Comparative Analysis of the Darcy and Brinkman Approximations for the Transition to Instability in a Porous Medium

Abstract

The stability of the evaporation front in a porous medium has been studied. The flow is described using the generalized Brinkman equation. The data obtained are compared with the results found within the Darcy approximation. It is shown that the use of the Brinkman approximation removes the unboundedness of the perturbation growth rate on small scales arising in the case of Darcy’s law. The interface becomes more stable; in the case of instability, the most unstable mode corresponds to a finite value of the wave number.