Impact of an intermediate layer on immiscible viscous fingering instability in radial Hele-Shaw cell

Abstract

We examine viscous fingering instability in a Hele-Shaw cell involving immiscible fluids with a three-layer fluid–fluid interface for radial flow, experimentally. The impact of introducing an intermediate layer on flow dynamics is explored, with particular attention to viscosity profiles. Our findings reveal that if the intermediate layer creates a non-monotonic viscosity profile, it significantly enhances the instability, leading to denser and more elongated fingering patterns. In particular, when the intermediate layer exhibits maximum viscosity, the growth of fingering patterns is suppressed after penetrating the intermediate layer, causing them to coalesce into a connected region. Key flow parameters such as the viscosity of the intermediate layer and the injection rate, strongly influence instability. Lowering the values of these parameters delays the suppression of instability. However, the injection volume of the intermediate layer decides whether the suppression of instability occurs. In contrast, when the intermediate layer has minimum viscosity, fingering patterns experience continuous growth with an early breakthrough. On the other hand, monotonic viscosity profiles result in less unstable flows due to smoother viscosity contrasts, causing the fingering patterns to channel and form less unstable configurations. These insights advance understanding of the interplay between viscosity profiles and flow parameters in controlling interfacial instabilities. The findings apply to CO${}_2$-enhanced oil recovery and groundwater remediation, offering strategies to optimize fluid displacement processes by tailoring flow conditions and viscosity contrasts.