Control of Viscous Fingering Instability for Complex Yield-Stress Fluids using a Tapered Cell

TL;DR

This study demonstrates experimental and theoretical control of viscous fingering in complex yield-stress fluids using a tapered cell, enabling stable fluid displacement and providing a predictive stability criterion.

Contribution

It introduces a novel experimental approach with a tapered cell and a generalized linear stability analysis for controlling viscous fingering in yield-stress fluids.

Findings

Stable flat interfaces achieved with specific gap gradients and flow rates.

Theoretical stability criterion accurately predicts stability regimes.

Control of fingering enhances efficiency in applications like enhanced oil recovery.

Abstract

Being a major limiting factor for the efficiency of various technologies, such as Enhanced Oil Recovery, the viscous fingering (or Saffman--Taylor) instability has been extensively studied, especially for simple Newtonian fluids. Here, we experimentally and theoretically demonstrate a vital control of inhibiting the viscous fingering instability for complex (yield-stress) fluids to generate a complete sweep with a flat interface. Using a rectangular tapered cell, we first experimentally show the feasibility of controlling the primary fingering instability of a complex yield-stress fluid when pushed by another less viscous one. We further develop a theoretical linear stability analysis generalized for complex fluids with a yield stress and a power-law form of viscosity to provide insights. With three complex solutions yielding different viscosity contrasts, we observe stable flat and unstable wavy interfaces depending on the gap gradient ($\alpha$) and injection flow rate ($Q$). Finally, the comparison reveals an agreeable theoretical stability criterion capable of predicting stable vs. unstable displacements for yield-stress fluids under various $\alpha$.