Competing Effects of Inertia and Permeability on Stability in Porous-Walled Suspension Flows

Particle-laden flows over porous substrates occur in many natural and engineered systems, from filtration and enhanced oil recovery to blood flow near biological interfaces. We perform a linear stability analysis of Couette–Poiseuille flow (CPF) of a Newtonian fluid laden with inertial particles overlying a porous wall. The system is modeled using a two-domain framework: a dusty-gas approximation for the particle-laden core flow and volume-averaged Navier–Stokes equations (VANS) within the porous layer. We examine how flow stability is affected by particle relaxation time, mass fraction, wall permeability, and imposed shear from the moving upper boundary. Results reveal new particle-induced disturbance modes that grow with increasing mass fraction but remain subdominant. Increasing permeability destabilizes the flow and diminishes the stabilizing effect of high particle inertia. Couette forcing reduces the critical Reynolds number across all cases, with highly permeable layers showing a non-monotonic response, initially enhancing, then suppressing instability. These findings highlight complex coupling between shear, particle dynamics, and porous-wall effects.