Pattern Formation of Three-Dimensional Electroconvection on a Charge Selective Surface.

Abstract

When a charge selective surface consumes or transports only cations or anions in the electrolyte, biased ion rejection initiates hydrodynamic instability, resulting in vortical fluid motions called electroconvection. In this Letter, we describe the first laboratory observation of three-dimensional electroconvection on a charge selective surface. Combining experiment and scaling analysis, we successfully categorized three distinct patterns of 3D electroconvection according to [(Ra_{E})/(Re^{2}Sc)] [electric Rayleigh number (Ra_{E}), Reynolds number (Re), Schmidt number (Sc)] as (i)polygonal, (ii)transverse, or (iii)longitudinal rolls. If Re increases or Ra_{E} decreases, pure longitudinal rolls are presented. On the other hand, transverse rolls are formed between longitudinal rolls, and two rolls are transformed as polygonal one at higher Ra_{E} or lower Re. In this pattern selection scenario, Sc determines the critical electric Rayleigh number (Ra_{E}^{*}) for the onset of each roll, resulting in Ra_{E}^{*}∼Re^{2}Sc. We also verify that convective ion flux by electroconvection (represented by an electric Nusselt number Nu_{E}) is fitted to a power law, Nu_{E}∼[(Ra_{E}-Ra_{E}^{*})/(Re^{2}Sc)]^{α_{1}}Re^{α_{2}}Pe^{α_{3}} [Péclet number (Pe)], where each term represents the characteristics of electroconvection, shear flow, and ion transport.