Viscous flowing film instability down an inclined plane in the presence of constant electromagnetic field

Zakaria, Kadry; Gamiel, Yasser

doi:10.1016/j.ijnonlinmec.2012.07.005

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…In the limit τ 0, we recover the expression h II − 1 2 + √ 3 c − 1 4 corresponding to a film flowing down an inclined plane in the absence of impose shear stress ( [49,53,54]).…”

Section: Solitary Wavesmentioning

confidence: 69%

Nonlinear dynamics of a liquid film flow over a solid substrate in the presence of external shear stress and electric field

Zakaria

Sirwah

2022

Eur. Phys. J. Plus

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Using approximation techniques, long-wave length framework and boundary-layer, the effects of electrostatic force and induced shear stress on the flow behavior down an inclined solid substrate are investigated. In general case, the considered model accounts in the presence of inertia regime and streamwise viscous diffusion with the influence of normal electric field and an imposed shear stress. Using the Galerkin weighted residual, two coupled evolution equations for the flow rate and film thickness are extracted. In the appropriate limit cases, the evolution equations obtained by previous authors are recovered. The primary instability has been analyzed using the Whitham wave hierarchy framework. In the nonlinear regime, the behavior of solitary waves arose on the surface of liquid film due to the effects of electrostatic force and imposed shear stress throughout three-dimensional dynamical systems. Some bifurcation points are reported. In both extremely viscous and electrogravity regimes, the Benney-like equation is extracted in a new form. By excluding contribution of external shear stress and viscous dispersion parameter, the interesting results of previous authors are recovered. In both weakly nonlinear and inertialess regimes, the bifurcation points of the three dynamical systems are discussed within the Kuramoto–Sivashinsky type equation.

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“…In the limit τ 0, we recover the expression h II − 1 2 + √ 3 c − 1 4 corresponding to a film flowing down an inclined plane in the absence of impose shear stress ( [49,53,54]).…”

Section: Solitary Wavesmentioning

confidence: 69%

Nonlinear dynamics of a liquid film flow over a solid substrate in the presence of external shear stress and electric field

Zakaria

Sirwah

2022

Eur. Phys. J. Plus

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“…By using equations ( 17)-( 20), the boundary conditions (15) and (16) where h is the local film thickness, pa is the atmospheric pressure. By introducing a stream function j, the dimensionless velocity components can be expressed as…”

Section: Governing Equations and Boundary Conditionsmentioning

confidence: 99%

“…In most technical applications, such as coating surfaces, any kind of microscopic instability is not conducive to the gloss of the finished product. Similarly, during laser cutting, we do not want surface waves at the melt interface, so exerting some influence can prevent instability and keep the flow steady [15]. Most of the researches on thin film flow have focused on Newtonian fluids.…”

Section: Introductionmentioning

confidence: 99%

Effect of odd viscosity on the stability of thin viscoelastic liquid film flowing along an inclined plate

Zhao

Jian

2021

Phys. Scr.

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A theory for the stability of a viscoelastic film flowing along an inclined wall which is considered the odd viscosity effect is investigated. Using the lubrication theory, a new liquid-gas interface evolution equation involving odd viscosity effect is derived. Linear stability analysis shows that the larger odd viscosity leads to the higher critical Reynolds number. While the higher viscoelastic parameter makes the critical Reynolds number lower. The weakly nonlinear study reveals that in the limited amplitude range, the supercritical stable region and the explosion region will decrease with the increase of the odd viscosity. Conversely, the unconditional stable region and the subcritical unstable region increase. Interestingly, the threshold of the supercritical stable region decreases with the increase of the odd viscosity. Therefore, by analysing the linear and non-linear stability of the evolution equation, we find that the odd viscosity stabilizes the flow, while the viscoelastic property destabilizes the flow.

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Modeling and analysis of two electrified films flow traveling down between inclined permeable parallel substrates

Zakaria

Alkharashi

2017

Acta Mech

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Viscous flowing film instability down an inclined plane in the presence of constant electromagnetic field

Cited by 4 publications

References 9 publications

Nonlinear dynamics of a liquid film flow over a solid substrate in the presence of external shear stress and electric field

Nonlinear dynamics of a liquid film flow over a solid substrate in the presence of external shear stress and electric field

Effect of odd viscosity on the stability of thin viscoelastic liquid film flowing along an inclined plate

Modeling and analysis of two electrified films flow traveling down between inclined permeable parallel substrates

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