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Rheology of dilute bubble suspensions in unsteady shear flows

Published online by Cambridge University Press:  21 March 2024

K. Ohie Open the ORCID record for K. Ohie [Opens in a new window] ,
Y. Tasaka Open the ORCID record for Y. Tasaka [Opens in a new window]  and
Y. Murai Open the ORCID record for Y. Murai [Opens in a new window]
K. Ohie*
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan
Y. Tasaka
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan
Y. Murai
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan
*
†Email address for correspondence: ohie@eis.hokudai.ac.jp
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Abstract

The viscoelasticity of a dilute bubble suspension is theoretically derived from the constitutive equation originally for a dilute emulsion proposed by Frankel & Acrivos (J. Fluid Mech., vol. 44, issue 1, 1970, pp. 65–78). Non-dimensionalization of the original tensor equation indicates that the viscoelasticity is systematized for a given void fraction by the capillary number $Ca$ and dynamic capillary number $Cd$, representing the bubble deformability and unsteadiness of bubble deformation. Comprehensive evaluation of the viscoelasticity according to the volume fraction, $Ca$ and $Cd$ reveals that whether the viscosity increases or decreases depends on whether $Ca$ or $Cd$ exceeds a common critical value. In addition, it is indicated that the bubble suspension has the most prominent viscoelasticity when the time scale of the shear deformation is the same as the relaxation time of the suspended bubble and when the bubbles keep a spherical shape, that is, $Ca \ll 1$ and $Cd = 1$. The applicability of this theory in flow prediction was examined in a Taylor–Couette system, and experimentally good agreement was confirmed.

JFM classification

Complex Fluids: Suspensions Drops and Bubbles: Bubble dynamics Non-Newtonian Flows: Viscoelasticity

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 983 , 25 March 2024 , A39
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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