Electrohydrodynamic instability of ion-concentration shock wave in electrophoresis

Abstract

Capillary electrophoresis techniques often involve ion-concentration shock waves in an electrolyte solution, propagating under the effect of an external electric field. These shock waves are characterized by self-sharpening gradients in ion concentrations and electrical conductivity that are collinear with the electric field. The coupling of electric field and fluid motion at the shock interface sometimes leads to an undesirable electrohydrodynamic (EHD) instability. Using linear stability analysis, we describe the motion of small-amplitude disturbances of an electrophoretic shock wave. Our analysis shows that the EHD instability results due to the competition between destabilizing electroviscous flow and stabilizing electromigration of the shock wave. The ratio of timescales corresponding to electroviscous flow and electromigration yields a threshold criterion for the onset of instability. We present a validation of this threshold criterion with published experimental data and also describe the physical mechanism underlying the EHD instability of the electrophoretic shock wave.

Isotachophoresis: Theory and Microfluidic Applications

“…182,217−219 The study also suggested that the value of ρ e E based on the above scaling empirically provides an upper threshold value of the electric field, which can be used to predict the onset of instability. Later, Gaur and Bahga 220 performed a detailed EHD instability analysis of a canonical single-interface ITP in an unbounded domain. They performed a linear stability analysis and showed that electroviscous flow destabilized ITP, while the electromigration of the shock wave had a stabilizing effect.…”

“…The ITP shock wave instability was found to set at low values of τ ev /τ em when the electroviscous flow dominated electromigration. Gaur and Bahga 220 hypothesized that the exact value of τ ev /τ em below which ITP instability sets in depends on the channel geometry. From eq 124, high values for the conductivity ratio, the channel depth, and the electric field promote instability, while high values for the fluid viscosity and the LE ion mobility have a stabilizing effect on ITP.…”

Recent progress in analytical capillary isotachophoresis

“…It was shown previously that working with ITP at high‐field strengths can show decreased accuracy because of the occurrence of electrohydrodynamic instabilities . Gaur and Bahga investigated this problem in detail and presented a mathematical description of electrohydrodynamic instability of a concentration shock wave that arises in nonlinear electrophoresis processes. On the example of a migrating ITP boundary (LE: 100 mM NaOH, 200 mM HEPES; TE: 72.48 mM 2,2‐bis(hydroxymethyl)‐2,2′,2″‐nitrilotriethanol (Bistris), 172.5 mM HEPES) they have shown that the instability results from the competition between destabilizing electroviscous flow and restoring electromigration.…”

Electrokinetic instability due to streamwise conductivity gradients in microchip electrophoresis

“…Besides the interfacially driven EOF, the gradients in the local electric field accompanied by conductivity gradients can lead to instabilities in the flow (Hoburg & Melcher 1977; Baygents & Baldessari 1998; El Moctar, Aubry & Batton 2003; Chen et al. 2005; Posner & Santiago 2006; Gaur & Bahga 2017; Sharan, Gupta & Bahga 2017). The electric field gradients lead to accumulation of free charge within the bulk fluid.…”