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Effect of magnetic field on the motion of two rigid spheres embedded in porous media with slip surfaces

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Abstract

A semi-analytical study for the Stokes flow approximation caused by two solid spheres of different sizes with slip surfaces, immersed in a porous medium in the presence of a transverse magnetic field, is investigated. The two spheres are translating with different velocities along the line joining their centers. A general solution is developed from the superposition of the essential solutions in two spherical frameworks with origins located at the centers of the two spheres. Numerical results for the normalized hydrodynamic drag force acting on each sphere are obtained with good convergence for various values of the Hartmann number which characterizes the presence of magnetic field, the permeability parameter which characterizes the porous medium, separation parameter, and velocity and size ratios of the spheres. Our drag results are in good agreement with the available solutions in the literature in the cases of no-slip surfaces and when the porous medium turns into a pure fluid.

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Acknowledgements

This research was funded by the Deanship of Scientific Research at  Princess  Nourah  bint  Abdulrahman University through the Fast-track Research Funding Program.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Kingdom of Saudi Arabia

    Shreen El-Sapa & Noura S. Alsudais

  2. Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt

    Shreen El-Sapa

Authors
  1. Shreen El-Sapa
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  2. Noura S. Alsudais
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Correspondence to Shreen El-Sapa.

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El-Sapa, S., Alsudais, N.S. Effect of magnetic field on the motion of two rigid spheres embedded in porous media with slip surfaces. Eur. Phys. J. E 44, 68 (2021). https://doi.org/10.1140/epje/s10189-021-00073-2

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  • DOI: https://doi.org/10.1140/epje/s10189-021-00073-2

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