Effects of non-uniform rheology on the motion of bubbles in a yield-stress fluid

Experimentally, when bubbles rise through yield-stress fluids they create a pathway that is preferentially followed by subsequent bubbles. The formation of such paths is not fully understood rheologically. Here, we instead study the effect of pathways, modelled as a pathway within which the yield stress is destroyed. We study how bubbles rise along such 'damaged' channels and how they may be trapped by a combination of capillary effects and the yield stress of the surrounding fluid. We then study the effects of these channels on distant bubbles. We show that the damaged channels attract bubbles that are mobile but lie at a distance well beyond the yielded envelope of the bubble. Angled channels also attract bubbles, that may either move along the channel or migrate outside. Experiments illustrate these behaviours, which are quantified in a series of two-dimensional computations. The study is motivated by interest in bubble release mechanisms in mined tailing ponds.