Elastohydrodynamic instabilities in pressure-driven flow through a poroelastic channel

The linear stability analysis of a pressure-driven flow through a saturated poroelastic channel sandwiched between two impermeable rigid walls is carried out in the present study. Mixture theory is employed to describe the dynamics of the interstitial fluid and elastic solid matrix. The resulting eigenvalue problem is solved using the pseudo-spectral method. Without the poroelastic solid matrix, the flow under consideration reduces to the classical plane Poiseuille flow for which the linear stability analysis predicts critical Reynolds number, $R{e}_c=5772$. However, the present study, predicts that $R{e}_c$ could be as low as 5 for the flow under consideration owing to the deformability of the solid matrix. Further analysis reveals the existence of three new modes of instability. For low $Re$, mode I dominates the instability, while at high $Re$, mode III dominates the instability with characteristic scaling ${\Gamma }_c\sim 1/Re$ where ${\Gamma }_c$ is a measure of the deformability of the solid matrix. The driving mechanism of the predicted instability is found to be the coupling between the fluid and solid due to the pressure perturbation. The energy exchange between the base state velocity gradient and normal velocity perturbation via the convection term in the linearised Navier–Stokes equation plays a supporting role to the pressure perturbations in introducing unstable modes.