Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field

Zakaria, Kadry; Sirwah, Magdy A.; Alkharashi, Sameh A.

doi:10.1016/j.ijnonlinmec.2011.11.010

Cited by 14 publications

(8 citation statements)

References 22 publications

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“…The authors in paper [7] have investigated the stability properties of time periodically streaming superposed magnetic fluids through porous media under the influence of an oblique alternating magnetic field. Also, Zakaria et al [8] have analyzed the effect of an externally applied electric field on the stability of a thin fluid film over an inclined porous plane, using linear and non-linear stability analysis in the long wave limit. Wray et al [9] have investigate the evolution and stability of a wetting viscous fluid layer flowing down the surface of a cylinder, and surrounded by a conductive gas.…”

Section: Introductionmentioning

confidence: 99%

Dynamical System of Three Magnetic Layers in the Presence of Porous Media

Alkharashi¹

2015

JAMP

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This paper concerns the linear stability of three viscous fluid layers in porous media. The system is composed of a middle fluid embedded between two semi-infinite fluids, in which the effect of the normal magnetic field is to introduce. The principle aim of this work is to investigate the influence of fluid viscosity and the porosity effect on the growth rate in the presence of normal magnetic field. The parameters governing the layers flow system, the magnetic properties and porosity effects strongly influence the wave forms and their amplitudes and hence the stability of the fluid. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained, where regions of stability and instability are identified. It is found that the stabilizing role for the magnetic field is retarded when the flow is in porous media. Moreover, the increase in the values of permeability parameters plays a dual role, in stability behavior. It has been found that the phenomenon of the dual (to be either stabilizing or destabilizing) role is found for increasing the permeability parameter. It is established that both the viscosity coefficient and the magnetic permeability damps the growth rate, introducing stabilizing influence. The role of the magnetic field and Reynolds number is to increase the amplitude of the disturbance leading to the destabilization state of the flow system, promote the oscillatory behavior. Influence of the various parameters of the problem on the interface stability is thoroughly discussed.

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Section: Introductionmentioning

confidence: 99%

Dynamical System of Three Magnetic Layers in the Presence of Porous Media

Alkharashi¹

2015

JAMP

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“…The two-dimensional analysis of Sadiq and Usha [36] confirmed that the substrate porosity in general destabilizes the film flow system and the shear-thinning rheology enhances this destabilizing effect. The influence of an externally applied electric field on the stability of a thin fluid film over an inclined porous plane is analyzed in Zakaria et al [41]. Both linear and non-linear stability analyses in the long-wave limit have been carried out.…”

Section: Introductionmentioning

confidence: 99%

Gravity-driven flow of a shear-thinning power-law fluid over a permeable plane

Cristo

Iervolino²,

Vacca³

2013

ams

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The flow of a thin layer of power-law fluid on a porous inclined plane is considered. The unsteady equations of motion are depth-integrated according to the von Karman momentum integral method. The variation of the velocity distribution with the depth is accounted for, and it is furthermore assumed that the flow through the porous medium is governed by the modified Darcy's law. The stability condition is deduced considering the hierarchy of kinematic and gravity waves. The response of the linearized model to a Dirac-delta disturbance in unbounded domain is analytically deduced, in both stable and unstable conditions 1624 C. Di Cristo, M. Iervolino and A. Vacca of flow. The influence of the effect of power-law exponent and bottom permeability on the disturbance propagation is finally analyzed, suggesting indications about the choice of the bottom permeability in order to improve the performance of industrial processes.

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“…The previous equation expresses the condition describing the conservation of interfacial charge. The terms in this equation represent accumulation, convection within the interface, concentration or dilution due to dilation of the interface, and ion migration to or from the interface due to conduction in the bulk [11]. The completion of the mathematical description of the problem requires two additional interfacial conditions determine the shape of the interface between the fluids.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…(77) into Eqs. (75), (78) and separating the real and imaginary parts (c 11 and c 21 are assumed to be real constants), we thus have the following dispersion relation:…”

Section: (Ii) the Second-order Problem (Order δ 2 )mentioning

confidence: 99%

Linear stability of a thin film flow along permeable wall under alternating electric field

Zakaria

Alkharashi

2016

Z Angew Math Mech

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This study considers the linear stability of two‐layer films of immiscible liquids confined between an upper impermeable solid plate and a lower porous rigid substrate. The fluids are subjected to a periodic electric field. Based on the von Kármán‐Pohlhausen method an integral boundary‐layer model for the film thickness, surface charge and the flow rate is derived. The dynamics of the liquid‐liquid interface is described for arbitrary amplitudes by evolution equations derived from the basic hydrodynamic equations using long wave approximation. The parameters governing the film flow system and the permeable substrate strongly effect the wave forms and their amplitudes and hence the stability of the fluid. Analytical and numerical simulations of this system of linear evolution equations are performed. The case of uniform electric field is considered as special case, it is found that, the permeability of the porous medium promotes the oscillatory behavior. While a stabilizing influence is observed for increasing of both the non‐dimensional conductivity and the electric conductivity ratio. When the case of alternating electric field is taken into account, the method of multiple scales is applied to obtain approximate solutions and analyze the stability picture. Stability behavior is noticed for the decreasing of the permeability parameter and the dielectric constant ratio of the fluids.

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Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field

Cited by 14 publications

References 22 publications

Dynamical System of Three Magnetic Layers in the Presence of Porous Media

Dynamical System of Three Magnetic Layers in the Presence of Porous Media

Gravity-driven flow of a shear-thinning power-law fluid over a permeable plane

Linear stability of a thin film flow along permeable wall under alternating electric field

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