Dissolution-Driven Convection in a Bidispersive Porous Medium With Chemical Reaction: Brinkman Model

The onset of dissolution-driven convection in a bi-dispersive horizontal porous layer with first-order chemical reaction is analyzed. Linear stability analysis and nonlinear stability analysis have been performed in the present study. To examine the linear stability of the system, the basic state is perturbed using small-amplitude disturbances. Thereafter, the normal modes are used to solve the nondimensional equations governing the system. The results show that the thresholds for linear stability and nonlinear stability coincide, demonstrating that the linear stability theory sufficiently describes the mechanism for the onset of convection. Variation of the critical Rayleigh number $Rc$ in terms of other physical parameters is analyzed. The results imply that the momentum transfer coefficient $\gamma$, the Damköhler number $D_c$, the Darcy number $Da$, and the permeability ratio ${\kappa }_r$ contribute in stabilizing the system. The results suggest that as the Damköhler number rises, the dissolution reaction soaks up some of the heat energy, which results in the surroundings being colder. Eventually, the system is stabilized since a greater temperature gradient is needed for the onset of convection. The rigid-rigid boundaries prove to be a more stable configuration in comparison to the rigid-free and free-free boundaries.