Nonlinear electrohydrodynamic waves on films falling down an inclined plane

González, Antonio; Castellanos, A.

doi:10.1103/physreve.53.3573

Cited by 79 publications

(69 citation statements)

References 12 publications

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“…Since the first term is positive, the magnetic field is destabilizing as found by Cowley and Rosensweig and Yecko 8,27 whereas capillary forces always stabilize the film for sufficiently large k. Dispersion relation (88) is similar to the electrohydrodynamic case, 20 where the electric field, for a perfectly conducting viscous film, was also found to be destabilizing. The equation for neutral stability is…”

Section: A Linear Theorysupporting

confidence: 50%

“…This equation is similar to the models for a perfectly conducting fluid film in a normal electric field. 19,20,26 The main difference in our model is the presence of a non-linear relationship for the magnetization that has been retained by keeping the next term in the asymptotic expansion.…”

Section: Reduced Modelmentioning

confidence: 99%

“…For ferrofluids with a linear relationship between magnetization and magnetic field, the dynamics are similar to electrified films. 10 There are many papers on the dynamics of electrified films [17][18][19][20][21] that can be used to understand ferrofluid dynamics; however, the two problems diverge for cases where the magnetic field is sufficiently large to warrant a non-linear relationship between magnetization and magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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Thin viscous ferrofluid film in a magnetic field

Conroy

Matar

2015

Physics of Fluids

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We consider a thin, ferrofluidic film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. Its dynamics are governed by a coupled system of the steady Maxwell's, the Navier-Stokes, and the continuity equations. The magnetization of the film is a function of the magnetic field and may be prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure and velocity fields inside the film. In addition, we investigate the problem in the limit of a large magnetic permeability. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape via use of the kinematic condition. The resultant one-dimensional equations are solved numerically using spectral methods. The magnetic effects give rise to a non-local contribution. We conduct a parametric study of both the linear and nonlinear stabilities of the system in order to evaluate the effects of the magnetic field. Through a linear stability analysis, we verify that the Maxwell's pressure generated from a normally applied magnetic field is destabilizing and can be used to control the size and shape of lobes and collars on the free surface. We also find that in the case of a falling drop, the magnetic field causes an increase in the velocity and capillary ridge of the drop. C 2015 AIP Publishing LLC.

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Section: A Linear Theorysupporting

confidence: 50%

Section: Reduced Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thin viscous ferrofluid film in a magnetic field

Conroy

Matar

2015

Physics of Fluids

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“…The study of the stability of interfacial electrohydrodynamic waves was initiated by Melcher [3] and Taylor and McEwan [13], and the role of interfacial stresses resulting from electrodes was reviewed by Melcher and Taylor [4]. Recent theoretical research in this field has focused on the nonlinear phenomena and corresponding mechanisms, such as nonlinear coherent structures (e.g., [2,5,8,10,11,[14][15][16][17][18][19][20]) and touchdown singularities (e.g., [7,21]). Considerable effects have been put into the modeling and numerical studies of nonlinear interfacial electrohydrodynamic waves.…”

Section: Introductionmentioning

confidence: 99%

“…The electric stresses have great impact on electrified free surfaces or interfaces, which can not only modify wave patterns but also change stability characteristics of the system. These influences are of great practical interest since they can lead to quantity (e.g., heat or mass) transfer enhancement (see, e.g., [5,11,12]). The study of the stability of interfacial electrohydrodynamic waves was initiated by Melcher [3] and Taylor and McEwan [13], and the role of interfacial stresses resulting from electrodes was reviewed by Melcher and Taylor [4].…”

Section: Introductionmentioning

confidence: 99%

Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Tao

2017

Advances in Mathematical Physics

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We are concerned with gravity-capillary waves propagating on the surface of a three-dimensional electrified liquid sheet under a uniform electric field parallel to the undisturbed free surface. For simplicity, we make an assumption that the permittivity of the fluid is much larger than that of the upper-layer gas; hence, this two-layer problem is reduced to be a one-layer problem. In this paper, we propose model equations in the shallow-water regime based on the analysis of the Dirichlet-Neumann operator. The modified Benney-Luke equation and Kadomtsev-Petviashvili equation will be derived, and the truly three-dimensional fully localized traveling waves, which are known as "lumps" in the literature, are numerically computed in the Benney-Luke equation.

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Analyticity for Kuramoto–Sivashinsky‐type equations in two spatial dimensions

Ioakim

Smyrlis

2015

Math Methods in App Sciences

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In this work, we investigate the analyticity properties of solutions of Kuramoto-Sivashinsky-type equations in two spatial dimensions, with periodic initial data. In order to do this, we explore the applicability in three-dimensional models of a spectral method, which was developed by the authors for the one-dimensional Kuramoto-Sivashinsky equation. We introduce a criterion, which provides a sufficient condition for analyticity of a periodic function u 2 C 1 , involving the rate of growth of r n u, in suitable norms, as n tends to infinity. This criterion allows us to establish spatial analyticity for the solutions of a variety of systems, including Topper-Kawahara, Frenkel-Indireshkumar, and Coward-Hall equations and their dispersively modified versions, once we assume that these systems possess global attractors.

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Nonlinear electrohydrodynamic waves on films falling down an inclined plane

Cited by 79 publications

References 12 publications

Thin viscous ferrofluid film in a magnetic field

Thin viscous ferrofluid film in a magnetic field

Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Analyticity for Kuramoto–Sivashinsky‐type equations in two spatial dimensions

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