Viscoplastic corner eddies

When viscously-dominated fluid in a corner is disturbed, eddies can form. Examples of this motion include flow through an abrupt contraction and over a cavity. Five decades ago, Moffatt (1964) calculated the slow viscous flow of Newtonian fluids in sharp corners, detailing his eponymous “Moffatt eddies”. In this study, we examine corner flows of Viscoplastic materials, a class of non-Newtonian fluids which exhibit a yield-stress below which they are solid-like. While a static unyielded plug forms at the tip of the corner, eddies analogous to those found by Moffatt (1964) can also form. We examine these viscoplastic eddies numerically, by computing finite element solutions using the augmented-lagrangian method, and analytically, by employing a visco-plastic boundary-layer formulation and scaling arguments. We measure the depth of the static plug as a function of Bingham number (dimensionless yield-stress), show that the process of a new eddy forming as the Bingham number is decreased is driven by the pressure in the yielded fluid above the static plug, and provide a heuristic argument for the critical Bingham number at which this occurs.