Double diffusive convection in bidispersive porous media with couple stresses effect and relatively large macropores

Abstract

In this study, we have investigated the problem of double-diffusive convection in a porous medium that exhibits bidispersive characteristics and is influenced by couple stresses. The model employed considers the Darcy theory in the micropores, while utilizing the Brinkman theory in the macropores. The system encompasses two competing effects: a temperature gradient that induces instability and a salt gradient that enhances system stability. The study involved conducting analyses of linear instability and nonlinear stability. The eigenvalue systems obtained from both the linear and nonlinear theories were solved using the Chebyshev collocation method. To ensure the accuracy of this numerical method, the results were cross-validated by comparing them with the analytical solution of the eigenvalue system derived from the linear instability theory. Notably, the Chebyshev collocation method exhibited high accuracy even in the presence of high-order derivatives arising from the couple stresses term. Finally, numerical computations were performed to determine and extensively discuss the linear instability thresholds and global nonlinear thresholds. The findings contribute valuable insights into the behavior of the system under investigation. The results show that the stability thresholds of bidisperse flow in porous media are lower than those of single-phase flow. Moreover, the results confirm the stabilizing effect of the Brinkman parameter, couple stresses parameter, and permeability ratio parameter. It has also noted the stabilizing effect of the concentration Rayleigh number if the layer is salted below and the destabilizing effect if the layer is salted above.