Scale dependence of flow structures in electroconvection

Electroconvection (EC) is a hydrodynamic instability that occurs when dissolved ions are driven from a bulk fluid towards an ion-selective surface under a sufficiently large applied voltage. This phenomenon can impact mass transfer and ion residence time in a wide range of electrochemical applications. Simulating EC in regimes relevant to industrial applications is challenging; its wide range of spatiotemporal scales requires costly computations with extremely high resolutions. This study considers chaotic EC in a symmetric binary electrolyte in a canonical geometry. Using direct numerical simulations (DNS), we show that the range of length scales spanned by the EC induced eddies is a strong function of ε, which is the ratio of the nominal Debye length to the macroscopic geometry length. The ratio of large eddy to small eddy size is shown to grow as ε^-0.8. Data normalization based on this power law resulted in collapse of statistics in an intermediate asymptotic layer where smallest eddies reside.