AN 'EXACT' SOLUTION FOR THE HYDRODYNAMIC INTERACTION OF A THREE-DIMENSIONAL FINITE CLUSTER OF ARBITRARILY SIZED SPHERICAL PARTICLES AT LOW REYNOLDS NUMBE

The slow motion of particles in an incompressible Newtonian fluid occurs in many physical processes and therefore the study of this problem is important both from a practical and theoretical point of view. This thesis contains an "exact" solution for the hydrodynamic interaction of a three-dimensional finite cluster of arbitrarily sized spherical particles at low Reynolds number. The theory developed is the most general solution to the problem of an assemblage of spheres in a three-dimensional unbounded media. The formulation is based on the boundary-collocation truncated-series solution technique where the orthogonality properties of the eigenfunctions in the azimuthal direction are used to satisfy the no-slip boundary conditions exactly on entire rings on the surface of each particle.;Detailed comparisons with the exact two sphere solutions shows the present theory to be accurate to at least five significant figures in predicting the translational and angular velocity components of the particles at all orientations for interparticle gap widths as close as 0.1 particle diameter. Solutions are presented for several interesting and intriguing configurations involving 3 or more spherical particles in a uniform flow, shear flow and Poiseuille flow. Advantage of symmetry about the origin is used for symmetric configurations to reduce the collocation matrix size by a factor of 64. Solutions for the force and torque on three dimensional clusters of up to 64 particles have been obtained demonstrating the multi-particle interaction effects that arise which would not be present if only pair interactions of the particles were considered. The method has the advantage of yielding a rather simple expression for the fluid velocity field which is of significance in the treatment of convective heat and mass transport problems in multiparticle systems. Among other interesting applications of the theory presented are the time dependent motion of three spheres with fixed interparticle spacings in shear flow and the motion of a single sphere in the presence of other fixed spheres to study the resuspension phenomena in a simple shear flow.