A note on Taylor’s electrohydrodynamic theory

Ajayi, Olasupo

doi:10.1098/rspa.1978.0214

Cited by 128 publications

(45 citation statements)

References 7 publications

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“…We summarize here the results of the theory and outline the solution procedure at first and second order. We also compare and contrast our predictions with the existing theories of Taylor (1966), Ajayi (1978), Esmaeeli & Sharifi (2011) and Lanauze et al (2013).…”

Section: Summary Of the Small-deformation Theorymentioning

confidence: 89%

“…We solve the governing equations for axisymmetric shapes in the limit of small deformations (Taylor 1966;Ajayi 1978;Rallison 1984), which occurs when surface tension is strong enough to overcome deformations due to electric stresses. This corresponds to the limit of Ca E → 0, and allows us to use an asymptotic approach in which we expand the drop deformation about the spherical shape and all the field variables in a small shape parameter δ whose relation with Ca E we explain later.…”

Section: Problem Solution By Domain Perturbationmentioning

confidence: 99%

“…The outward unit normal, tangent vector and curvature of the interface are also obtained as (Ajayi 1978)…”

Section: Shape Parametrization and Expansionmentioning

confidence: 99%

“…As a result, agreement with experiments was limited to very small deformations, and a number of more detailed theories have been proposed over the years to improve upon this. First, Ajayi (1978) extended Taylor's theory by retaining terms to second order in capillary number, but also neglected transients and charge convection. His results, quite surprisingly, showed worse agreement with experiments than the simpler model of Taylor in the case of oblate drops, which is a consequence of the latter approximation.…”

Section: Introductionmentioning

confidence: 99%

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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: Summary Of the Small-deformation Theorymentioning

confidence: 89%

Section: Problem Solution By Domain Perturbationmentioning

confidence: 99%

“…The outward unit normal, tangent vector and curvature of the interface are also obtained as (Ajayi 1978)…”

Section: Shape Parametrization and Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Das¹,

Saintillan²

2016

J. Fluid Mech.

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“…A validation of the EHD model is also performed (see the Supplemental Material [34]). The deformation of a leaky dielectric droplet in a leaky dielectric medium is considered following the extension [35] of Taylor's electrohydrodynamic theory [24] verified by experimental investigations [36]. The theory shows that the deformation parameter D can be expressed as a function of the electric capillary number (C E ¼ ε c R 0 E 2 =σ), ratios of viscosities, conductivities, and electric permittivities between the droplet and ambient media.…”

Section: B Model Validationmentioning

confidence: 99%

Deformation and Interaction of Droplet Pairs in a Microchannel Under ac Electric Fields

Chen

Song

et al. 2015

Phys. Rev. Applied

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The deformation and interaction of a droplet pair in an electric field determine the success of droplet coalescence. Electric intensity and initial droplet separation are crucial parameters in this process. In this work, a combined theoretical and numerical analysis is performed to study the electrohydrodynamics of confined droplet pairs in a rectangular microchannel under ac electric fields. We develop a theoretical model to predict the relationship between critical electric intensity and droplet separation. A geometrical model relating the initial droplet separation to the cone angle is also established to determine the critical separation for partial coalescence. These models are validated by comparisons with existing experimental observations. According to the initial separation and electric intensity, five regimes of droplet interactions are classified by direct numerical simulations, namely noncoalescence, coalescence, partial coalescence, ejection after coalescence, and ejection with partial coalescence. According to their controlling mechanisms, the five regimes are distinguished by three well-defined boundaries. The detailed dynamics of the partial coalescence phenomenon is resolved when the droplet separation exceeds the critical value. A dynamic liquid bridge between the droplets is sustained by the competition between surface tension and electric stress. The dynamics of ejected microjets at the exterior ends are also addressed to show their responses to the oscillating electric field. The full understanding of the droplet dynamics under electric fields can be used to predict the droplet fusion behaviors and thus to facilitate the design of droplet-based microfluidic devices.

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Coalescence of Drops

Sinaiski¹,

Lapiga²

2007

Separation of Multiphase, Multicomponent Systems

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A note on Taylor’s electrohydrodynamic theory

Cited by 128 publications

References 7 publications

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Deformation and Interaction of Droplet Pairs in a Microchannel Under ac Electric Fields

Coalescence of Drops

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