Viscous fingering in a horizontal flow through a porous medium induced by chemical reactions under isothermal and adiabatic conditions.

In this work we analyze the viscous fingering instability induced by an autocatalytic chemical reaction in a liquid flowing horizontally through a porous medium. We have analyzed the behavior of the system for isothermal as well as adiabatic conditions. The kinetics of the reaction is chosen so that the rate depends on the concentration of only a single species. Since the reaction is autocatalytic the system admits a traveling wave solution. For endothermic reactions the concentration wave and temperature wave are mirror images, whereas for an exothermic reaction they are similar or parallel. The viscosity of the fluid is assumed to depend strongly on the concentration of the product and temperature of the medium. The dependence of viscosity on concentration (decrease with concentration) can destabilize the traveling wave resulting in the formation of viscous fingers. We have performed a linear stability analysis to determine the stability of the base traveling wave solution. The stability predictions have been confirmed by nonlinear simulations of the governing equations based on a finite difference scheme. We observe that including the temperature dependency of viscosity stabilizes the flow for an endothermic reaction, i.e., regions which exhibited viscous fingering now demonstrate stable displacement. For exothermic systems, however, the system exhibits less stable behavior under adiabatic conditions, i.e., it is destabilized by both concentration and temperature dependencies of viscosity.

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