Reduced and increased flow resistance in shear-dominated flows of Oldroyd-B fluids

Abstract

We present a comprehensive analytical and numerical study of shear-dominated flows of Oldroyd-B fluids. Starting from transient ideal Couette flow, we show that less work is required to increase the shear rate than to decrease it. Generalizing this observation to non-homogeneous steady flows, we show that reduced flow resistance is present around streamlines with increasing shear rate and increased flow resistance is present around streamlines with decreasing shear rate. We demonstrate this effect in smoothly converging or diverging Couette and Poiseuille flows. Finally, we show that the reduced flow resistance observed in the flow past a cylinder in a straight channel is caused by the contraction-expansion-like flow that takes place at the sides of the cylinder. Our findings are validated by a wide parametric analysis regarding the geometrical characteristics of the flow domains and the material parameters of the Oldroyd-B model. • Shear-thinning and shear-thickening effects can be predicted by the Oldroyd-B model. • Reduced flow resistance is present along streamlines with increasing shear rate. • Increased flow resistance is present along streamlines with decreasing shear rate. • The variations in pressure drop and drag force in viscoelastic flows are explained.