Nonmodal instability of a stratified plane-channel suspension flow with fine particles.

Abstract

We consider the nonmodal instability and transient growth of small disturbances in a plane-channel suspension flow with a nonuniform concentration profile of fine noncolloidal particles accumulated in two localized layers, symmetric about the channel axis. A single-velocity model of an effective Newtonian fluid with a finite particle volume fraction is employed. It is established that fine particles distributed nonuniformly in the main flow significantly modify the growth rate of the first mode in a wide range of governing parameters. The most pronounced destabilizing effect is produced by the particles localized in the vicinity of the walls. A parametric study of the so-called optimal disturbances showed that they are streaks elongated in the flow direction, similar to the optimal disturbances in the flow devoid of particles. The transverse wave number of the optimal disturbances depends strongly on the location of the particle layers. Even when the particle mass concentration (averaged over the channel cross section) is small (of the order of a percent) and the particles are localized in the middle between the walls and the channel axis, the energy of the optimal disturbances is by several orders of magnitude larger than in dusty-gas and pure-fluid flows. When the particle layers are located in the vicinity of the walls or the channel axis, the nonmodal instability mechanism is less pronounced, as compared to the flow devoid of particles.