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 µm by 155 µm. 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 kV cm −1 , and upstream propagating waves were observed at 1.5 kV 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.

Convective instability of electrokinetic flows in a cross-shaped microchannel

“…The details of these derivations can be found in Lin et al (2004) and Chen et al (2005). The non-dimensional modified ohmic model governing equations are therefore given as,…”

“…Chen et al (2005) measured regions of exponential spatial growth for convective instability in a high-aspect-ratio T-shaped microchannel. They analysed the distribution of spanwise-averaged perturbation amplitude (scalar perturbation energy) with increasing streamwise coordinate of their flow.…”

“…Storey et al (2005) presented a depth-averaged version of the Lin et al governing equations which compared well with the complete three-dimensional model for high-aspectratio channels. Chen et al (2005) presented preliminary experiments and detailed stability analyses using depth-averaged linearized equations for the study of convective instability in the T-shaped intersection of two microchannel flow streams. In those experiments, Chen et al visualized coherent wavelike disturbances that were convected downstream with the electro-osmotic flow.…”

Sample dispersion in isotachophoresis

“…between the LE and TE if no other plateau mode species are present). Peak mode analytes do not typically significantly contribute to local conductivity (Chen et al 2005). In this latter modality, peak widths are determined in part by the thickness of the dispersed boundary between adjoining species.…”

“…All dispersion models have also neglected the effects of electrohydrodynamic body forces associated with the coupling of conductivity gradients and diffusion at ITP interfaces. Such coupling creates regions of net free charge in the bulk liquid (outside the electric double layer) that can modify electrokinetic flow and lead to instabilities (Lin et al 2004;Chen et al 2005;Sounart & Baygents 2007;Santos & Storey 2008;Persat & Santiago 2009).…”