Fluid Mixing from Viscous Fingering

TL;DR

This paper investigates viscous fingering in miscible fluids, using high-resolution simulations and a new dynamic model to quantify and understand the mixing process and the effects of viscous instability.

Contribution

It introduces a novel two-equation dynamic model that accurately predicts mixing metrics in viscous fingering flows, validated by high-resolution numerical simulations.

Findings

The model accurately reproduces the evolution of concentration variance and dissipation rate.

Viscous fingering significantly influences the mixing rate and interfacial area creation.

The simulation demonstrates the complex interplay between channeling and mixing dynamics.

Abstract

Viscous fingering is a well-known hydrodynamic instability that sets in when a less viscous fluid displaces a more viscous fluid. When the two fluids are miscible, viscous fingering introduces disorder in the velocity field and exerts a fundamental control on the rate at which the fluids mix. We present a fluid dynamics video of the mixing process in a viscously unstable flow, generated from a high-resolution numerical simulation using a computational strategy that is stable for arbitrary viscosity ratios. We develop a two-equation dynamic model of concentration variance and mean dissipation rate to quantify the degree of mixing in such a displacement process. The model reproduces accurately the evolution of these two quantities as observed in high-resolution numerical simulations and captures the nontrivial interplay between channeling and creation of interfacial area as a result of viscous fingering.