KELVIN-HELMHOLTZ AND RAYLEIGH-TAYLOR INSTABILITY OF STREAMING FLUIDS WITH SUSPENDED DUST PARTICLES FLOWING THROUGH POROUS MEDIA

The linear Kelvin-Helmholtz (K-H) instability and Rayleigh Taylor (R-T) instability of two superposed streaming incompressible fluids flowing through porous medium is investigated considering the combined effects of suspended dust particles and surface tension. The linearized hydrodynamic equations are solved and the general dispersion relation is obtained using the normal mode analysis by applying the appropriate boundary conditions. We find that the dispersion relation is modified due to the simultaneous presence of porosity, suspended dust particles, permeability, and surface tension. The conditions of K-H instability as well as R-T instability are obtained for the porous media with suspended dust particles, permeability, dynamic viscosity, and surface tension. It is observed that the condition of K-H instability depends upon medium porosity, suspended dust particles, viscosity, permeability, and surface tension, but the condition of R-T instability depends on surface tension only. From the graphical interpretation we find that the density of suspended dust particles and medium porosity has a stabilization effect on the growth rate of unstable K-H mode. The dynamic viscosity, medium porosity, surface tension, and density of suspended dust particles have a stabilizing effect while Atwood number causes destabilization on the growth rate of unstable R-T mode.