Multi-layer channel flows with yield stress fluids

We present results of a computational study of visco-plastically lubricated plane channel multi-layer flows, in which the yield stress fluid layers are unyielded at the interface. We demonstrate that symmetric 3-layer flows may be established for wide ranges of viscosity ratio (m), Bingham number (B) and interface position (yi), for Reynolds numbers Re ≤ 100. Here an inner Newtonian layer is sandwiched between 2 layers of Bingham fluid. Results are presented illustrating the variation of development length with the main dimensionless parameters and for different inlet sizes. We also show that these flows may be initiated by injecting either fluid into a steady flow of the other fluid. The flows are established quicker when the core fluid is injected into a channel already full of the outer fluid. In situations where the inner fluid flow rate is dominant we observed inertial symmetry breaking in the symmetric start-up flows as Re was increased. Asymmetry is also observed in studying temporal nonlinear stability of these flows, which appear stable up to moderate Re and significant amplitudes. In general the flows destabilize at lower Re and perturbation amplitudes than do the analogous core-annular pipe flows, but 1-1 comparison is hard. When the flow is stable the decay characteristics are very similar to those of the pipe flows. In the final part of the paper we explore more exotic flow effects. We show how flow control could be used to position layers asymmetrically within the flow, and how this effect might be varied transiently. We demonstrate that more complex layered flows can be stably achieved, e.g. a 7-layered flow is established. We also show how a varying inlet position can be used to “write” in the yield stress fluid: complex structures that are advected with the flow and encapsulated within the unyielded fluid.