Debye-Hueckel solution for steady electro-osmotic flow of a micropolar fluid in a cylindrical microcapillary

TL;DR

This paper derives analytical solutions for steady electro-osmotic flow of a micropolar fluid in a cylindrical microcapillary, highlighting how micropolarity affects flow characteristics under the Debye-Hueckel approximation.

Contribution

It provides the first analytical expressions for flow, stress, and microrotation in micropolar fluids within microcapillaries under electro-osmotic conditions.

Findings

Flow speed increases with microcapillary radius.

Stress tensor is localized near the wall.

Couple stress tensor is uniform across the cross-section.

Abstract

Analytic expressions for the speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting steady, symmetric and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-Hueckel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. As the aciculate particles in a micropolar fluid can rotate without translation, micropolarity influences fluid speed, fluid flux, and one of the two non-zero components of the stress tensor. The axial speed in a micropolar fluid intensifies as the radius increases. The stress tensor is confined to the region near the wall of the microcapillary but the couple stress tensor is uniform across the cross-section.