Coherent structures in electrokinetic instability with orthogonal conductivity gradient and electric field

Abstract

Electro-osmotic flow in a configuration with a center stream flowing between two parallel sheath streams with mismatched electrical conductivities is known to exhibit an electrokinetic instability (EKI). This flow instability, with orthogonal conductivity gradient and electric field, is characterized by either wavy or pearl-necklace type structures depending upon the relative conductivities of center and sheath streams. In this paper, we propose a physical mechanism underlying such wavy and pearl-necklace type structures of the EKI. In order to verify the proposed mechanism, we perform EKI experiments in a cross-shaped microchannel at varying electric fields and for two flow configurations wherein the center stream has either higher or lower conductivity than the sheath streams. Using dynamic mode decomposition of time-resolved experimental data, we identify the spatio-temporal coherent structures that represent the dynamics of instability. These coherent structures provide a comprehensive validation of the proposed physical mechanism. In addition, experimentally observed coherent structures provide valuable insight into the dynamics and the spatio-temporal scales of the EKI.