Electrokinetic Control of Viscous Fingering

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.

* Fixed a few typos * Added new discussion of possible liquid pairs * Added new references

References in corpus (2)

• Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena
• Interfacial dynamics in transport-limited dissolution

Cited by in corpus (5)

• Linear stability analysis of transient electrodeposition in charged porous media: suppression of dendritic growth by surface conduction
• Dielectric breakdown by electric-field induced phase separation
• Controlling fluid adhesion force with electric fields
• Impact of Network Heterogenity on Nonlinear Electrokinetic Transport in Porous Media
• Electrically-controlled self-similar evolution of viscous fingering patterns in radial Hele-Shaw flows