Viscoplastic fluid displacement flows in horizontal channels: Numerical simulations

We study numerically isoviscous displacement flows of a Bingham fluid by a Newtonian fluid in a horizontal plane channel. We consider a heavy-light displacement flow with a laminar imposed flow. We analyze the flow from various perspectives, using the three dimensionless parameters that largely describe the flow: the Bingham number (Bn), the densimetric Froude number (Fr) and the Reynolds number (Re). In particular, we are able to categorize three classes for the main flow regimes, viz., center-type and slump-type, no-back-flow and temporary-back-flow, and stable and unstable displacements, for which we also quantify their transition boundaries versus the aforementioned dimensionless numbers. We show that the appearance of unstable flows can eventually lead to a number of different flow patterns, such as sinusoidal shaped wave and periodic-detachment forms. In addition, we study in depth an interesting feature exclusively associated to viscoplastic fluid displacements, i.e., the formation of static residual layers on the upper/lower walls of the channel. We also study the evolution of the key displacement flow features, i.e., the trailing and leading fronts, and classify certain secondary flow features related to the leading front, such as plug-like, inertial tip, semi-detached and fully-detached fronts. Finally, we quantify the velocity of the leading front at long times.