Stokes flow of a micropolar fluid past an assemblage of spheroidal particle-in-cell models with slip

Abstract

In a cell model it is assumed that the three-dimensional assemblage may be considered to consist of a number of identical unit cells, each of which contains a particle surrounded by a fluid envelope with a fictitious surface (free surface) containing a volume of fluid sufficient to make the fractional void volume in the cell identical to that in the entire assemblage. The quasi-steady axisymmetric translational motion of a spherical or spheroidal cell of an incompressible micropolar fluid is investigated utilizing the cell model method. The inner particle of the cell is assumed to be solid and the outer to be fictitious. Linear velocity and microrotation slip boundary conditions on the surface of the solid particle are proposed. Normalized mobility is obtained for both spherical and spheroidal particles in the cell model and is represented graphically. Expressions for the superficial fluid velocity through an assemblage of spherical and spheroidal particles are obtained.