Linear Stability Analysis of Phase Inversion-Induced Viscous Fingering

When the less viscous fluid displaces the high viscosity fluid in a porous medium driven by the pressure gradient, the interface between them is likely to be unstable. In this study, we explore various salient features of such a system leading to viscous finger formation when phase inversion takes place via a linear stability analysis using lubrication approximation which is corroborated by experiments. The theoretical model developed here concerns the onset of instability point that results in morphological changes in the system. The theoretical predictions show system instability to the random perturbations to the interface on reducing the interfacial tension and increasing density difference \((\rho_{D})\) . Also, higher viscosity ratio \((\mu_{r} > 1)\) , drives the system toward stability. This estimate is attributed to the steep concentration gradient near the interface. The formulated model also predicts finger spacing (λ). This theoretical investigation corroborates well with the experimental observations of the viscous finger spacing in the radial geometry.