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.

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

References in corpus (6)

• Analysis of electrolyte transport through charged nanopores
• Desalination shocks in microstructures
• Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena
• Exact solutions and physical analogies for unidirectional flows
• Asymmetric collapse by dissolution or melting in a uniform flow
• Interfacial dynamics in transport-limited dissolution

Cited by in corpus (12)

• Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations
• Freezing point depression and freeze-thaw damage by nano-fuidic salt trapping
• Linear stability analysis of transient electrodeposition in charged porous media: suppression of dendritic growth by surface conduction
• Vortices of Electro-osmotic Flow in Heterogeneous Porous Media
• A review of one-phase Hele-Shaw flows and a level-set method for non-standard configurations
• Dielectric breakdown by electric-field induced phase separation
• Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments
• Delayed Hopf bifurcation and control of a ferrofluid interface via a time-dependent magnetic field
• Numerical study on viscous fingering using electric fields in a Hele-Shaw cell
• 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