Finger behavior of a shear thinning fluid in a Hele-Shaw cell

TL;DR

This paper provides a theoretical analysis of finger formation in a shear thinning fluid within a Hele-Shaw cell, revealing how finger width diminishes as surface tension effects decrease, especially for weak shear thinning.

Contribution

It introduces a novel hodographic transformation approach to analyze the Saffman-Taylor instability with non-Newtonian fluids in Hele-Shaw cells.

Findings

Finger width approaches zero at low surface tension

Weak shear thinning effects are effectively modeled

Non laplacian field behavior is accounted for in the analysis

Abstract

We make a theoretical study of the behavior of a simple fluid displacing a shear thinning fluid confined in a Hele-Shaw cell. To study the Saffman-Taylor instability when the displaced fluid is non Newtonian we face the problem of having a field which is non laplacian. By means of an hodographic transformation we are able to solve the problem in the case of weak shear thinning while taking into account the non laplacian character of the equation. Our results predict that the finger width decreases towards zero for small values of the surface tension parameter which is inversely proportional to the finger velocity.