Predicting yielding in the pressure-driven flow of a Bingham fluid in a serpentine channel

The use of foams in applications such as enhanced oil recovery and varicose vein sclerotherapy has led to renewed interest in their flow as yield stress fluids. In each application one seeks to determine the ability of a foam to displace another fluid from a tortuous channel. We simulate the pressure-driven flow of a Bingham fluid through a serpentine two-dimensional channel to predict the effects of varying the channel geometry on the size and location of the unyielded regions in which the fluid is either stationary or moving as a plug. We discuss the implications for the effective displacement of blood in varicose vein sclerotherapy.