Rayleigh-Taylor Instability of Viscous-Viscoelastic Fluids in Presence of Suspended Particles Through Porous Medium

Kumar, Pardeep

doi:10.1515/zna-1996-1-203

Cited by 16 publications

(9 citation statements)

References 6 publications

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“…Such parallel flows exist in packed-bed reactor, in the chemical industry, in petroleum production engineering, in boiling, and many other processes. The instability of a plane interface between two uniform superposed fluids through a porous medium was investigated by Kumar [13]. The KHI for flow in porous media was studied by El-Sayed [14].…”

Section: The Introductionmentioning

confidence: 99%

Electrohydrodynamic linear stability of finitely conducting flows through porous fluids with mass and heat transfer

Moatimid¹,

Allah²

2010

Applied Mathematical Modelling

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a b s t r a c tIn this work, a linear stability analysis is used to investigate a capillary surface waves between two horizontal finite fluid layers. The system is acted upon by a vertical periodic electric field. The problem examines few representatives of porous media. It is also includes finite conductivity, mass and heat transfer. It is assumed that the basic flow is two-dimensional streaming flow. A general dispersion relation governing the linear stability is derived. In contrast with our previous work [23], the present problem shows that the stability criterion depends on the mass and heat transfer parameter. The present study recovers some special cases upon appropriate data choices. The presence of finite conductivity's together with the dielectric permeability's make the uniform electric field plays a dual role in the stability criterion. This shows some analogy with the nonlinear stability theory. In addition, the mass and heat transfer parameter as well as the Darcy's coefficients play a stabilizing role in the stability picture. In case of the Rayleigh-Taylor instability, by means of the Whittaker technique, the parametric excitation of the electrohydrodynamic surface waves is obtained. The transition curve equations are calculated up to the fourth order for a small dimensionless parameter. The analytical results are numerically confirmed.Ó 2010 Elsevier Inc. All rights reserved. The introductionThe instability of a plane interface between two superposed fluids of different densities, when it occurs, is called the Rayleigh-Taylor instability (RTI). This instability was first investigated by Rayleigh [1]. Taylor [2] studied the stability of a heterogeneous fluid accelerated in a direction perpendicular to the plane of stratification. The RTI has been addressed in several studies owing to its importance in stratified system, among which planetary and stellar atmosphere are of two examples. The effect of the external forces has an importance, mainly, in planetary and stellar systems. Coriolis and centrifugal forces are more common in these systems. They play an important role in determining many phenomena including the RTI. Different properties of fluids have been included in the RTI through theoretical investigation. Chandrasekhar [3] has given a detailed account of these investigations. The Kelvin-Helmholtz instability (KHI) arises when two superposed fluids are in relative motion. The model of the classical KHI involves a horizontal interface between two fluids with different parallel, uniform, and horizontal velocities. In the KHI problem, the effect of streaming is destabilizing in the sense as given by Chandrasekhar [3]. This instability, which arises as a consequence of a relative drift velocity of two fluids along the surface of discontinuity, has a great relevance to various physical phenomena such as commentary tails and the magnetospherical boundary. The KHI has attracted the attention of many researchers, due to shear flow in stratified fluids, and its dominant 0307-904X/$ -see front matter Ó

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Section: The Introductionmentioning

confidence: 99%

Electrohydrodynamic linear stability of finitely conducting flows through porous fluids with mass and heat transfer

Moatimid¹,

Allah²

2010

Applied Mathematical Modelling

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“…Such parallel flows exist in packed bed reactor in the chemical industry, in petroleum production engineering, in boiling in porous media (countercurrent flow of liquid and vapor), and in many other processes. The instability of a plane interface between two uniform superposed fluids through a porous medium was investigated by Kumar [20], and the KHI for flow in porous media was studied by El-Sayed [21]. They used linear stability analysis to obtain a characteristic equation for the growth rate of the disturbance.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Kelvin-Helmholtz instability of two miscible ferrofluids in porous media

Moatimid

2005

Z. angew. Math. Phys.

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The nonlinear theory of the Kelvin-Helmholtz instability is employed to analyze the instability phenomenon of two ferrofluids through porous media. The effect of both magnetic field and mass and heat transfer is taken into account. The method of multiple scale expansion is employed in order to obtain a dispersion relation for the first-order problem and a GinzburgLandau equation, for the higher-order problem, describing the behavior of the system in a nonlinear approach. The stability criterion is expressed in terms of various competing parameters representing the mass and heat transfer, gravity, surface tension, fluid density, magnetic permeability, streaming, fluid thickness and Darcy coefficient. The stability of the system is discussed in both theoretically and computationally, and stability diagrams are drawn.

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“…The instability of a plane interface between two uniform superposed streaming fluids through porous media was investigated by many researchers for different cases. [26][27][28] Also, for the flow through porous media, it is convenient to take into account the existence of the suction/injection velocities at the boundaries of the porous structures. The suction/injection of the liquid/vapor at the boundaries is assumed to induce streaming velocities in the normal direction to the flow.…”

Section: Introductionmentioning

confidence: 99%

Kelvin-Helmholtz instability for flow in porous media under the influence of oblique magnetic fields: A viscous potential flow analysis

2013

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In this paper, the Kelvin-Helmholtz instability of viscous incompressible magnetic fluid fully saturated porous media is achieved through the viscous potential theory. The flow is considered to be through semi-permeable boundaries above and below the fluids through which the fluid may either be blown in or sucked out, in a direction normal to the main streaming direction of the fluid flow. An oblique magnetic field, mass, heat transfer, and surface tension are present across the interface. Through the linear stability analysis, a general dispersion relation is derived and the natural curves are plotted. Therefore, the linear stability condition is discussed in some depth. In view of the multiple time scale technique, the Ginzburg–Landau equation, which describes the behavior of the system in the nonlinear approach, is obtained. The effects of the orientation of the magnetic fields on the stability configuration in linear, as well as nonlinear approaches, are discussed. It is found that the Darcy's coefficient for the porous layers plays a stabilizing role. The injection of the fluids at both boundaries has a stabilizing effect, in contrast with the suction at both boundaries.

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Rayleigh-Taylor Instability of Viscous-Viscoelastic Fluids in Presence of Suspended Particles Through Porous Medium

Cited by 16 publications

References 6 publications

Electrohydrodynamic linear stability of finitely conducting flows through porous fluids with mass and heat transfer

Electrohydrodynamic linear stability of finitely conducting flows through porous fluids with mass and heat transfer

Nonlinear Kelvin-Helmholtz instability of two miscible ferrofluids in porous media

Kelvin-Helmholtz instability for flow in porous media under the influence of oblique magnetic fields: A viscous potential flow analysis

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