Slow Motion of a Porous Sphere Translating Along the Axis of a Circular Cylindrical Pore Subject to a Stress Jump Condition

• Published in: Transport in porous media Vol. 102; no. 1; pp. 91 - 109
• Main Authors: Saad, E. I., Faltas, M. S.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2014; Springer; Springer Nature B.V
• Subjects: Boundary conditions; Brinkman model; Circularity; Civil Engineering; Classical and Continuum Physics; Collocation methods; Computational fluid dynamics; Coordinates; Cylindrical coordinates; Drag; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Exact sciences and technology; Fluid flow; Fourier transforms; Geotechnical Engineering & Applied Earth Sciences; Hydrocarbons; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Incompressible flow; Industrial Chemistry/Chemical Engineering; Pollution, environment geology; Sedimentary rocks; Shape effects; Spherical coordinates; Viscous fluids; Normalized drag force; Circular cylindrical pore; Porous sphere; Stress jump; stress; models; interfaces; Fourier transformation; permeability; coordinates; hydrodynamics; transport; velocity; particles; boundary conditions; porous media; methodology
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-013-0263-6

The coupled flow problem of an incompressible axisymmetrical quasisteady motion of a porous sphere translating in a viscous fluid along the axis of a circular cylindrical pore is discussed using a combined analytical–numerical technique. At the fluid–porous interface, the stress jump boundary condition for the tangential stress along with continuity of normal stress and velocity components are employed. The flow through the porous particle is governed by the Brinkman model and the flow in the outside porous region is governed by Stokes equations. A general solution for the field equations in the clear region is constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinate systems. The boundary conditions are satisfied first at the cylindrical pore wall by the Fourier transforms and then on the surface of the porous particle by a collocation method. The collocation solutions for the normalized hydrodynamic drag force exerted by the clear fluid on the porous particle is calculated with good convergence for various values of the ratio of radii of the porous sphere and pore, the stress jump coefficient, and a coefficient that is proportional to the permeability. The shape effect of the cylindrical pore on the axial translation of the porous sphere is compared with that of the particle in a spherical cavity; it found that the porous particle in a circular cylindrical pore in general attains a lower hydrodynamic drag than in a spherical envelope.