Bubble entrapment condition in Bingham materials

Abstract

We investigate the entrapment condition of initially spherical and ellipsoidal Newtonian bubbles in viscoplastic materials using direct numerical simulations. For a spherical bubble, the entrapment condition depends on the balance between the buoyancy force and the force exerted by the yield stress of the viscoplastic material. For non-spherical bubbles, surface tension may yield the surrounding material to minimize the surface energy of the bubble. The yielding of the surrounding material by surface tension force facilitates the rising motion of bubbles. Although surface tension may yield the surrounding material and start the rising motion, the bubble may get entrapped later if the stress exerted by buoyancy force is less than the yield stress of the material. We evaluate the yield-stress parameter for different bubble shapes over a range of non-dimensional parameters to predict the critical yield-stress parameter for the entrapment of a bubble. • The critical yield stress parameter decreases at very high viscosity ratios. • The yield stress parameter is a constant at low viscosity ratios. • Yield stress resistive force depends on the maximum cross-sectional area normal to the buoyancy. • The critical yield stress parameter is independent of the initial shape of the bubble. • Non-spherical bubbles may be momentarily mobile due to surface tension effects.