• Open Access

Oscillations of small bubbles and medium yielding in elastoviscoplastic fluids

Marco De Corato, Brice Saint-Michel, George Makrigiorgos, Yannis Dimakopoulos, John Tsamopoulos, and Valeria Garbin
Phys. Rev. Fluids 4, 073301 – Published 1 July 2019

Abstract

We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluids and driven by an acoustic pressure field. We model the rheological behavior of the yield-stress fluid using the recently developed elastoviscoplastic constitutive equation that takes into account the elastic and viscoplastic deformations of the material [Saramito, J. Non-Newton. Fluid Mech. 158, 154 (2009)]. Assuming that the bubble remains spherical during the pressure driving, we reduce the problem to a set of ordinary differential equations and an integrodifferential equation, which we solve numerically for the case of two yield-stress fluids, i.e., a soft Carbopol gel and a stiffer kaolin suspension. We find that depending on the amplitude and frequency of the pressure field, the radial oscillations of the bubble produce elastic stresses that may or may not suffice to yield the surrounding material. We evaluate the critical amplitude of the acoustic pressure required to achieve yielding and we find a good agreement between numerical simulations and an analytical formula derived under the assumption of linear deformations. Finally, we examine the bubble oscillation amplitude for a very wide range of applied pressures both below and above the critical value to assess the impact of yielding on the bubble dynamics. This analysis could be used to identify a signature of yielding in experiments where the radial dynamics of a bubble is measured. More generally, these results can be used to rationalize the optimal conditions for pressure-induced bubble release from yield-stress fluids, which is relevant to various biomedical and industrial applications, including the oil industry and food processing.

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  • Received 18 March 2019

DOI:https://doi.org/10.1103/PhysRevFluids.4.073301

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsPolymers & Soft Matter

Authors & Affiliations

Marco De Corato1,*, Brice Saint-Michel1, George Makrigiorgos2,†, Yannis Dimakopoulos2, John Tsamopoulos2,‡, and Valeria Garbin1,§

  • 1Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
  • 2Fluid Mechanics and Rheology Laboratory, Department of Chemical Engineering, University of Patras, Patras 26500, Greece

  • *Present address: Institute for Bioengineering of Catalonia (IBEC), Baldiri i Reixac 10-12, 08028 Barcelona, Spain.
  • Present address: Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, USA.
  • tsamo@chemeng.upatras.gr
  • §v.garbin@imperial.ac.uk

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Vol. 4, Iss. 7 — July 2019

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