The effect of viscosity ratio and Peclet number on miscible viscous fingering in a Hele-Shaw cell: A combined numerical and experimental study

TL;DR

This study investigates how viscosity ratio and Peclet number influence miscible viscous fingering in a Hele-Shaw cell through combined experiments and numerical simulations, revealing complex pattern formation and the limitations of current models.

Contribution

It provides a comprehensive experimental dataset and compares it with numerical models, highlighting the need for improved dispersion modeling to accurately predict fingering patterns.

Findings

Fingering complexity increases with viscosity ratio and Peclet number.

Onset of fingering is delayed due to Taylor dispersion stabilization.

Current models partially predict breakthrough times but struggle with fine-scale finger features.

Abstract

The results from a series of well characterised, unstable, miscible displacement experiments in a Hele Shaw cell with a quarter five-spot source-sink geometry are presented, with comparisons to detailed numerical simulation. We perform repeated experiments at adverse viscosity ratios from 1 - 20 and Peclet numbers from 10$^4$ - 10$^6$ capturing the transition from 2D to 3D radial fingering and experimental uncertainty. The open-access dataset provides time-lapse images of the fingering patterns, transient effluent profiles, and meta-information for use in model validation. We find the complexity of the fingering pattern increases with viscosity ratio and Peclet number, and the onset of fingering is delayed compared to linear displacements, likely due to Taylor dispersion stabilisation. The transition from 2D to 3D fingering occurs at a critical Peclet number that is consistent with recent experiments in the literature. 2D numerical simulations with hydrodynamic dispersion and different mesh orientations provide good predictions of breakthrough times and sweep efficiency obtained at intermediate Peclet numbers across the range of viscosity ratios tested, generally within the experimental uncertainty. Specific finger wavelengths, tip shapes, and growth are hard to replicate; model predictions using velocity dependent longitudinal dispersion or simple molecular diffusion bound the fingering evolution seen in the experiments, but neither fully capture both fine-scale and macroscopic measures. In both cases simulations predict sharper fingers than the experiment. A weaker dispersion stabilisation seems necessary to capture the experimental fingering at high viscosity ratio, which may also require anisotropic components. 3D models with varying dispersion formulations should be explored in future developments to capture the full range of effects at high viscosity ratio and Peclet number.