Buoyancy-driven exchange flow of immiscible yield-stress fluids in a vertical closed-ended container

Abstract We have numerically studied the buoyancy-driven flow of two immiscible yield-stress fluids in a vertical closed-ended pipe. Having assumed that the fluids of interest obey the bi-viscous model, we have relied on the finite-volume-method (FVM) in order to capture the late-time shape of the interface assumed to be initially flat. We have been able to recover a variety of well-established fluid-flow phenomena observed experimentally in this particular exchange flow for both Newtonian and yield-stress fluids. We have reached to the conclusion that, for immiscible fluids, the yield stress and/or the viscosity of the fluids can have a stabilizing effect on the interface under certain conditions. Our numerical results also suggest that surface tension and contact angle can play a key role in stabilizing the interface if properly chosen. A threshold curve is obtained for the “no-flow” zone and its variation with the fluids’ rheology and the contact angle is determined for bi-viscous fluids. In cases where fluids’ rheology and/or the wall's wetting property cannot be altered, shaking the vessel in the vertical direction is proposed as an active means for stabilizing the interface provided that its amplitude and frequency are within a certain range.