(519e) Preferential Concentration Driven Instability of Sheared Gas-Solid Suspension

We examine the linear stability of a homogeneous gas-solid suspension of small Stokes number particles, with a moderate mass loading, subject to a simple shear flow. The modulation of the gravitational force exerted on the suspension, due to preferential concentration of particles in regions of low vorticity, in response to an imposed velocity perturbation, can lead to an algebraic instability. Since the fastest growing modes have wavelengths small compared with the characteristic length scale (U/Γ) and oscillate with frequencies large compared with Γ, U being the settling velocity and Γ the shear rate, we apply the WKB method, a multiple scale technique. This analysis reveals that the instability comes from the coupling of a number density mode driven by preferential concentration in regions where the velocity disturbance reduces the base state vorticity and a momentum mode driven by the particle number density variations. The growth of the amplitude of particle concentration and fluid velocity disturbances is characterized as a function of the wavenumber and Reynolds number(Re = U² /Γν) using both the asymptotic theory and a numerical solution of the linearized equations.