Archive of Mechanical Engineering

Abstract

The perspective of the current analysis is to represent the incompressible viscous flow past a low permeable spheroid contained in a fictitious spheroidal cell. Stokes approximation and Darcy's equation are adopted to govern the flow in the fluid and permeable zone, respectively. Happel's and Kuwabara's cell models are employed as the boundary conditions at the cell surface. At the fluid porous interface, we suppose the conditions of conservation of mass, balancing of pressure component at the permeable area with the normal stresses in the liquid area, and the slip condition, known as Beavers-Joseph-Saffman-Jones condition to be well suitable. A closed-form analytical expression for hydrodynamic drag on the bounded spheroidal particle is determined and therefore, mobility of the particle is also calculated, for both the case of a prolate as well as an oblate spheroid. Several graphs and tables are plotted to observe the dependence of normalized mobility on pertinent parameters including permeability, deformation, the volume fraction of the particle, slip parameter, and the aspect ratio. Significant results that influence the impact of the above parameters in the problem have been pointed out. Our work is validated by referring to previous results available in literature as reduction cases.