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

Pourzahedi, Ali and Chaparian, Emad and Roustaei, Ali and Frigaard, Ian A. (2022) Flow onset for a single bubble in a yield-stress fluid. Journal of Fluid Mechanics, 933. A21. ISSN 0022-1120 (https://doi.org/10.1017/jfm.2021.1055)

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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 and the ratio of the yield stress to the buoyancy stress . For a given geometry, bubbles are static for 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 increases and for large the yield-capillary number determines the static boundary. In this limit, although bubble shape is important, bubble orientation is not. Two-dimensional planar and axisymmetric bubbles are studied.