Numerical Simulations of Miscible Channel Flow with Chemical Reactions

We study the pressure-driven miscible displacement of one fluid by another in a horizontal channel in the presence of an exothermic chemical reaction. We solve the continuity, Navier-Stokes, and energy conservation equations coupled to convective-discussion equations of the reactant and product. The viscosity is assumed to depend on the volume fraction of the reactant and product as well as the temperature. The effects of relevant parameters such as the Reynolds number, Schmidt number, Damköhler number and viscosity ratio of the reactant and product are studied. Our results indicate that increasing the intensity of the chemical reaction by increasing the Damkohler number and decreasing the dimensionless activation energy increases the displacement rate. We have also found that increasing Reynolds number leads to more pronounced instabilities and roll-up phenomena, which in turn promote rapid displacement of the resident fluid inside the channel. Variation of the relative significance of the heat of reaction and the Schmidt numbers of the reactants and products, however, has a negligible influence on the displacement rates for the parameter ranges considered in the present work.