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

Zakaria, Kadry; Alkharashi, Sameh A.

doi:10.1007/s00707-017-1847-y

Cited by 13 publications

(4 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Equation ( 112), we can study the stability or instability of the considered system for any arbitrary value of the constant ∆C 2 , without any loss of generality, given that we only consider the complex wave speed's imaginary component Im(∆c); i.e., we will only take into account phrases that contain the Reynolds number R 1 . In the following figures, we note that the system is stable or unstable if Im(∆c) ≶ 0, respectively [52]. Equation ( 112) is used to control the stability behavior and illustrate the stabilizing and destabilizing characteristics of the system under consideration for linear stability.…”

Section: Dispersion Relation and Stability Analysismentioning

confidence: 99%

Electrohydrodynamic Couette–Poiseuille Flow Instability of Two Viscous Conducting and Dielectric Fluid Layers Streaming through Brinkman Porous Medium

El-Sayed,

Amer,

Alfayzi

2023

Mathematics

View full text Add to dashboard Cite

The electrohydrodynamic plane Couette–Poiseuille flow instability of two superposed conducting and dielectric viscous incompressible fluids confined between two rigid horizontal planes under the action of a normal electric field and pressure gradient through Brinkman porous medium has been analytically investigated. The lower plane is stationary, while the upper one is moving with constant velocity. The details of the base state mathematical model and the linearized model equations for the perturbed state are introduced. Following the usual procedure of linear stability analysis for viscous fluids, we derived two non-dimensional modified Orr–Sommerfeld equations and obtained the associated boundary and interfacial conditions suitable for the problem. The eigenvalue problem has been solved using asymptotic analysis for wave numbers in the long-wavelength limit to obtain a very complicated novel dispersion relation for the wave velocity through lengthy calculations. The obtained dispersion equation has been solved using Mathematica software v12.1 to study graphically the effects of various parameters on the stability of the system. It is obvious from the figures that the system in the absence of a porous medium and/or electric field is more unstable than in their presence. It is found also that the velocity of the upper rigid boundary, medium permeability, and Reynolds number have dual roles on the stability on the system, stabilizing as well as destabilizing depending on the viscosity ratio value. The electric potential, dielectric constant and pressure gradient are found to have destabilizing influences on the system, while the porosity of the porous medium, density ratio and Froude number have stabilizing influences. A depth ratio of less than one has a dual role on the stability of the system, while it has a stabilizing influence for values greater than one. It is observed that the viscosity stratification brings about a stabilizing as well as a destabilizing effect on the flow system.

show abstract

Section: Dispersion Relation and Stability Analysismentioning

confidence: 99%

Electrohydrodynamic Couette–Poiseuille Flow Instability of Two Viscous Conducting and Dielectric Fluid Layers Streaming through Brinkman Porous Medium

El-Sayed,

Amer,

Alfayzi

2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…Here, the boundary constraints are information about the obtained solutions of the governing equations at certain places, such as the lower and the upper substrates, in addition the interface between the fluids (Shankar and Sharma (2004), Wu and Chou (2005), Ozen et al (2006), Zakaria et al(2009), Hayat et al (2016), Alkharashi and Gamiel (2017), Tomar et al (2007); Zakaria and Alkharashi (2017)).…”

Section: Boundary Conditionsmentioning

confidence: 99%

Performance Evaluation of Insoluble Surfactants on the Behavior of Two Electric Layers

Alkharashi¹,

Assaf²,

Alhamad³

et al. 2019

JAFM

View full text Add to dashboard Cite

The purpose of this study is to establish the effects of insoluble surfactants on the stability of two layers flow down an inclined wall in the limit of Stokes and long-wavelength approximations. The dynamics of the liquid-liquid interface is described for arbitrary amplitudes by evolution equations derived from the basic hydrodynamic equations, in which the fluids are subjected to a uniform electric field. The principle aim of this work is to investigate the interfacial stability as well as the growth rate in the presence of insoluble surfactants. The parameters governing the flow system, such as Marangoni, Weber, capillary numbers and the inclined substrate strongly affect the waveforms and their amplitudes and hence the stability of the fluid. Approximate solutions of this system of linear evolution equations are performed. epending on the selected parameters, the phenomenon of the dual role is found with respect to the electric Weber number as well as the viscosity ratio. The interfacial waves will be more stable due to the growth of the Marangoni number while, while the opposite effect is found for the increase in capillary number. In the longwave perturbations, the stability process is found to confirm the stabilizing effect of the Marangoni number and the destabilizing influence of both capillary and Reynolds numbers, whereas the dual role is observed for the dielectric ratio.

show abstract

“…The flow stability is reduced due to the medium porosity. Many researches [16][17][18][19][20][21][22][23][24][25][26][27] investigated the problem of liquid-film flow on a solid surface. In [16], the authors discussed a condensate Newtonian film on a vertical plate subjected to a normal magnetic field in the case of small magnetic Reynolds number where the viscous and Joule's heating are ignored.…”

Section: Introductionmentioning

confidence: 99%

“…The results reveal an unstable influence of the Casson number on the film motion whereas the Forchheimer number enhances the stability. Zakaria and Alkharashi [27] considered the flow of two superposed viscous films confined by two porous inclined plates subjected to an electric field. They deduced a system of differential equations describe the development of interface, surface charge and flow rate using an integral method based on the long wave assumption.…”

Section: Introductionmentioning

confidence: 99%

Hydromagnetic instability of a thin viscoelastic layer on a moving column

Assaf

Alkharashi

2019

Phys. Scr.

View full text Add to dashboard Cite

The issue of hydromagnetic instability for a viscoelastic condensate film streaming down on a normal moving cylinder is discussed. As the visco-elasticity, heat-transfer influence or the magnetic field are included into the governing equations, the results become more suitable with the real situation. The nonlinearity enhances the accuracy of the results. The flow stability is weakened by the reduction of the volume of cylinder. However, the response of the system due to the temperature difference is uncertain. Moreover, the increment of magnetic field can enhance the stability. In contrast to the linear-results, the flow can be stabilized by the rheology.

show abstract

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

Cited by 13 publications

References 24 publications

Electrohydrodynamic Couette–Poiseuille Flow Instability of Two Viscous Conducting and Dielectric Fluid Layers Streaming through Brinkman Porous Medium

Electrohydrodynamic Couette–Poiseuille Flow Instability of Two Viscous Conducting and Dielectric Fluid Layers Streaming through Brinkman Porous Medium

Performance Evaluation of Insoluble Surfactants on the Behavior of Two Electric Layers

Hydromagnetic instability of a thin viscoelastic layer on a moving column

Contact Info

Product

Resources

About