The onset of electrohydrodynamic instability in isoelectric focusing

Abstract

The onset of electrohydrodynamic motion in a thin layer of liquid has been investigated for the case in which the electrical conductivity varies linearly across the liquid layer. It is shown that a finite conductivity gradient can be quiescently sustained, provided certain requirements are satisfied. Dimensional analysis shows, and numerical computations confirm, that the conditions for the onset of motion in the layer can be characterized by two dimensionless parameters: the electrical Rayleigh number, and the dimensionless conductivity gradient. Interest in the problem stems from experiments on isoelectric focusing (IEF), an electrically-driven separation process used to purify peptide and protein mixtures. Previous experiments had led to the postulate that, as conductivity gradients developed during IEF, electrohydrodynamic convection would arise to disrupt the separation process. The theory developed here supports such a postulate.