Nonlinear evolution of the travelling waves at the surface of a thin viscoelastic falling film

Sirwah, Magdy A.; Zakaria, Kadry

doi:10.1016/j.apm.2012.04.006

Cited by 7 publications

(5 citation statements)

References 50 publications

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“…7-9 a rich dynamical behavior characterized by appearance of nonlinear waves is illustrated. The motion of the film in two spatial dimensions with a rotating cylinder and without surface tension exhibits a solitary waves that corresponds to the decomposition of the nonlinear waves in previous models [12][13][14].…”

Section: The Tanh-function Methodssupporting

confidence: 59%

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Thin Film Motion of an Ideal Fluid on the Rotating Cylinder Surface

Zhukov,

Morad

2013

Preprint

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The shallow water equations describing the motion of thin liquid film on the rotating cylinder surface are obtained. These equations are the analog of the modified Boussinesq equations for shallow water and the Korteweg-de Vries equation. It is clear that for rotating cylinder the centrifugal force plays the role of the gravity. For construction the shallow water equations (amplitude equations) usual depth-averaged and multi-scale asymptotic expansion methods are used. Preliminary analysis shows that a thin film of an ideal incompressible fluid precesses around the axis of the cylinder with velocity which differs from the angular velocity of rotating cylinder. For the mathematical model of the liquid film motion the analytical solutions are obtained by the Tanh-Function method. To illustrate the integrability of the equations the Painlevé analysis is used. The truncated expansion method and symbolic computation allows to present an auto-Bäcklund transformation. The results of analysis show that the exact solutions of the model correspond to the solitary waves of different types.

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Section: The Tanh-function Methodssupporting

confidence: 59%

“…To determine the solutions for various cases studied in this paper analytical schemes are used. The results for the nonlinear PDE (4.32) are presented and compared with the previous works and experimental situation [12][13][14].…”

Section: The Painlevé Test Of the Kdv Equationmentioning

confidence: 94%

Thin Film Motion of an Ideal Fluid on the Rotating Cylinder Surface

Zhukov,

Morad

2013

Preprint

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“…The physical properties of such a fluid constitute its density = 0.98 × 10 3 Kg/m 3 , limiting viscosity = 0.79 Ns/m 2 , kinematic viscosity ] = 806 × 10 −6 Nsm/Kg, surface tension = 40 × 10 −3 N/m, and viscoelastic coefficient Γ 0 = 0.04 Ns 2 /m 2 . Hydrodynamic stability studies for the mixture of above polymer have been reported by Andersson and Dahl [12], Sadiq and Usha [13], Lin and Chen [14], and Sirwah and Zakaria [15] for thin films.…”

Section: Introductionmentioning

confidence: 79%

“…When is a function of and the flow is on a planar wall, (15) becomes a fourth-order linear differential equation with constant coefficients, which can be straightforwardly solved. On a topographical substrate when Marangoni and surface-tension effects are neglected, (15) reduces to the form ( )( 2 / 2 ) + ( ) = 0. For an eigenvalue , the eigenfunction could be explicitly solved using a series solution technique for the above second-order differential equation at ordinary points ̸ = (1/2 )cos −1 (1/ ).…”

Section: Temporal Linear Stability and Resultsmentioning

confidence: 99%

Influence of Temperature Gradient on the Stability of a Viscoelastic Film with Gradually Fading Memory over a Topography with Ridges and Furrows

Iqbal

2013

Chinese Journal of Engineering

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A long-wave evolution equation is derived using an asymptotic analysis, and the linear stability of a viscoelastic film flowing along the direction of parallel grooves over a uniformly heated topography is studied. A numerical approach adopting spectral collocation technique is used to demarcate the stable and unstable flow regimes. The combined influence of thermocapillarity and viscoelasticity on the films stability is analyzed. By accounting the bottom topography comprising longitudinal gutters, the possibilities of regulating the film dynamics under iso- and nonisothermal conditions and/or optimizing design structure of an apparatus for desirable flow outcomes have been focussed.

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“…Many scientific and industrial problems involve the flow of thin liquid films (see, for instance [1][2][3][4][5][6][7][8]). Thin film technology is used extensively in many applications including microelectronics, optics, magnetism, hard and corrosion resistant coatings, biotechnology, micro-mechanics, lasers, and medicine.…”

Section: Introductionmentioning

confidence: 99%

The effect of an electric field on the rotating flows of a thin film using a perturbation technique

2019

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The motion of a thin suspended film of an incompressible fluid under the effect of an external electric field is studied. The effects of the interfacial Maxwell stress, surface tension and intermolecular forces are studied, in which the forces are included in the Navier–Stokes equations. The perturbation technique is used to solve the given model. The obtained results show that, the fluid moves in a rotating pattern and the fluid particles move along the streamlines with different velocities. The free boundaries show good agreement with experimental data. In addition, the stability criteria are examined in the present model.

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Nonlinear evolution of the travelling waves at the surface of a thin viscoelastic falling film

Cited by 7 publications

References 50 publications

Thin Film Motion of an Ideal Fluid on the Rotating Cylinder Surface

Thin Film Motion of an Ideal Fluid on the Rotating Cylinder Surface

Influence of Temperature Gradient on the Stability of a Viscoelastic Film with Gradually Fading Memory over a Topography with Ridges and Furrows

The effect of an electric field on the rotating flows of a thin film using a perturbation technique

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