Viscous fingering with chemical reaction: effect of in-situ production of surfactants

Abstract

Viscous fingering experiments are performed in a radial Hele-Shaw cell for a liquid–liquid system in the presence of a well-characterized interfacial reaction capable of changing the surface tension on the time scale of the experiments. The reaction is a neutralization of a fatty acid by an alkaline material to form a surfactant, which exhibits first-order kinetics for the surface tension as a function of time. The experiments are carried out for capillary numbers, $Ca$, high enough for the fingering to always be in the fractal regime, and for a wide range of Damköhler numbers, $Da$. The fingers are typically wider in the presence of the chemical reaction than the non-reactive case. We observe two different-behaviours of the reactive fingering patterns. For intermediate values of $Da, 0.5 < Da < 4$, the fractal dimension $d_{f}$ is higher than the classical value measured for the non-reactive fingering patterns and reaches a maximum of about 1.9. For both small ($Da < 0.5$) and high $Da (Da > 4)$, the reactive fingering patterns are similar to the fingers with no reaction: the fractal dimension is found to be the same for both systems. These effects are consistent with the hypothesis that Marangoni stresses are present and produce wider fingers.