Deformation and stability of drops and bubbles in an electric field

Cheng, Kun; Chaddock, J. B.

doi:10.1016/0375-9601(84)90491-2

Cited by 49 publications

(19 citation statements)

References 4 publications

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“…Grigor'ev et al (1999) concluded that as the gas permittivity is normally much smaller than that of the liquid, only the second mechanism identified by Sherwood (1988) could possibly be applicable to bubbles, with the conditions being met by assuming a good conductivity inside the bubble (and hence a constant interior potential) as the result of a large mobility of charge being present on the interface between the two phases. (An earlier study by Cheng & Chaddock (1984) using a free energy argument was unable to find critical conditions beyond which bubbles would become unstable. They attributed this result to the fact that the prolate spheroid shape they assumed for the bubble was too approximate, but still expected the bubble to disintegrate if sufficient elongation was incurred due to the application of the electric field.)…”

Section: Introductionmentioning

confidence: 86%

Critical strength of an electric field whereby a bubble can adopt a steady shape

Shaw

Spelt

2009

Proc. R. Soc. A.

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The electrically induced steady-state solutions of a gas bubble in a dielectric liquid under the action of a steady electric field are considered using the leaky dielectric model. Representing the shape deformation by a sum of spherical harmonics, it is shown that for a given parameter set there exists a critical value of the ratio of the electric to surfaces stresses beyond which no steady states exist, thus implying bubble instability and possible fragmentation. Previous studies imply that bubble instability can only be achieved if either the dielectric constant or the conductivity of the gaseous contents of the bubble is large. We show that on accounting for compressibility of the bubble, no such restriction applies for bubble instability. Below these critical values, multiple steady states are found. It is shown that a more approximate model, which assumes that the bubble is a prolate ellipsoid, can be used to represent the results for weak electric fields, but cannot be used for the prediction of the critical value of the strength of the electric field beyond which no steady-state exists.

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Section: Introductionmentioning

confidence: 86%

Critical strength of an electric field whereby a bubble can adopt a steady shape

Shaw

Spelt

2009

Proc. R. Soc. A.

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“…A number of researchers have explored the case of a suspended drop in a uniform electric field, including Taylor [10], Landau and Lifshitz [46], Cheng and Chaddock [47], Sozou [48], Baygents and Rivette [17,49], and Tomar et al [18]. For this case, the geometry and electric field alignment are identical to that for the dielectric drop in the preceding section, as shown in Fig.…”

Section: Deforming Spheroidal Dropmentioning

confidence: 93%

A ghost fluid, level set methodology for simulating multiphase electrohydrodynamic flows with application to liquid fuel injection

Daily

2010

Journal of Computational Physics

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“…In the absence of electric field and neglecting the line tension, the solutions to (2.1), (2.2) and (2.6) can be obtained by solving an ordinary differential equation, see [30,39]. In the presence of electric field, the non-local Maxwell stress (2.5) makes the analytical and numerical solutions to (2.1), (2.2) and (2.6) or (2.7) challenging problems.…”

Section: Problem Statementmentioning

confidence: 99%

“…The energy-based approach in EHD has been employed by Cheng & Chaddock [39] to analyse the deformation and stability of spheroidal homogeneous bubbles in an electric field where the effect of the solid substrate is neglected. In the subsequent work [30], the authors obtained the shape profile of a bubble elongating in the electric field and determined the departure size at different electric field strength.…”

Section: Introductionmentioning

confidence: 99%

“…In the subsequent work [30], the authors obtained the shape profile of a bubble elongating in the electric field and determined the departure size at different electric field strength. Cheng & Chaddock's [30,39] approach was based on the assumption of ellipsoidal shapes and the closed-form solutions to the electrostatic problem where the concept of (Maxwell) stress was not needed at all, and hence cannot be directly used for numerical simulations. Our work extends the energy-based approach to heterogeneous bubbles of general geometries and under general boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Equilibrium shapes of a heterogeneous bubble in an electric field: a variational formulation and numerical verifications

Wang

Liu

2017

Proc. R. Soc. A.

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The equilibrium shape of a bubble/droplet in an electric field is important for electrowetting over dielectrics (EWOD), electrohydrodynamic (EHD) enhancement for heat transfer and electrodeformation of a single biological cell among others. In this work, we develop a general variational formulation in account of electro-mechanical couplings. In the context of EHD, we identify the free energy functional and the associated energy minimization problem that determines the equilibrium shape of a bubble in an electric field. Based on this variational formulation, we implement a fixed mesh level-set gradient method for computing the equilibrium shapes. This numerical scheme is efficient and validated by comparing with analytical solutions at the absence of electric field and experimental results at the presence of electric field. We also present simulation results for zero gravity which will be useful for space applications. The variational formulation and numerical scheme are anticipated to have broad applications in areas of EWOD, EHD and electro-deformation in biomechanics.

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Deformation and stability of drops and bubbles in an electric field

Cited by 49 publications

References 4 publications

Critical strength of an electric field whereby a bubble can adopt a steady shape

Critical strength of an electric field whereby a bubble can adopt a steady shape

A ghost fluid, level set methodology for simulating multiphase electrohydrodynamic flows with application to liquid fuel injection

Equilibrium shapes of a heterogeneous bubble in an electric field: a variational formulation and numerical verifications

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