EFFECT OF PARTICLE INERTIA ON THE INSTABILITY OF A PARTICLE-LADEN FLOW

The instability of a particle-laden flow subjected to velocity shear a nd differential particle loading was studied using the perturbation me thod. The momentum equations for particles and fluid are coupled at th e order of the perturbation variable. The fluid-induced particle fluct uation is included explicitly. Therefore, it is not necessary to assum e that particles are immobile at the perturbation time-scale (i.e. lar ge Stokes number). A modified Rayleigh equation was derived. For a pie ce-wise linear velocity distribution and a step-function particle conc entration distribution, the dispersion equation is an eighth-order pol ynomial equation, which was solved using the numerical and symbolic co mputation software MATHEMATICA. It was found that particle inertia not only modifies the shear instability but also gives rise to a second i nstability that depends critically on differential particle loading. T he effects of particle mass loading, the Stokes number (the ratio of t he particle response time and the flow time-scale), and the wave numbe r of an infinitesimal disturbance, were examined. Copyright (C) 1996 E lsevier Science Ltd.