The yield limit for a single bubble trapped in a damaged viscoplastic fluid

Bubbles rising in yield-stress fluids leave behind pathways in the memory of the fluid. These in turn influence the trajectories of subsequent bubbles released. Qualitatively, the effect manifests as a damaged pathway, modelled here as a low-viscosity Newtonian fluid within the surrounding viscoplastic fluid. Secondary bubbles are attracted towards these pathways, as is observed computationally and experimentally. Here we explore the effect of a damaged path on the release of a trapped bubble, captured by the critical yield number upper Y Subscript c Y c Yc . We show that proximity to a damaged path increases upper Y Subscript c Y c Yc , but eventually beyond a critical distance there is no influence on upper Y Subscript c Y c Yc . We explore the effects of shape and surface tension on the aforementioned proximity results.