The wall-mode elasto-inertia instability of viscoelastic plane Poiseuille flow with porous walls

Linear stability analysis (LSA) of pressure-driven channel flow of an Oldroyd-B fluid with porous walls reveals a new elasto-inertial wall mode, absent in impermeable channel with viscoelastic fluids. The presence of porous walls induces Tollmien-Schlichting (TS) instability in Newtonian fluids. We used the modified Darcy-Brinkman-Oldroyd-B model to establish comprehensive equations and boundary conditions. Flow stability is governed by non-dimensional parameters: Reynolds number (Re), Permeability parameter (α), porous thickness ratio (δ), Weissenberg number (Wi), and solvent-to-solution viscosity ratio (β). At low Re numbers (<800), where TS instability occurs due to the large permeability, increasing Wi number initially stabilizes the TS mode. However, with a further increase in Wi (~25), the new elasto-inertial wall mode becomes destabilized. Neutral stability curves show that porous walls decrease the critical Reynolds number (Re_cr) and destabilize the Oldroyd-B fluid compared to impermeable channels. We also observed the non-monotonic effect of the Wi on flow stability, similar to that in impermeable channels. Notably, increasing the porous layer permeability (low α) shifts the threshold of Wi to lower values. To study the effect of β, we increased it from low values to 1 (the Newtonian case). At high permeability (α=50), for β>0.9, increasing destabilizes the flow and decreases Re_cr​. While in channels with impermeable walls, increasing β stabilizes the flow throughout this range.