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Structural stability of a porous channel of electrical flow affected by periodic velocities

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Abstract

This paper investigates the effect of periodic velocity on the stability of two interfacial waves propagating between three layers of immiscible incompressible fluids. The flow propagates saturated in porous media under the influence of an electric field. The viscous potential theory is used to simplify the mathematical procedure, by which viscosity is accumulated on the separating surface rather than in the bulk of fluids. The dispersion relation is shown to be the result of coupled simultaneous Mathieu equations with complex coefficients. The mathematical difficulty in delaying the two Mathieu equations was overcome using the method of multiple time scales. The stability was discussed analytically and numerically by drawing some diagrams and obtaining the transition curves. In the presence and absence of stream periodicity, the linear stage of interface progress is visualized. Depending on the physical quantities used, it has been determined that the upper fluid speed dampens the wave more than the lower and middle velocities. It was discovered that the viscosity ratio of the upper interface, as opposed to the lower viscosity ratio, helps stabilize the liquid sheet. The upper layer porosity has a dual role depending on the sensitivity and significance of the sheet thickness.

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References

  1. Funada T, Joseph DD (2001) Viscous potential flow analysis of Kelvin-Helmholtz instability in a channel. J Fluid Mech 445:263–283

    Article  MathSciNet  MATH  Google Scholar 

  2. Ozen O, Aubry N, Papageorgiou DT, Petropoulos PG (2006) Electrohydrodynamic linear stability of two immiscible fluids in channel flow. Electrochim Acta 51(25):5316–5323

    Article  Google Scholar 

  3. Li F, Ozen O, Aubry N (2007) Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel. J Fluid Mech 583:347–377

    Article  MathSciNet  MATH  Google Scholar 

  4. Sisoev GM, Matar OK, Sileri D, Lawrence CJ (2009) Wave regimes in two-layer microchannel flow. Chem Eng Sci 64:3094–3102

    Article  Google Scholar 

  5. Sahu KC, Matar OK (2010) Stability of plane channel flow with viscous heating. ASME J Fluids Eng 132(1):011202

    Article  Google Scholar 

  6. Yang L-J, Xu B-R, Fu Q-F (2012) Linear instability analysis of planar non-Newtonian liquid sheets in two gas streams of unequal velocities. J. Non-Newton. Fluid Mech. 167–168:50–58

    Article  MATH  Google Scholar 

  7. Awasthi MK (2013) Viscous potential flow analysis of magnetohydrodynamic Rayleigh-Taylor instability with heat and mass transfer. Int J Dyn Control 2(3):254–261

    Article  Google Scholar 

  8. DiCarlo DA (2013) Stability of gravity-driven multiphase flow in porous media: 40Years of advances. Water Resour Res 49:4531–4522

    Article  Google Scholar 

  9. Sirwah MA (2014) Sloshing waves in a heated viscoelastic fluid layer in an excited rectangular tank. Phys Lett A 378:3289–3300

    Article  MathSciNet  MATH  Google Scholar 

  10. Chattopadhyay G, Usha R (2016) On the Yih–Marangoni instability of a two-phase plane Poiseuille flow in a hydrophobic channel. Chem Eng Sci 145(12):214–232

    Article  Google Scholar 

  11. AlHamdan AR, Alkharashi SA (2016) Stability characterization of three porous layers model in the presence of transverse magnetic field. J Math Res 8(2):69–81

    Article  Google Scholar 

  12. Alkharashi SA, Gamiel Y (2017) Stability characteristics of periodic streaming fluids in porous media. Theoret Math Phys 191(1):580–601

    Article  MathSciNet  MATH  Google Scholar 

  13. Usha R, Sahu KC (2019) Interfacial instability in pressure-driven core-annular pipe flow of a Newtonian and a Herschel-Bulkley fluid. J Nonnewton Fluid Mech 271:104144

    Article  MathSciNet  Google Scholar 

  14. Alkharashi SA (2019) A model of two viscoelastic liquid films traveling down in an inclined electrified channel. Appl Math Comput 355:553–575

    MathSciNet  MATH  Google Scholar 

  15. Fayazov KS, Khajiev IO (2022) Estimation of conditional stability of the boundary-value problem for the system of parabolic equations with changing direction of time. Rep Math Phys 88(3):419–431

    Article  MathSciNet  MATH  Google Scholar 

  16. Alkharashi SA, Al-Hamad Kh, Alrashidi A (2022) An approach based on the porous media model for multilayered flow in the presence of interfacial surfactants. Pramana - J Phys 96:140

    Article  Google Scholar 

  17. Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Oxford Univ. Press, Oxford

    MATH  Google Scholar 

  18. Iervolino M, Pascal JP, Vacca A (2018) Instabilities of a power-law film over an inclined permeable plane: a two-sided model. J Nonnewton Fluid Mech 259:111–124

    Article  MathSciNet  Google Scholar 

  19. Sirwah MA, Zakaria K (2019) Dynamics of surface waves of a ferrofluid film. Wave Motion 84:8–31

    Article  MathSciNet  MATH  Google Scholar 

  20. Roberts SA, Kumar S (2009) AC electrohydrodynamic instabilities in thin liquid films. J Fluid Mech 631:255–279

    Article  MathSciNet  MATH  Google Scholar 

  21. Sahu KC, Valluri P, Spelt PDM, Matar OK (2007) Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid. Phys Fluids 19:122101

    Article  MATH  Google Scholar 

  22. Alkharashi SA (2007) The effect of the porosity property on the dynamics of some fluids, Master thesis, Tanta University

  23. Liu Y, Dong M, Wu X (2021) Receptivity of inviscid modes in supersonic boundary layers to wall perturbations. J Eng Math 128:20

    Article  MathSciNet  MATH  Google Scholar 

  24. Sahu KC, Matar OK (2010) Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel-Bulkley fluid. Phys Fluids 22:112103

    Article  Google Scholar 

  25. Kahouadji L, Batchvarov A, Adebayo IT, Jenkins Z, Shin S, Chergui J, Juric D, Matar OK (2022) A numerical investigation of three-dimensional falling liquid films. Environ Fluid Mech 22:367–382

    Article  Google Scholar 

  26. Zakaria K, Sirwah MA, Elmorabie KhM, Eldeen SN (2019) Sloshing waves in electrified fluid layers in an excited rectangular container. Appl Ocean Res 91:101902

    Article  Google Scholar 

  27. Sileri D, Sahu KC, Matar OK (2011) Two-fluid pressure-driven channel flow with wall deposition and ageing effects. J Eng Math 71:109–130

    Article  MathSciNet  MATH  Google Scholar 

  28. Alkharashi SA (2012) Stability of viscous fluids in the presence f the porosity effect, Ph.D. thesis Tanta University

  29. Kiran GR, Murthy VR, Radhakrishnamacharya G (2019) Pulsatile flow of a dusty fluid thorough a constricted channel in the presence of magnetic field. Mater Today Proc 19:2645–2649

    Article  Google Scholar 

  30. Hosham HA, Hafez NM (2022) Global dynamics and bifurcation analysis for the peristaltic transport through nonuniform channels. J Comput Nonlinear Dyn 17:061001–061011

    Article  Google Scholar 

  31. Drazin PG, Reid WH (1981) Hydrodynamic stability. Univ. Press, Cam bridge

    MATH  Google Scholar 

  32. Alkharashi SA, Sirwah MA (2021) Dynamical responses of inclined heated channel of MHD dusty fluids through porous media. J Eng Math 130:5

    Article  MathSciNet  MATH  Google Scholar 

  33. Nayfeh AH (1979) Nonlinear oscillations. Wiley, Virginia

    MATH  Google Scholar 

  34. Zakaria K, Sirwah M, Alkharashi S (2008) Temporal stability of superposed magnetic fluids in porous media. Phys Scr 77:1–20

    Article  MATH  Google Scholar 

  35. Assaf A, Alkharashi SA (2019) Hydromagnetic instability of a thin viscoelastic layer on a moving column. Physica Scripta 94:045201

    Article  Google Scholar 

  36. Sirwah MA, Zakaria K (2013) Nonlinear evolution of the travelling waves at the surface of a thin viscoelastic falling film. Appl Math Model 37:1723–1752

    Article  MathSciNet  MATH  Google Scholar 

  37. Alkharashi SA, Assaf A, Al-Hamad Kh, Alrashidi A (2019) Performance evaluation of insoluble surfactants on the behavior of two electric layers. J Appl Fluid Mech 12(2):573–586

    Article  Google Scholar 

  38. Hafez NM, Assaf A (2023) Electrohydrodynamic stability and heat and mass transfer of a dielectric fluid flowing over an inclined plane through porous medium with external shear stress. Eur Phys J Plus 138:28

    Article  Google Scholar 

  39. Alkharashi SA, Al-Hamad Kh, Alrashidi A (2023) Outlining the impact of structural properties of a multilayered porous channel with oscillating velocities and fields. Dyn Atmos Oceans 12:101366

    Article  Google Scholar 

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Acknowledgements

This work was supported and funded by” The Research Program of Public Authority for Applied Education and Training in Kuwait”, Project No. (TS-22-07).

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Authors and Affiliations

  1. Department of Laboratory Technology, College of Technological Studies, PAAET, Shuwaikh, Kuwait

    Sameh A. Alkharashi & Wafa Alotaibi

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  1. Sameh A. Alkharashi
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  2. Wafa Alotaibi
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All authors reviewed the manuscript.

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Correspondence to Sameh A. Alkharashi.

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Alkharashi, S.A., Alotaibi, W. Structural stability of a porous channel of electrical flow affected by periodic velocities. J Eng Math 141, 3 (2023). https://doi.org/10.1007/s10665-023-10278-3

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  • DOI: https://doi.org/10.1007/s10665-023-10278-3

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