Stability of Poiseuille flow of a viscoelastic fluid in an anisotropic porous layer with oblique principal axes

Abstract

This study investigates the hydrodynamic stability of fluid flow in a horizontal anisotropic porous layer, where the saturating fluid is a Navier-Stokes-Voigt type of viscoelastic fluid, with Darcy and Brinkman terms. The permeability exhibits transverse isotropy, but intriguingly, the orientation of the longitudinal principal axes remains arbitrary. This configuration is sufficient to produce qualitatively novel flow patterns, such as a tilted plane of motion or inclined lateral cell walls. The Chebyshev collocation method is adopted to obtain the generalized eigenvalue problem, which is then solved numerically. The analysis traces neutral stability curves, defining the threshold for instability and identifies the critical Reynolds number for different values of the Kelvin-Voigt parameter, the porous parameter, the ratio of effective viscosity to fluid viscosity, the mechanical anisotropy parameter and the orientation angle of the principal axis. Instability is observed exclusively within a specific range of the Kelvin-Voigt parameter, which is significantly influenced by other governing parameters. Remarkably, the emergence of closed neutral stability curves is identified indicating the necessity of two distinct Reynolds numbers to fully characterize the linear stability of the base flow. The orientation angle is found to either stabilize or destabilize the fluid flow, depending on the value of anisotropy parameter. Additionally, this research revisits the isotropic case, correcting an incomplete analysis by Kumar et al. (Int. J. Non-Linear Mech. vol. 167, pp. 104885, 2024) and providing accurate numerical solution as a comprehensive correction to their work.