Linear instability of a viscoelastic Poiseuille flow confined between porous walls*

This research investigates the linear instability of an Oldroyd-B fluid flow confined between porous walls. The study focuses on analyzing the impact of dimensionless parameters, including permeability parameter (α=L/√K), Weissenberg number (Wi=λU_max/L), and depth ratio (δ=H/L), on the flow stability. Here L represents the channel half-width, K is the permeability, λ is the relaxation time, U_max is the maximum velocity, and H is the thickness of the porous layer. Throughout the entire range of Weissenberg numbers (0≤Wi≤10), increasing the permeability parameter up to certain value leads to an increase in the critical Reynolds number, indicating enhanced flow stability. Notably, this behavior deviates from that of Newtonian flow, as Weissenberg numbers increase, multimodal instabilities for smaller values of α occur. Remarkably, larger Wi numbers also trigger multimodal instability in larger permeability parameters. Furthermore, our study uncovers that at small permeability parameters, increasing the depth ratio has a destabilizing effect on the flow, resulting in a decrease in the critical Reynolds number. These observations suggest the potential of controlling flow instability in viscoelastic fluids by varying the permeability and the thickness for a fixed porosity of porous walls.