Axisymmetric deformation and stability of a viscous drop in a steady electric field

Lac, Étienne; Homsy, G. M.

doi:10.1017/s0022112007007999

Cited by 189 publications

(253 citation statements)

References 27 publications

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“…The method shares similarities with that of Lanauze et al (2015) but makes use of a finite-volume algorithm for the solution of the charge convection equation. We first solve Laplace's equation for the electric potential using a single-layer potential (Sherwood 1988;Baygents et al 1998;Lac & Homsy 2007;Lanauze et al 2015), yielding the integral equation…”

Section: Appendix a Axisymmetric Boundary Element Methodsmentioning

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: Appendix a Axisymmetric Boundary Element Methodsmentioning

confidence: 99%

“…The first term on the right hand side captures the tangential electric force arising from the action of the tangential field on the interfacial charge. The second term captures normal electric stresses and can be interpreted as a jump in an electric pressure p E (Lac & Homsy 2007).…”

Section: Problem Formulationmentioning

confidence: 99%

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Das¹,

Saintillan²

2016

J. Fluid Mech.

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“…The integral equations for a finite drop in an axial electric field can be found in Lac & Homsy (2007), for example.…”

Section: Appendix B Boundary Integral Equations For the Electric Fiementioning

confidence: 99%

Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

Wang

Papageorgiou

2011

J. Fluid Mech.

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The nonlinear dynamics of a viscous filament surrounded by a second viscous fluid arranged in a core-annular configuration when a radial electric field acts in the annular region, are studied analytically and computationally using boundary element methods. The flow is characterized by the viscosity ratio, an electric Weber number measuring the strength of the electric field, a geometrical parameter measuring the thickness of the undisturbed annular region, as well as a computational parameter that fixes the wavenumber of the undulations. Axisymmetric solutions are computed by direct numerical simulations in the Stokes limit for general values of the parameters when the two fluids have equal viscosities, and an asymptotic theory is carried out to produce a novel evolution equation for thin film dynamics valid when the undisturbed annular thickness is small and the viscosity ratio is of order one. It is established (in agreement with previous computations in the absence of electric fields) that a sufficiently thick annulus enables thread breakup while a sufficiently thin one (approximately one fifth of the undisturbed thread radius for the case of equal viscosities, for instance) suppresses pinching and drives the interface to approach the tube wall asymptotically without actually touching it. The present simulations show that the electric field affects the dynamics drastically in several ways. First, it promotes interfacial wall touchdown in finite time and a comparison between direct simulations and the asymptotic solutions are in fair agreement. Second, the electric field acts to suppress pinching in the sense that solutions that lead to jet breakup due to a thick enough viscous annulus are driven to wall touchdown. When pinching takes place we find that the ultimate pinching solutions are self-similar and recover the non-electrified ones to leading order for the range of parameters studied.

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“…Good agreements are obtained with theoretical predictions for small C E . Disparities at large C E are also observed because the theory is only valid for small deformation [37,38].…”

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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Axisymmetric deformation and stability of a viscous drop in a steady electric field

Cited by 189 publications

References 27 publications

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

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

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