Linear stability analysis on the onset of viscous fingering due to a non monotonic viscosity profile for immiscible fluids

TL;DR

This paper presents a linear stability analysis revealing that a non-monotonic viscosity profile can destabilize the interface between immiscible fluids in a Hele-Shaw cell, contrary to classical predictions.

Contribution

It introduces a theoretical analysis showing how viscosity gradients at the interface induce instability, expanding understanding of viscous fingering phenomena.

Findings

Viscosity gradients destabilize the fluid interface.

Classical stability predictions are challenged by the presence of viscosity gradients.

The dispersion relation is significantly affected by viscosity profile variations.

Abstract

The onset of viscous fingering in the presence of a non monotonic viscosity profile is investigated theoretically for two immiscible fluids. Classical fluid dynamics predicts that no unstable behavior may be observed when a viscous fluid pushes a less viscous one in a Hele-Shaw cell. Here, we show that the presence of a viscosity gradient at the interface between both fluids destabilize the interface facilitating the spread of the perturbation. The influence of the viscosity gradient on the dispersion relation is analyzed.