Transient deformation of freely‐suspended liquid droplets in electrostatic fields

Haywood, R. J.; Renksizbulut, Metin; Raithby, G. D.

doi:10.1002/aic.690370904

Cited by 30 publications

(18 citation statements)

References 32 publications

(31 reference statements)

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“…The latter theory predicted a monotonic drop deformation leading to the steady drop shape predicted by Taylor (1966). Yet, both experiments (Lanauze et al 2015) and numerical simulations (Haywood et al 1991;Supeene et al 2008) show non-monotonic deformations in cases leading to steady …”

Section: Introductionmentioning

confidence: 90%

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Das¹,

Saintillan²

2016

J. Fluid Mech.

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The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the MelcherTaylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of Taylor (1966), there have been numerous computational and theoretical studies to predict the deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel small-deformation theory accurate to second order in electric capillary number O(Ca 2 E ) for the complete Melcher-Taylor model that includes transient charge relaxation, charge convection by the flow, as well as transient shape deformation. The main result of the paper is the derivation of coupled evolution equations for the induced electric multipoles and for the shape functions describing the deformations on the basis of spherical harmonics. Our results, which are consistent with previous models in the appropriate limits, show excellent agreement with fully nonlinear numerical simulations based on an axisymmetric boundary-element formulation and with existing experimental data in the small-deformation regime.

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Section: Introductionmentioning

confidence: 90%

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Das¹,

Saintillan²

2016

J. Fluid Mech.

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“…Haywood et al (25) studied without the creeping flow approximation the transient deformation of electrified drops for both liquid-liquid and liquid-gas systems. Although these investigators were not able to follow the drops to breakup, they showed that good agreement exists between their computations and previous experimental and theoretical results.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Drop Formation in an Electric Field

Notz¹,

Kim²,

Basaran³

1999

Journal of Colloid and Interface Science

119

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“…It is concluded that the drops are elongated along the electric field, and the deformation depends on the ratio of drop-to-media permittivity, and that the ratio has a critical value. The theoretical critical value is [7] d m c ( ) 20.8,…”

Section: Cases Results and Discussionmentioning

confidence: 99%

“…As an important and fundamental problem in EHD studies, behavior of freely-suspended liquid drops subjected to electrostatic fields has been studied extensively. A lot of theoretical, numerical and experimental results have been accumulated [3][4][5][6][7] .…”

Section: Electrohydrodynamics Lattice Boltzmann Method Drop Deformamentioning

confidence: 99%

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Application of the lattice Boltzmann method to electrohydrodynamics: Deformation and instability of liquid drops in electrostatic fields

Huang

Liu

2007

Chin. Sci. Bull.

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It is attractive and meaningful to apply the lattice Boltzmann method (LBM) to electrohydrodynamic (EHD) problems. As an important and fundamental problem in EHD, the behavior of freely-suspended liquid drops subjected to electrostatic fields was simulated with a 2-D LBM by means of the permittivity-density relation proposed by the authors and Peng's multiphase LBM which can obtain high liquid-to-vapor density ratio and low liquid-phase compressibility. The phenomena and laws of deformation, especially the instable behavior of the liquid drops were well simulated. And two important critical parameters, i.e. the critical permittivity ratio and the critical electric-field strength were obtained. These results agree with the corresponding theories and experiments. The simulations show the particular advantages and potential of the LBM in studying multiphase electrohydrodynamic problems.

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Transient deformation of freely‐suspended liquid droplets in electrostatic fields

Cited by 30 publications

References 32 publications

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Dynamics of Drop Formation in an Electric Field

Application of the lattice Boltzmann method to electrohydrodynamics: Deformation and instability of liquid drops in electrostatic fields

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