Research on the Interfacial Instability of Non-Newtonian Fluid Displacement Using Flow Geometry

Abstract

The variation of the classical viscous fingering instability is studied numerically in this work. An investigation of the viscous fingering phenomenon of immiscible displacement in the Hele–Shaw cell (HSC), where the displaced fluid is a shear-thinning fluid, was carried out numerically using the volume of fluid (VOF) method by adding a minor depth gradient or altering the geometry of the top plate in the HSC. The findings demonstrate how the presence of depth gradients can change the stability of the interface and offer a chance to regulate and adapt the fingering instability in response to the viscous fingering properties of air driving non-Newtonian fluids under various depth gradients. The relative breadth will shrink under the influence of the depth gradient, and the negative consequences of the gradient will be increasingly noticeable. Specifically, under different power-law indices, we found that with the enhancement of shear-thinning characteristics (lower power-law exponent n) in both positive and negative depth gradients, the fingers that protrude from the viscous fingers become shorter and thicker, resulting in higher displacement efficiency. Additionally, several modifications were performed to the upper plate’s design, and the findings revealed that the shape had no effect on the viscous fingering and only had an impact on the longitudinal amplitude. Based on the aforementioned traits, we may alter the HSC’s form or depth gradient to provide high-quality and effective work. © 2023 by the authors.