# Electrokinetic Control of Viscous Fingering

## TL;DR

This paper develops a theory for controlling viscous fingering in electrolytes using electrokinetic effects, predicting that electric current can stabilize or destabilize interfaces in porous media, with applications in oil recovery and soil remediation.

## Contribution

It introduces a novel theoretical framework for electrokinetic control of viscous fingering, extending classical fluid instability analysis to include electric fields and electrokinetic phenomena.

## Key findings

- Viscous fingering can be modulated by the electric current to flow rate ratio.
- Beyond a critical injection ratio, stability depends only on flow and current directions.
- Electrokinetic effects can be used to control fluid interfaces in porous media.

## Abstract

We present a theory of the interfacial stability of two immiscible electrolytes under the coupled action of pressure gradients and electric fields in a Hele-Shaw cell or porous medium. Mathematically, our theory describes a phenomenon of "Vector Laplacian Growth", in which the interface moves in response to the gradient of a vector-valued potential function through a generalized mobility tensor. Physically, we extend classical Saffman-Taylor problem to electrolytes by incorporating electrokinetic phenomena. A surprising prediction is that viscous fingering can be controlled by varying the injection ratio of electric current to flow rate. Beyond a critical injection ratio, stability depends only upon the relative direction of flow and current, regardless of the viscosity ratio. Possible applications include porous materials processing, electrically enhanced oil recovery, and electrokinetic remediation of contaminated soils.