Linear stability analysis of particle-laden flows in channels with porous walls

Suspension flows with small particle inertia are encountered in environmental, industrial, pharmaceutical, and geological applications. However, the stability of this type of flow in the presence of porous media is poorly understood. We investigate the effects of porous surfaces on flow stability by performing linear stability analysis of dilute particle-laden flows in channels bounded by rigid, homogenous, and isotropic porous walls. The particles field is two-way coupled with the fluid field through Stokes drag only. Particles are assumed to be uniform, solid, and spherical with a significantly smaller size than the characteristic scale of the flow. Brinkman equation is adopted to characterize the fluid behavior inside the porous layers. It is found that porous walls exert destabilizing effects on the system. Increasing the porous layer permeability or thickness triggers instabilities at smaller Reynolds numbers. The presence of porous walls therefore may work as a strategy to enhance efficiency in mixing processes. Our results also reveal that increasing the particles size results in a monotonic rise in the critical Reynolds number, which is in contrast with the particle-laden flow in a channel with impermeable walls where stability alternates with particles size.