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Thermophoresis of Cylindrical Particle Immersed in Brinkman Fluid

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Abstract

This paper reports an analytical study for the thermophoresis of a circular cylindrical aerosol particle embedded in a porous medium of constant porosity based on the Brinkman model. The Knudsen number is supposed to be in the slip-flow regime. The Peclet and Reynolds numbers are small, therefore the convective effects are neglected, and the problem can be considered quasi-steady. The porous medium is supposed to be homogeneous, isotropic and the solid phase is in thermal equilibrium with the fluid through the voids of the medium. In the analysis of motion, at the surface of the particle, we consider the following effects: temperature jump, thermal creep, viscous slip, and thermal stress slip. Formulas for thermophoretic velocity and force are derived. The novelty of the problem is the permeability parameter which characterizing the Brinkman flow. The effect of this parameter is shown through several plots for thermophoretic velocity and force against the thermal properties of the particle and porous medium. The limiting cases of Stokes and Darcy’s flows and the case of no thermal slip are discussed. results are also compared with the corresponding values for the case of spherical particles.

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Authors and Affiliations

  1. Department of Mathematics and Computer science, Faculty of Science, Alexandria University, Alexandria, Egypt

    M. S. Faltas &  Kareem E. Ragab

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  1. M. S. Faltas
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  2. Kareem E. Ragab
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Correspondence to Kareem E. Ragab.

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Faltas, M.S., Kareem E. Ragab Thermophoresis of Cylindrical Particle Immersed in Brinkman Fluid. Colloid J 83, 676–687 (2021). https://doi.org/10.1134/S1061933X2106003X

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  • DOI: https://doi.org/10.1134/S1061933X2106003X

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