Conditions for static bubbles in viscoplastic fluids

We consider the slow motion of a gas bubble in a cylindrical column filled with a viscoplastic fluid, modeled here as a Herschel-Bulkley fluid. Because of the yield stress of the fluid, it is possible that a bubble will remain trapped in the fluid indefinitely. We adapt Prager's two variational principles to our problem. From these variational principles we develop two general stopping conditions, i.e., for a given bubble we can calculate a critical Bingham number above which the bubble will not move. The first condition is derived by bounding the velocity field and the second condition by bounding the stress field. We illustrate these conditions by considering specific bubble shapes, e.g., axisymmetric bubbles. We also develop a condition for bubble motion. (C) American Institute of Physics.