Side branched patterns, coalescence and stable interfaces during radial displacement of a viscoelastic fluid

TL;DR

This study investigates how the viscosity ratio and viscoelasticity influence interfacial patterns during radial displacement in a Hele-Shaw cell, combining experiments and mathematical modeling to understand pattern stability and finger coalescence.

Contribution

It introduces a mathematical model linking viscosity ratio to finger spacing and demonstrates the impact of viscoelasticity on interfacial pattern morphology.

Findings

Higher viscosity ratios lead to more stable interfaces.

Model predictions closely match experimental finger spacing.

Viscoelasticity significantly affects pattern growth and coalescence.

Abstract

We explore the interfacial instability that results when a Newtonian fluid (a glycerol-water mixture, inner fluid) displaces a viscoelastic fluid (a dense cornstarch suspension, outer fluid) in a radial Hele-Shaw cell. As the ratio of viscosities of the inner and outer fluids is increased, side branched interfacial patterns are replaced by more stable interfaces that display proportionate growth and finger coalescence. We correlate the average finger spacing with the most dominant wavelength of interfacial instability, computed using a mathematical model that accounts for viscous fingering in miscible Hele-Shaw displacements. The model predictions on the role of viscosity ratio on finger spacing are in close agreement with the experimental observations. Our study lends insight into the significant contribution of the viscoelasticity of the outer fluid on the morphology and growth of interfacial patterns.