Convective and absolute electrokinetic instability with conductivity gradients

Abstract

Electrokinetic flow instabilities occur under high electric fields in the presence of electrical conductivity gradients. Such instabilities are a key factor limiting the robust performance of complex electrokinetic bio-analytical systems, but can also be exploited for rapid mixing and flow control for microscale devices. This paper reports a representative flow instability phenomenon studied using a microfluidic T-junction with a cross-section of 11 $\umu$m by 155 $\umu$m. In this system, aqueous electrolytes of 10:1 conductivity ratio were electrokinetically driven into a common mixing channel by a steady electric field. Convectively unstable waves were observed with a nominal threshold field of $0.5\,\hbox{kV}\,\hbox{cm}^{-1}$, and upstream propagating waves were observed at $1.5\,\hbox{kV}\,\hbox{cm}^{-1}$. A physical model has been developed for this instability which captures the coupling between electric and flow fields. A linear stability analysis was performed on the governing equations in the thin-layer limit, and Briggs–Bers criteria were applied to select physically unstable modes and determine the nature of instability. The model predicts both qualitative trends and quantitative features that agree very well with experimental data, and shows that conductivity gradients and their associated bulk charge accumulation are crucial for such instabilities. Comparison between theory and experiments suggests the convective role of electro-osmotic flow. Scaling analysis and numerical results show that the instability is governed by two key controlling parameters: the ratio of dynamic to dissipative forces which governs the onset of instability, and the ratio of electroviscous to electro-osmotic velocities which governs the convective versus absolute nature of instability.