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

Published online by Cambridge University Press:  23 December 2021

Ali Pourzahedi ,
Emad Chaparian Open the ORCID record for Emad Chaparian [Opens in a new window] ,
Ali Roustaei  and
Ian A. Frigaard Open the ORCID record for Ian A. Frigaard [Opens in a new window]
Ali Pourzahedi
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada
Emad Chaparian*
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
Ali Roustaei*
Affiliation:
School of Engineering Science, College of Engineering, University of Tehran, Tehran 14155-6619, Iran
Ian A. Frigaard
Affiliation:
Department of Mechanical Engineering, University of British Columbia, 2054-6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
*
†Email addresses for correspondence: emad@math.ubc.ca; aroustaei@ut.ac.ir
†Email addresses for correspondence: emad@math.ubc.ca; aroustaei@ut.ac.ir
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Abstract

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.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Non-Newtonian Flows: Plastic materials Drops and Bubbles: Bubble dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A21
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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