Linear instability of a two-layer flow with differential particle loading

Abstract

The linear instability of an unbounded, two-layer particle-laden flow subjected to infinitesimal perturbations was investigated. The two-phase flow model employed in this study is dissipative because of a viscous mechanism through which momentum is transferred between the perturbed interstitial fluid and the suspended particles. The momentum interchange was found to depend critically on the ratio of the particle response time and the time scales of the perturbation. The dispersion equation for a flow system of large time scale ratio was solved analytically. Two unstable modes were found to coexist. The effects of three nondimensional parameters, a mean particle loading parameter, a differential loading parameter, and a relative offset between shear and the two layer interface, on two unstable modes were examined. In particular, if the velocity boundary layer is shifted toward the layer of low particle loading and the mean particle loading parameter increases, the most unstable mode ‘‘switches’’ from a long-wave instability to a short-wave instability.