Semi-analytic velocity profile for a Bingham fluid in a curved channel

TL;DR

This paper derives a semi-analytic velocity profile for a Bingham fluid in a curved channel, enabling predictions of flow initiation and flux based on channel curvature and yield stress.

Contribution

It introduces a semi-analytic expression for the velocity profile of Bingham fluids in curved channels, accounting for yield surfaces and curvature effects.

Findings

Velocity profile depends on channel curvature and yield stress.

Predicts pressure gradient needed to initiate flow.

Analyzes flux and plug region width variations with curvature.

Abstract

We derive an expression for the velocity profile of a pressure-driven yield-stress Bingham fluid flowing around a 2D concentric annulus. The formula requires the numerical solution of a nonlinear equation for the positions of the yield surfaces. The results allow the prediction of the effects of channel curvature on the pressure gradient required to initiate flow for given yield stress, and for the width of the plug region and the flux through the channel at different curvatures.