Hydrodynamic analysis of porous spheres with infiltrated peripheral shellsin linear flow fields

The velocity fields inside and around porous spheres with infiltrated perip heral shells were solved for three different far-field flows: simple shear, planar elongation and uniaxial extension. The flow was considered to obey Stokes' law around the porous sphere and Brinkman's extension of Darcy's la w within an infiltrated spherical shell beneath the sphere surface. The inf iltrated layer, resulting from capillary action, was assumed to have a thic kness that remained unaffected when the porous sphere was subjected to exte rnal flow fields. The cumulative hydrodynamic force exerted by the fluid up on the solid portion of the porous sphere was calculated for spherical caps with planar fracture surfaces. The magnitude of the tensile component of t he hydrodynamic force per unit area of the base of the cap was shown to inc rease with the size of the cap and with the thickness of the infiltrated la yer. On the other hand, the magnitude of the shear component of the hydrody namic force per unit area of the base of the cap exhibited a maximum for a given cap size. The cap size that maximized the shear force increased with the thickness of the infiltrated layer. However, in contrast to the tensile force, for a constant cap size, the shear force did not necessarily increa se with the thickness of the infiltrated layer. The hydrodynamic force exer ted by the fluid upon the solid was found to increase with the inverse of t he permeability of the porous sphere. The limit for very low permeability w as compared to the case of an impermeable sphere. In the case of the tensil e force, there was a difference between the low permeability limit for a pe rmeable sphere and the value corresponding to an impermeable sphere. This d ifference could be attributed to the presence of fluid within the permeable sphere. The fluid contained in the permeable sphere could transmit pressur e to the solid, a contribution absent in the case of an impermeable sphere. (C) 2001 Elsevier Science Ltd. All rights reserved.