Reactive-diffusive phenomena in two-dimensional, anisotropic media

Non-linear reaction-diffusion processes with cross-diffusion in two-dimensional, anisotropic media are analyzed by means of an implicit, iterative, time-linearized approximate factorization technique as functions of the anisotropy of the heat and species diffusivity tensors, the Soret and Dufour cross-diffusion effects, and five types of boundary conditions. It is shown that anisotropy and cross-diffusion deform the reaction front and affect the front velocity, and the magnitude of these effects increases as the magnitude of the off-diagonal components of the heat and species diffusivity tensors is increased. It is also shown that the five types of boundary conditions employed in this study produce similar results except when there is either strong anisotropy in the species or heat diffusivity tensors and there are no Soret and Dufour effects, or the species and heat diffusivity tensors are isotropic, but the anisotropy of the Soret and Dufour effects is important. If the species and heat diffusivity tensors are isotropic, the effects of either the Soret or the Dufour cross-diffusion effects are small for the cases considered in this study. The time required to achieve steady state depends on the anisotropy of the heat and diffusivity tensors, the cross-diffusion effects, and the boundary conditions.