Stability of Dusty Flow Between Two Rotating Coaxial Cylinders

Abstract

The criterion for stability of dusty fluid flow between two coaxially rotating cylinders is derived by an examination of the stability of the basic flow to arbitrary perturbations. The perturbation equations are explored under the assumption that the relaxation time tarque (= m/k) of the dust particles is small. It is observed that the flow is always stable if Rayleigh's criterion meu>eta/sup 2/ is satisfied. The principle of exchange of stabilities is discussed and the characteristic value problem is solved under the narrow-gap approximations.