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Clouds of bubbles in a viscoplastic fluid

Published online by Cambridge University Press:  21 September 2021

Emad Chaparian Open the ORCID record for Emad Chaparian [Opens in a new window]  and
Ian A. Frigaard Open the ORCID record for Ian A. Frigaard [Opens in a new window]
Emad Chaparian*
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada
Ian A. Frigaard
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, BC, V6T 1Z4, Canada
*
†Email address for correspondence: emad@math.ubc.ca
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Abstract

Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number $Y$, the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction $\phi$ that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of $0\le \phi \le 0.31$, together with lower and upper estimates.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Multiphase flow Non-Newtonian Flows: Plastic materials
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , R3
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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