A hydrodynamic bifurcation in electroosmotically-driven periodic flows

TL;DR

This paper discovers a new inertial instability in electro-osmotically driven flows, revealing a bifurcation to a flow with a strong mean component at low Reynolds numbers, with implications for microfluidic device design.

Contribution

It introduces a novel inertial bifurcation in electro-osmotic flows with spatially periodic wall velocities, expanding understanding of flow stability in microfluidic systems.

Findings

Instability occurs at Reynolds numbers around 20-30.

Flow bifurcation leads to a flow with a strong mean component.

Flow loses symmetry through a supercritical bifurcation.

Abstract

In this paper we report a novel inertial instability that occurs in electro-osmotically driven channel flows. We assume that the charge motion under the influence of an externally applied electric field is confined to a small vicinity of the channel walls that, effectively, drives a bulk flow through a prescribed slip velocity at the boundaries. Here, we study spatially-periodic wall velocity modulations in a two-dimensional straight channel numerically. At low slip velocities, the bulk flow consists of a set of vortices along each wall that are left-right symmetric, while at sufficiently high slip velocities, this flow loses its stability though a supercritical bifurcation. Surprisingly, the new flow state that bifurcates from a left-right symmetric base flow has a rather strong mean component along the channel, which is similar to pressure-driven velocity profiles. The instability sets in at rather small Reynolds numbers of about 20-30, and we discuss its potential applications in microfluidic devices.