Formation of Liquid Columns on Liquid–Liquid Interfaces under Applied Electric Fields

Dong, Junhang; Almeida, Valmor F. de; Tsouris, Costas

doi:10.1006/jcis.2001.7845

Cited by 11 publications

(6 citation statements)

References 18 publications

(23 reference statements)

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“…There is a critical voltage above which the interface becomes unstable, initial undulations are followed by the appearance of sharp, drop-emitting peaks of the conducting fluid, which eventually develop into liquid columns. − The behavior has been observed at various liquid/liquid and liquid/vapor interfaces. According to the theory, , the critical wavenumber, k̃ , is where ρ A and ρ B are the densities of the two liquids, γ AB is the interfacial tension, and g is the acceleration due to gravity. The critical voltage (for the case where liquid A is a perfect insulator and liquid B is perfectly conductive) is 56,57 where h is the vertical displacement of the interface.…”

Section: Discussionmentioning

confidence: 99%

“…[55][56][57][58] The behavior has been observed at various liquid/liquid and liquid/vapor interfaces. According to the theory, 56,57 the critical wavenumber, k ˜, is where F A and F B are the densities of the two liquids, γ AB is the interfacial tension, and g is the acceleration due to gravity. The critical voltage (for the case where liquid A is a perfect insulator and liquid B is perfectly conductive) is 56,57 where h is the vertical displacement of the interface.…”

Section: Discussionmentioning

confidence: 99%

“…According to the theory, 56,57 the critical wavenumber, k ˜, is where F A and F B are the densities of the two liquids, γ AB is the interfacial tension, and g is the acceleration due to gravity. The critical voltage (for the case where liquid A is a perfect insulator and liquid B is perfectly conductive) is 56,57 where h is the vertical displacement of the interface. If we assume that h ≈ 1/k ˜, i.e., the perturbation being of the order of the capillary constant (the characteristic length scale at a flat liquid/liquid interface), then eq 10 becomes essentially identical to eq 6.…”

Section: Discussionmentioning

confidence: 99%

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Contact Angle Saturation in Electrowetting

2005

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Electrowetting is the phenomenon of contact angle decrease under the influence of an external voltage applied across the solid/liquid interface. Electrowetting offers an interesting possibility to enhance the wettability of hydrophobic materials without altering the chemical composition of the system and thus could be incorporated in various microfluidic devices. Electrowetting is fundamentally an electrocapillary effect occurring on an insulated solid electrode (hence the change of the solid/liquid interfacial tension with voltage follows Lippmann's equation). A limiting contact angle value larger than zero is achieved even at very large external voltages. Saturation precludes full wetting of the substrate and restricts the magnitude of the capillary force variation. Contact angle saturation has been given various interpretations (e.g., charge trapping, air ionization) but appears to reflect a natural thermodynamic limit rather than being simply a defective property. The limiting value of the contact angle is given by the Young equation when the value of the solid/liquid interfacial tension reaches zero. The model is in excellent agreement with our own results and often gives an adequate description of published data. It also suggests that the saturation limit is determined by the material properties of the system and electrowetting at voltages exceeding this threshold is essentially a nonequilibrium process.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Contact Angle Saturation in Electrowetting

2005

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“…A comparison between experiment and lubrication theory (for a finite-length electrode) is made in Griffing et al (2004) and agreement is reasonable. A striking experimental demonstration of the instability due to a vertical field in the absence of a shear flow can be found in Dong, de Almeida & Tsouris (2001), where the field induces the formation and protrusion of liquid columns of one liquid into a second immiscible liquid with different electrical properties. Even though the observed phenomenon is three-dimensional, a fundamental understanding of two-dimensional nonlinear interfacial electrohydrodynamics is a suitable starting point and is one of the aims of the present work.…”

Section: Introductionmentioning

confidence: 99%

Wave evolution on electrified falling films

Tseluiko

Papageorgiou

2006

J. Fluid Mech.

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The nonlinear stability of falling film flow down an inclined flat plane is investigated when an electric field acts normal to the plane. A systematic asymptotic expansion is used to derive a fully nonlinear long-wave model equation for the scaled interface, where higher-order terms must be retained to make the long-wave approximation valid for long times. The effect of the electric field is to introduce a non-local term which comes from the potential region above the liquid film. This term is always linearly destabilizing and produces growth rates proportional to the cubic power of the wavenumber – surface tension is included and provides a short wavelength cutoff. Even in the absence of an electric field, the fully nonlinear equation can produce singular solutions after a finite time. This difficulty is avoided at smaller amplitudes where the weakly nonlinear evolution is governed by an extension of the Kuramoto–Sivashinsky equation. This equation has solutions which exist for all time and allows for a complete study of the nonlinear behaviour of competing physical mechanisms: long-wave instability above a critical Reynolds number, short-wave damping due to surface tension and intermediate growth due to the electric field. Through a combination of analysis and extensive numerical experiments, we find parameter ranges that support non-uniform travelling waves, time-periodic travelling waves and complex nonlinear dynamics including chaotic interfacial oscillations. It is established that a sufficiently high electric field will drive the system to chaotic oscillations, even when the Reynolds number is smaller than the critical value below which the non-electrified problem is linearly stable. A particular case of this is Stokes flow.

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“…Formation of liquid columns and extraction of jets by electric fields were studied in seminal experiments of Raco [15] and Taylor [13], and have been a source of investigation at intervals since then. Electrically supported liquid columns have been subjected to stability investigations both experimentally and theoretically [16,17,18,19], and the formation of such columns rising against the gravitational force have been shown experimentally [20,21].…”

Section: Introductionmentioning

confidence: 99%

Static and dynamic response of a fluid–fluid interface to electric point and line charge

Ellingsen¹,

Brevik²

2012

Annals of Physics

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We consider the behavior of a dielectric fluid-fluid interface in the presence of a strong electric field from a point charge and line charge, respectively, both statically and, in the latter case, dynamically. The fluid surface is elevated above its undisturbed level until balance is reached between the electromagnetic lifting force, gravity and surface tension. We derive ordinary differential equations for the shape of the fluid-fluid interface which are solved numerically with standard means, demonstrating how the elevation depends on field strength and surface tension coefficient. In the dynamic case of a moving line charge, the surface of an inviscid liquid-liquid interface is left to oscillate behind the moving charge after it has been lifted against the force of gravity. We show how the wavelength of the oscillations depends on the relative strength of the forces of gravity and inertia, whereas the amplitude of the oscillations is a nontrivial function of the velocity at which the line charge moves. * Corresponding author.Email addresses: simen.a.ellingsen@ntnu.no (SimenÅ. Ellingsen), iver.h.brevik@ntnu.no (Iver Brevik) 1 Fax number: +47 73593491. Telephone: +47 73593554.

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Formation of Liquid Columns on Liquid–Liquid Interfaces under Applied Electric Fields

Cited by 11 publications

References 18 publications

Contact Angle Saturation in Electrowetting

Contact Angle Saturation in Electrowetting

Wave evolution on electrified falling films

Static and dynamic response of a fluid–fluid interface to electric point and line charge

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