On the instability of particle-laden flows in channels with porous walls

We investigate the stability of flows with low particle volume fractions in channels featuring porous walls. The particles, which are neutrally buoyant, interact with the carrier fluid through the Stokes drag force. Our study explores stability concerning particle relaxation time and mass fraction, employing different porous walls with varying permeabilities while maintaining a fixed porosity of 0.6. Our results reveal that in highly permeable porous walls, flow stability is mainly governed by the porous structure. The particle volume fraction and relaxation time exert relatively minor destabilizing and stabilizing effects, respectively. However, as porous wall permeability decreases, flow behavior becomes more sensitive to the particle volume fraction. In such cases, higher particle volume fractions and longer relaxation times contribute to stabilization. This suggests that particles and porous walls can effectively control flow, either maintaining laminar flow or inducing a transition to turbulence. We also analyze the impact of the momentum transfer coefficient at the porous surface, τ, on flow stability. Finally, we compare marginal stability curves obtained for various commonly used porous materials to conclude our study.