Nonlinear EHD stability of cylindrical walters B' fluids: effect of an axial time periodic electric field

Moatimid, Galal M.; Mostapha, Doaa R.; Zekry, Marwa H.

doi:10.1016/j.cjph.2021.08.023

Cited by 18 publications

(6 citation statements)

References 23 publications

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“…where ξ r ðtÞ and ξ i ðtÞ can be performed by employing the real and imaginary description of the parameters λ and ω 2 . Therefore, using ( 9) and (11) with (22) one can find the following parts The polar representation for the same system is given in Figure 2(a) except that the graph is considered in Figure 4(a). ν ¼ 0:7:…”

Section: The Representation In the Equivalent Linearized Approachmentioning

confidence: 99%

“…[15][16][17][18] Computed the elevation surface wave propagating at the surface of a fluid is described by the Helmholtz-Duffing oscillator. [19][20][21][22] It is known that this family is integrable, that is, its exact solution is available in the absence of the damping effect. Otherwise, if the damping effect and somewhat other friction forces are taken into consideration, a non-integral differential equation will arise, that is, its exact solution is not available.…”

Section: Introductionmentioning

confidence: 99%

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Properties of complex damping Helmholtz–Duffing oscillator arising in fluid mechanics

El‐Dib

2022

Journal of Low Frequency Noise, Vibration and Active Control

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The current paper presents the first treatment to obtain the solution of a complex Helmholtz–Duffing oscillator. This model has described the elevation of the surface waves in fluid mechanics. The non-perturbative approach is used to convert the nonlinear oscillator to a linear oscillator to derive the solution of the complex nonlinear oscillator. This paper has opened the path for a new way to study more complex nonlinear elevation of surface waves.

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Section: The Representation In the Equivalent Linearized Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Properties of complex damping Helmholtz–Duffing oscillator arising in fluid mechanics

El‐Dib

2022

Journal of Low Frequency Noise, Vibration and Active Control

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“…An interface movement nonlinear characteristic equation was produced via the nonlinear stability approach. Due to the substantial interest in several practical chemistries and engineering applications, a nonlinear stability investigation of cylindrical Walters B' fluid was investigated [20]. The porous material had been entirely penetrated by the axial time-periodic electric field of the system.…”

Section: Greek Symbols English Symbolsmentioning

confidence: 99%

Effects of Uniform/Periodic Magnetic Fields on the Nonlinear Stability of Double Interfaces Between Three Magnetic Fluids Saturated in Porous Media

Moatimid

Sayed

Zekry

2022

Preprint

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The current manuscript tackles the interaction between three viscous magnetic fluids placed on three layers and saturated in porous media. Two of them fill half the spaces above and below a thin layer that lies in the middle region. All layers are laterally extended to infinity in both horizontal directions. All fluids move in the same horizontal direction with different uniform velocities and are driven by pressure gradients. The system is stressed by tangential stationary/periodic magnetic fields. The viscous potential theory (VPT) is used to simplify the mathematical procedure. The motion of the fluids is described by the Brinkman-Darcy equations, and Maxwell equations are used for the magnetic field. The nonlinear technique is typically relying on solving linear equations of motion and presenting the nonlinear boundary conditions. The novelty of the problem concerns the nonlinear stability of the double interface under the impact of periodic magnetic fields. Therefore, the approach has resulted in two nonlinear characteristic differential equations governing the surface displacements. Accordingly, the development amplitudes of surface waves are designated by two nonlinear Schrödinger equations. Stability is theoretically analyzed; the nonlinear stability criterion is derived, and the corresponding nonlinear stability conditions are explored in detail. Approximate bounded solutions of the perturbed interfaces are estimated. Additionally, the thickness of the intermediate layer as a function of time is plotted. The impact of different parameters on the stability profile is investigated. For the middle layer, it is found that magnetic permeability, as well as viscosity, have a stabilizing effect. By contrast, the basic streaming, as well as permeability, have a destabilizing influence. The analysis of the periodic case shows that the lower interface is much more stable than the upper one. Engineering applications like petroleum products manufacturing and the electromagnetic field effect can be used to control the growth of the perturbation and then the recovery of crude oil from the pores of reservoir rocks.

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“…They took a nonlinear methodology, relying on the solution of the underlying linear equations of motion and the applicable nonlinear border restrictions. The nonlinear instability of a cylindrical-shaped interface connecting two incompressible viscoelastic liquids was scrutinized 27 . A time-periodic field acted on the system as well as the simplified formulation of the VPF was adopted to reduce the mathematical manipulation.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear EHD instability of two viscoelastic fluids under the influence of mass and heat transfer

Moatimid

Zekry

Ibrahim

2023

Sci Rep

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This study attempts to provide an approach to studying the nonlinear stability of a vertical cylindrical interface between two Oldroyd-B prototypes. An unchanged axial electric field influences the system, and porous medium, and the effects of heat and mass transfer (MHT) are considered. Hsieh's modulation and the viscous potential flow (VPT) are used to abbreviate the mathematical analysis. The viscoelastic Oldroyd-B model significant role in geothermal, engineering and industrial enhancement motivated us to carry out this in-depth investigation. The methodology of the nonlinear technique depends mainly on solving the linear equations of motion and applying the appropriate nonlinear boundary conditions. Numerous non-dimensional physical numbers are exposed using a non-dimensional technique. The stability conditions are theoretically achieved and numerically verified. As a limiting case, the linear dispersion equation is accomplished, and a set of stability diagrams is reachable. Together with the nonlinear stability method, a Ginzburg–Landau equation is derived. Subsequently, both theoretical and numerical methods are used to achieve the nonlinear stability criteria. Furthermore, a precise perturbed approach for surface deflection is achieved theoretically and numerically using the Homotopy perturbation method and the extended frequency conception. Along with the linear approach, it is found that the structure becomes unstable by the Laplace, Reynolds, Weber, and elasticity quantities as well as the linear MHT parameter. Furthermore, the stability zones are enhanced in the nonlinear instability approach.

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Nonlinear EHD stability of cylindrical walters B' fluids: effect of an axial time periodic electric field

Cited by 18 publications

References 23 publications

Properties of complex damping Helmholtz–Duffing oscillator arising in fluid mechanics

Properties of complex damping Helmholtz–Duffing oscillator arising in fluid mechanics

Effects of Uniform/Periodic Magnetic Fields on the Nonlinear Stability of Double Interfaces Between Three Magnetic Fluids Saturated in Porous Media

Nonlinear EHD instability of two viscoelastic fluids under the influence of mass and heat transfer

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