On a phase-ﬁeld model for electrowetting

Eck, Christof; Fontelos, Marco A.; Grün, Günther; Klingbeil, F.; Vantzos, Orestis

doi:10.4171/ifb/211

Cited by 43 publications

(53 citation statements)

References 34 publications

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“…Additional complexities in wetting include the presence of an electric field (electrowetting, e.g. Eck et al (2009)). There are numerous other applications where phase-field models provide a powerful modelling tool.…”

Section: (A) Physical Motivationmentioning

confidence: 99%

Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains

et al. 2012

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We derive a new, effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by fourth-order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly heterogeneous domains. To the best knowledge of the authors, this seems to be the first attempt of upscaling the Cahn-Hilliard equation in such domains. The new homogenized equation should have a broad range of applicability owing to the well-known versatility of phase-field models. The additionally introduced feature of systematically and reliably accounting for confined geometries by homogenization allows for new modelling and numerical perspectives in both science and engineering. Our results are applied to wetting dynamics in porous media and to a single channel with strongly heterogeneous walls.

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Section: (A) Physical Motivationmentioning

confidence: 99%

Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains

et al. 2012

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“…The movement of a drop on a surface has been dynamically modeled with the help of a phase-field model. 22 Also, a finite element method for EWOD devices between two parallel plates has been proposed, 23,24 and a shape-inverse approach calculates the curvature. 25 All of these models require CFD tools.…”

Section: ' Measurement Resultsmentioning

confidence: 99%

Wettability Increase by “Corona” Ionization

Virgilio

Bermejo²,

Castañer³

2011

Langmuir

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The wettability of a surface has been shown, for many years now, to increase by the application of a voltage difference between the liquid droplet and the substrate, 1À3 which, most often, is a conductor covered by a dielectric (electrowetting on the dielectric, EWOD). There are basically two explanations of the phenomenon. The first one considers that the solidÀliquid surface tension is modulated by the electrostatic energy stored by the unit area in the effective capacitance created by the liquid and the substrate. 4 The second explanation considers that there is a net force acting on the electric charge that accumulates at the triple line (TPL) formed among the air, the solid substrate, and the liquid. 5,6 In fact, irrespectively of the explanation given, the contact angle decrease is independent of the polarity of the applied voltage, and the LippmannÀYoung 7 equation for the static contact angle change,has been experimentally demonstrated 8 for a wide range of voltage values prior to a saturation regime. In eq 1, θ 0 is the contact angle before the voltage is applied, θ V is the contact angle after a voltage V is applied, ε 0 is the vacuum permittivity, ε r and d are the relative permittivity and the thickness of the dielectric layer, respectively, and γ LV is the surface tension of the liquidÀgas interface. This increase in wettability contrasts with the decrease in wettability observed after electron bombardment. 9 In a recent paper, 10 we preliminarily discussed a contactless method to increase the wettability by creating the charging conditions of the TPL by air ionization using a corona charge instrument. We are providing in this article a more detailed discussion and systematic measurements of the observations we have made using this technique.Corona ionizers are based on the ionization of molecules of the surrounding air by the application of a sufficiently high potential between specific geometry electrodes (e.g., pin to plane) creating a large electric field gradient. 11 The control of static charge on insulating materials is a widespread use of this technique in the semiconductor industry to avoid undesired electrostatic discharge (ESD). In fact, this is the only practical way to neutralize static charge because grounding has no effect on the level of charge in insulators.In this article, we have used corona ionization to build electrostatic charge on a EWOD structure and analyze the effects this may have on the contact angle between a drop and the surface. Our preliminary experiments reported in ref 10 did show that the contact angle decreased after exposure to corona ionization, and this observation motivated the detailed study of the phenomenon that we report here. There are few works relating electrowetting to air ionization. Vallet et al. 12 attributed to air ionization the saturation phenomena of the contact angle, Blake 13 used a corona charging procedure to assist the study of contact angle change for a constant speed moving substrate, and Arifin et al. 14 investigated the effect of the e...

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“…Onsager's principle itself is a generalization of Helmholtz's minimal dissipation principle [46]. Applications of Onsager's extremum principle to multiphase fluid problems can be found in [41,47,48,49] among others.…”

Section: Derivation Of the Cahn-hilliard-stokes-darcy Model Via Onsagmentioning

confidence: 99%

Two‐phase flows in karstic geometry

Han

Sun

Wang

2013

Math Methods in App Sciences

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Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications.In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits and in porous media must be considered together. Geometric configurations that contain both conduit (or vug) and porous media are termed karstic geometry. Despite the importance of the subject, little work has been done on multi-phase flows in karstic geometry.In this paper we present a family of phase field (diffusive interface) models for two phase flow in karstic geometry. These models together with the associated interface boundary conditions are derived utilizing Onsager's extremum principle. The models derived enjoy physically important energy laws. Uniquely solvable first and second order in time numerical schemes that preserve the associated energy law are presented as well.

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On a phase-ﬁeld model for electrowetting

Cited by 43 publications

References 34 publications

Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains

Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains

Wettability Increase by “Corona” Ionization

Two‐phase flows in karstic geometry

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