The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of slip eccentric spherical particle-in-cell models with Happel and Kuwabara boundary conditions is investigated. A linear slip, Basset type, boundary condition on the surface of the spherical particle is used. Under the Stokesian approximation, a general solution is constructed from the superposition of the basic solutions in the two spherical coordinate systems based on the particle and fictitious spherical envelope. The boundary conditions on the particle's surface and fictitious spherical envelope are satisfied by a collocation technique. Numerical results for the normalized drag force acting on the particle are obtained with good convergence for various values of the volume fraction, the relative distance between the centers of the particle and fictitious envelope and the slip coefficient of the particle. In the limits of the motions of the spherical particle in the concentric position with cell surface and near the cell surface with a small curvature, the numerical values of the normalized drag force are in good agreement with the available values in the literature.

The Stokes axisymmetrical flow caused by a sphere translating in a micropolar fluid perpendicular to a plane wall at an arbitrary position from the wall is presented using a combined analytical-numerical method. A linear slip, Basset type, boundary condition on the surface of the sphere has been used. To solve the Stokes equations for the fluid velocity field and the microrotation vector, a general solution is constructed from fundamental solutions in both cylindrical, and spherical coordinate systems. Boundary conditions are satisfied first at the plane wall by the Fourier transforms and then on the sphere surface by the collocation method. The drag acting on the sphere is evaluated with good convergence. Numerical results for the hydrodynamic drag force and wall effect with respect to the micropolarity, slip parameters and the separation distance parameter between the sphere and the wall are presented both in tabular and graphical forms. Comparisons are made between the classical fluid and micropolar fluid. (2000). 76A05, 76D99. Mathematics Subject Classification

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The method of associated matrices is used to obtain Galerkin type representations. Fundamental solutions are then obtained for the cases of a point body couple and a point microstretch force. A formula for calculating the total couple acting on a rigid body rotating axi-symmetrically in a microstretch fluid is deduced. A generalized reciprocal theorem is deduced. An application for a rigid sphere rotating in a microstretch fluid is discussed. The results of the application are represented graphically.

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