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This article is cited in 11 scientific papers (total in 11 papers)
Stability characteristics of periodic streaming fluids in porous
media
S. A. Alkharashiab, Y. Gamielc a Quesna Technical College, Tanta Technical Commercial Institute, Ministry of Higher Education, Tanta, Egypt
b Applied Science Department, College of Technological Studies, The Public Authority for Applied Education and Training, Adiliya, Kuwait
c Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt
Abstract:
We study the linear stability of a three-layer flow of immiscible liquids located in a periodic normal electric field. We consider certain porous media assumed to be uniform, homogeneous, and isotropic. We analytically and numerically simulate the system of linear evolution equations of such a medium. The linearized problem leads to a system of two Mathieu equations with complex coefficients of the damping terms. We study the effects of the streaming velocity, permeability of the porous medium, and the electrical properties of the flow of a thin layer (film) of liquid on the flow instability. We consider several special cases of such systems. As a special case, we consider a uniform electric field and solve the transition curve equations up to the second order in a small dimensionless parameter. We show that the dielectric constant ratio and also the electric field play a destabilizing role in the stability criteria, while the porosity has a dual effect on the wave motion. In the case of an alternating electric field and a periodic velocity, we use the method of multiple time scales to calculate approximate solutions and analyze the stability criteria in the nonresonance and resonance cases; we also obtain transition curves in these cases. We show that an increase in the velocity and the electric field promote oscillations and hence have a destabilizing effect.
Keywords:
linear stability, periodic electric field, porous media, Mathieu equation, streamline.
Received: 13.01.2016 Revised: 03.02.2016
Citation:
S. A. Alkharashi, Y. Gamiel, “Stability characteristics of periodic streaming fluids in porous
media”, TMF, 191:1 (2017), 126–150; Theoret. and Math. Phys., 191:1 (2017), 580–601
Linking options:
https://www.mathnet.ru/eng/tmf9150https://doi.org/10.4213/tmf9150 https://www.mathnet.ru/eng/tmf/v191/i1/p126
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Abstract page: | 346 | Full-text PDF : | 108 | References: | 33 | First page: | 13 |
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