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Deformation of an encapsulated bubble in steady and oscillatory electric fields

Published online by Cambridge University Press:  06 April 2018

Yunqiao Liu Open the ORCID record for Yunqiao Liu [Opens in a new window] ,
Dongdong He ,
Xiaobo Gong Open the ORCID record for Xiaobo Gong [Opens in a new window]  and
Huaxiong Huang
Yunqiao Liu
Affiliation:
Key Laboratory of Hydrodynamics (Ministry of Education), Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China
Dongdong He
Affiliation:
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong 518172, China
Xiaobo Gong*
Affiliation:
Key Laboratory of Hydrodynamics (Ministry of Education), Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, China
Huaxiong Huang
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada The Fields Institute for Research in Mathematical Sciences, Toronto, Ontario M5T 3J1, Canada
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we investigate the dynamics of an encapsulated bubble in steady and oscillatory electric fields theoretically, based on a leaky dielectric model. On the bubble surface, an applied electric field generates a Maxwell stress, in addition to hydrodynamic traction and membrane mechanical stress. Our model also includes the effect of interfacial charge due to the jump of the current and the stretching of the interface. We focus on the axisymmetric deformation of the encapsulated bubble induced by the electric field and carry out our analysis using Legendre polynomials. In our first example, the encapsulating membrane is modelled as a nearly incompressible interface with bending rigidity. Under a steady uniform electric field, the encapsulated bubble resumes an elongated equilibrium shape, dominated by the second- and fourth-order shape modes. The deformed shape agrees well with experimental observations reported in the literature. Our model reveals that the interfacial charge distribution is determined by the magnitude of the shape modes, as well as the permittivity and conductivity of the external and internal fluids. The effects of the electric field on the natural frequency of the oscillating bubble are also shown. For our second example, we considered a bubble encapsulated with a hyperelastic membrane with bending rigidity, subject to an oscillatory electric field. We show that the bubble can modulate its oscillating frequency and reach a stable shape oscillation at an appreciable amplitude.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Electrohydrodynamic effects Biological Fluid Dynamics: Membranes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 567 - 596
Copyright
© 2018 Cambridge University Press 

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