An analytic velocity profile for pressure-driven flow of a Bingham fluid in a curved channel

We derive an expression for the velocity profile of a pressure-driven yield-stress fluid flowing around a two-dimensional concentric annulus. This result allows 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. We use it to validate numerical simulations of the flow from a straight channel into a curved channel which show how the fluid first yields everywhere before reaching the predicted velocity profile.