# Control of radial miscible viscous fingering

## TL;DR

This paper analyzes the stability of radial viscous fingering in miscible fluids, revealing how initial radius, advection, and diffusion influence instability, and proposes a control measure based on initial radius with experimental validation.

## Contribution

It introduces a stability criterion for radial viscous fingering based on initial radius, Péclet number, and log-mobility ratio, combining linear stability analysis, nonlinear simulations, and experiments.

## Key findings

- Stability boundary approximated by M = α(r₀) Pe^{-0.55}.
- Instability decreases with larger initial radius r₀.
- Experimental results qualitatively agree with numerical predictions.

## Abstract

We investigate the stability of radial viscous fingering (VF) in miscible fluids. We show that the instability is decided by an interplay between advection and diffusion during initial stages of flow. Using linear stability analysis and nonlinear simulations, we demonstrate that this competition is a function of the radius $r_0$ of the circular region initially occupied by the less viscous fluid in the porous medium. For each $r_0$, we further determine the stability in terms of P\'eclet number ($Pe$) and log-mobility ratio ($M$). The $Pe-M$ parameter space is divided into stable and unstable zones--the boundary between the two zones is well approximated by $M =\alpha(r_0) Pe^{-0.55}$. In the unstable zone, the instability is reduced (enhanced) with an increase (decrease) in $r_0$. Thus, a natural control measure for miscible radial VF in terms of $r_0$ is established. Finally, the results are validated by performing experiments which provide a good qualitative agreement with our numerical study. Implications for observations in oil recovery and other fingering instabilities are discussed.