Stability of Plane Parallel Flow Revisited for Particle–Fluid Suspensions

Abstract

An alternative model is proposed for hydrodynamic stability of plane parallel flow of an incompressible Newtonian fluid with suspended solid particles. For heavy particle-laden dusty gases with negligible particle volume fraction, the effective complex-form mean velocity in the modified Orr–Sommerfeld equation derived by the present model is showed to be essentially identical to the well-known Saffman's classical results. In the limit cases of small or large Stokes number of particles, simple formulas are derived for the effective Reynolds number ratio of the particle-laden suspension to the clear fluid without particles under otherwise identical conditions. The derived formula for particles of finite particle-to-fluid density ratio and small Stokes number is verified by comparing predicted results with known data, although a comparison of the derived formula with known results for particles of finite density ratio and large Stokes number cannot be made here due to the lack of available data. It is hoped that the present work could offer a conceptually novel and relatively simplified model for hydrodynamics of solid particle–fluid suspensions.