The implications of a fluid yield stress

Abstract

While we now have a relatively good understanding of low-Reynolds-number hydrodynamics, and elegant techniques to dissect it, one cannot truly say the same for yield-stress fluids. For these materials, the nonlinearity associated with the yield stress complicates analysis and prevents the use of many of the techniques used for slow viscous flow. Simultaneously, the presence of a yield stress introduces a range of new features into the problem beyond those of traditional Stokes flow. Accordingly, in this essay, we discuss the impact of a yield stress in the relatively simple setting of two-dimensional, steady, inertialess flow. The main goals are to establish intuition for the dramatically different features that can be introduced to the flow by the yield stress, and to outline the various tools available to the modeller to construct and interpret these flows.