  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.
