Electroosmotic flow in Hele-Shaw configurations with non-uniform surface charge

TL;DR

This paper provides an analytical and numerical study of electroosmotic flow in Hele-Shaw cells with non-uniform surface charge, demonstrating how to generate complex flow patterns for potential on-chip applications.

Contribution

The study derives analytical solutions for electroosmotic flow with non-uniform surface charge and shows how to create complex flow fields by superposing simple charge distributions.

Findings

Flow in the outer region forms a dipole pattern.

Superposition enables complex flow control.

Analytical results validated by numerical simulations.

Abstract

We present an analytical study, validated by numerical simulations, of electroosmotic flow in a Hele-Shaw cell with non-uniform surface charge patterning. Applying the lubrication approximation and assuming thin electric double layer, we obtain a pair of uncoupled Poisson equations which relate the pressure and the stream function, respectively, to gradients in the zeta potential distribution parallel and perpendicular to the applied electric field. We solve the governing equations for the fundamental case of a disk with uniform zeta potential and show that the flow-field in the outer region takes the form of a pure dipole. We illustrate the ability to generate complex flow-fields around smooth convex regions by superposition of such disks with uniform zeta potential and a uniform pressure driven flow. This method may be useful for future on-chip devices, allowing flow control without the need for mechanical components.