Analytical study of effects of finger-growth velocity on reaction characteristics of reactive miscible viscous fingering by using a convection–diffusion–reaction model

Abstract

Reactive miscible viscous fingering occurs when a reactive and miscible less-viscous liquid displaces a more-viscous liquid. Effects of bulk finger-growth velocity on reaction characteristics of miscible viscous fingering with a chemical reaction were studied analytically by using a convection–diffusion–reaction model. The model assumes the existence of a distinct interface between both liquids, assumes the existence of a two-dimensional, steady, stagnated flow field in the less-viscous liquid, and assumes an infinite chemical reaction rate. The model was then used to determine the reaction characteristics, such as the location of the reaction surface and the profile of the product, as functions of the velocity and initial reactant concentrations. The results reveal that the effects of the velocity on the reaction characteristics can be divided into low-, intermediate-, and high-velocity regions. In the low-velocity region, the reaction characteristics strongly depend on the reactant concentrations. In the intermediate-velocity region, the dependence of the reaction characteristics on the reactant concentrations decreases with increasing velocity. In the high-velocity region, the reaction characteristics are nearly independent of the reactant concentrations. Experiments confirm the existence of these three velocity regions predicted by the model.