Numerical study of immiscible viscous fingering in chemically reactive Hele-Shaw flows: Production of surfactants

Abstract

Viscous fingering on chemically reactive and immiscible interface is simulated by the phase-field method. The reaction produces surfactants on the interface to reduce local interfacial tension. Parametric analysis regarding the influences of reaction, determined by the dimensionless Damkohler number (Da) and the saturated capillary coefficient (epsilon(s)), on the fingering prominence at a prescribed breakthrough time is presented. The injection rate and viscosity ratio are also varied to observe their influences on the patterns. Transported by the fountain flows formed in the fingers, the produced surfactants tend to accumulate on the sides of fingers to weaken the local interfacial tension so that great variation of capillary effect will exist along the interface, especially for an intermediate range of Da. The weaker local capillary effect on a finger's side could result in prominent side-branching instability. Nonmonotonic behavior regarding the prominence of fingering instability for continuously increased injection flow rate observed in experiments is confirmed and explained qualitatively by the simulations. A reference capillary number (Ca-R) is proposed which is capable to monotonically describe the viscous fingering associated with both temporal and spatial changes of interfacial tension by reaction.