On the use of biphasic mixture theory for investigating the linear stability of viscous flow through a channel lined with a viscoelastic porous bio-material

Linear stability of viscous fluids flowing through a two-dimensional channel lined with a poroelastic layer which is saturated with the same viscous fluid is numerically studied in this work. Having assumed that the solid matrix of the poroelastics layer obeys the standard linear solid (SLS) model, the basic flow/deformation was obtained for this fluid-solid-interaction (FSI) problem using the "biphasic mixture theory". The vulnerability of the basic solution so-obtained to infinitesimally-small, normal-mode perturbations was then investigated using a temporal, normal-mode, linear stability analysis. An eigenvalue problem was obtained which was solved numerically using the Chebyshev pseudo-spectral collocation method. The main objective of the present work was to investigate the role played by the inhomogeneity/anisotropy of the poroelastic layer on the critical Reynolds number for the core flow. From the obtained results, we have reached the conclusion that anisotropy has no significant effect on the stability picture of the main flow. The effect of inhomogeneity on the critical Reynolds number, however, was found to be significant and highly dependent on the permeability number being smaller or larger than a threshold.