The effect of viscoelastic flow on instabilities of plane Poiseuille problem with porous walls

The primary aim of this study is to investigate the linear stability of pressure-driven viscoelastic flow in a channel with porous walls at the top and bottom. Unlike the Newtonian flows, the polymer solutions create destabilizing effects in streamwise perturbations at different Reynolds numbers in smooth channels. The porous media in the same system, on other hand, also have a significant impact on destabilizing the flow. Here, we combined these two destabilizers and studied different types of unstable modes analytically and numerically by varying the dimensionless parameters that govern the flow stability (Reynolds number, permeability parameter α=H/κ^1/2, elasticity number E=λμ/(ρL² ), and the ratio of solvent to solution viscosity β=μ_s/μ, while the depth ratio is constant; here, ρ is the fluid density, μ is the fluid viscosity, λ is the relaxation time, and L is the channel half-width). Also, using the linear stability analysis for a wide range of Reynolds number and wavenumber indicates that due to the elasticity, the critical condition and stability behavior of channel flow with porous walls change considerably.