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The instability of a particle-laden flow subjected to velocity shear and differential particle loading was studied using the perturbation method. The momentum equations for particles and fluid are coupled at the order of the perturbation variable. The fluid-induced particle fluctuation is included explicitly. Therefore, it is not necesary to assume that particles ar e immobile at the perturbation time-scale (i.e. large Stokes number). A modified Rayleigh equation was derived. For a piece-wise linear velocity distribution and a sept-function particle concentration distribution, the dispersion equation is an eighth-order polynomial equation, which was solved using the numerical and symbolic computation software Mathematica. It was found that particle inertia not only modifies the shear instability but also gives rise to a second instability that depends critically on differential particle loading. The effects of particle mass loading, the Stokes number (the ratio of the particle response time and the flow time-scale), and the wave number of an infinitesimal disturbance, were examined.
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