Nonlinear Convection in a Sparsely Packed Porous Medium Due to Compositional and Thermal Buoyancy

Abstract

Soret-driven convection in a two-component fluid layer subject to vertical temperature and concentration gradients is investigated analytically and numerically. The Darcy-Lapwood-Brinkman model for the momentum equation and the Boussinesq approximation is used to study the linear and weakly nonlinear properties of convection in two-component fluid in a sparsely packed porous medium due to compositional and thermal buoyancy. We have derived a nonlinear twodimensional Landau-Ginzburg equation with real coefficients near the onset of stationary convection at the supercritical pitchfork bifurcation. We have studied the Nusselt number contribution from Landau-Ginzburg equation at the onset of stationary convection. Two coupled nonlinear one-dimensional Landau-Ginzburg type equations with complex coefficients near the onset of oscillatory convection at the supercritical Hopf bifurcation are derived and the stability regions of travelling and standing waves are discussed.