Abstract

Many natural flows and industrial processes involve materials that can behave simultaneously as solids and fluids, producing strong localization and sharp transitions in flow structure. Yield-stress fluids provide a useful framework for exploring these effects. In this talk, I examine how yield stress reshapes mixing and transport by studying a canonical system: a Bingham fluid stirred by a cylinder moving along a circular path in an initially stratified domain. In the Newtonian limit, mixing proceeds through stretching and folding of interfaces, diffusion across streamlines, and the advective transport supplied by shed vortices. Introducing a finite yield stress reorganizes the flow in fundamental ways. Vortex shedding becomes confined within a finite radius or is suppressed entirely, giving rise to three distinct regimes determined by the fate of these vortices. The resulting interplay between yielded and unyielded regions localizes motion, restricts advective pathways, and produces persistent unmixed structures. These findings provide a mechanistic picture of why yield-stress fluids mix poorly, clarify how small rheological variations alter flow topology, and offer insight into transport in systems where localized deformation, layering, or plug-like behaviour plays a central role.