The onset of double diffusive reaction-convection in an anisotropic porous layer

The onset of double diffusive reaction-convection in a horizontal anisotropic porous layer saturated with binary mixture, which is heated and salted from below and subjected to chemical equilibrium on the boundaries, is studied analytically using both linear and nonlinear stability analyses. A linear stability analysis is performed to investigate how the dissolution or precipitation of reactive component affects the onset of convection. The Darcy model is employed as momentum equation. The effect of mechanical and thermal anisotropy parameters, reaction rate, Lewis number, solute Rayleigh number, and normalized porosity on the stability of the system is investigated. We find that the chemical reaction may be stabilizing or destabilizing and that the anisotropic parameters have significant influence on the stability criterion. The effect of various parameters on the stationary, oscillatory, and finite amplitude convection is shown graphically. A weak nonlinear theory based on the truncated representation of Fourier series method is used to find the finite amplitude Rayleigh number and heat and mass transfer. (C) 2011 American Institute of Physics. [doi:10.1063/1.3598469]