Electroconvection

Despite its wide study, electroconvection in the most basic configuration is not well understood. The simplest problem is linear stability of one dimensional ionic conduction of an electrolyte into two parallel, charge selective surfaces such as an electrode or ion exchange membrane. There have been extensive studies on this configuration, though the question of stability is still not clear to this day. There are two primary routes to electroconvection. One is bulk electroconvection due to volumetric body forces in the nearly electroneutral fluid. The other mechanism is instability at the solid surfaces due to electroosmosis. Dukhin classified these electroosmotic flows as either the first or second kind.

Electroosmosis of the first kind is the slip at a surface due to tangential electric fields and the equilibrium diffuse charge in the double layer. Zholkovskij et al. found that this instability could occur in principle but would not exist for any realistic aqueous electrolyte. Electroosmosis of the second kind refers to slip at the surface driven by an extended space charge region that develops when an electrochemical cell is approaching or exceeding the limiting current. The stability due to second kind electroosmosis was well studied in recent work by Zaltzman and Rubinstein. Their work found that basic conduction can be unstable and the resulting convection could provide an explanation for the overlimiting conductance in cation exchange membranes.

The second route to convection is due to volumetric body forces in the bulk of the nearly electroneutral fluid. The literature has several contradictory papers as to whether such a bulk instability can even occur. It seemed that this disagreement was resolved in 2005 by Lerman, Rubinstein, and Zaltzman. Using new calculations and analysis, they found no evidence of bulk instability and the conclusion of this 2005 paper was that bulk electroconvection did not exist.

However, the story is not complete. The claim of no electroconvection pertained to a symmetric aqueous, low molecular weight electrolyte with order unity electroconvection Peclet number. However, when the Peclet number tends to infinity and when the ionic diffusivities are equal, the bulk electroconvection model transforms into the leaky dielectric model applied by Hoburg and Melcher to study stability of doped liquid dielectrics. In this and related models of liquids with non-uniform electric conductance the conduction state of the above mentioned type is unstable. A natural question is, how do the two models relate to each other, and in particular, what are the stability characteristics of conduction under bulk electroconvection at large Peclet numbers? This question is addressed in our recent paper.

Student researchers: David Boy, Mark Cavalowsky
Collaborators: Isaac Rubinestein and Boris Zaltzman, Ben Gurion University of the Negev, Israel.

Conference Talks:

• Storey, B.D., Zaltzman, B. and Rubinstein, I. 2007 Bulk electroconvection at high Peclet numbers, APS Division of Fluid Dynamics Meeting, Salt Lake City, UT. (Abstract) (Presentation)
• Boy, D. and Storey, B.D. 2006 The role of Faradaic reactions in microchannel flows, APS Division of Fluid Dynamics Meeting, Tampa. (Abstract) (Presentation)

• Storey, B.D., Zaltzman, B., & Rubinstein, I. 2007 Bulk electroconvective instability at high Peclet numbers. Physical Review E, 76, 041501. Full Text