On Kelvin-Helmholtz instability of particulate two-fluid flow

A hydrodynamic model is used to study Kelvin-Helmholtz (KH) instability of the interface between two particle-laden inviscid fluids moving with two different uniform mean velocities. Explicit eigen-equation is derived to study the effect of suspended particles on the growth rate of KH instability. For dusty gases with negligible volume fraction of heavy particles and small particle-to-fluid mass ratio, the real and imaginary parts of leading-order asymptotic expression derived by the present model for the growth rate are shown to be identical to the earlier results derived by the classical Saffman model established for dusty gases. Beyond the known results, explicit leading-order asymptotic expressions for the effect of suspended particles on the growth rate are derived for several typical cases of basic interest. It is shown that the suspended particles can decrease or increase the growth rate of KH instability depending on the Stokes numbers of the particles and whether the particles are heavier or lighter than the clean fluid. Compared to the mass density of the clean fluid, our results based on leading-order asymptotic solutions show that heavier particles and lighter particles have opposite effects on the growth rate of KH instability, while the effect of neutrally buoyant particles on the growth rate of KH instability is negligible.