Flow onset for a single bubble in a yield-stress fluid

We use computational methods to determine the minimal yield stress required in order to hold static a buoyant bubble in a yield-stress liquid. The static limit is governed by the bubble shape, the dimensionless surface tension (gamma) and the ratio of the yield stress to the buoyancy stress (Y). For a given geometry, bubbles are static for Y > Y-c, which we determine for a range of shapes. Given that surface tension is negligible, long prolate bubbles require larger yield stress to hold static compared with oblate bubbles. Non-zero gamma increases Y-c and for large gamma the yield-capillary number (Y/gamma) determines the static boundary. In this limit, although bubble shape is important, bubble orientation is not. Two-dimensional planar and axisymmetric bubbles are studied.