the stability of a liquid with a nonuniformly distributed heavy admixture

The effect of the transverse temperature gradient on the stability of steady motion of a viscous incompressible liquid in a plane vertical layer bounded by two infinite solid surfaces is studied. The motion of the liquid is caused by sedimentation of heavy solid spherical particles distributed nonuniformly across the layer and by the horizontal temperature gradient. Spectra of decrements of small normal perturbations are calculated for different particle sizes and different degrees of nonuniformity of the distribution of admixture particles. The stability of a steady flow of the liquid with an admixture decreases with increasing temperature gradient and increasing particle radius and increases with a tendency of the particles to a uniform distribution.