The numerical methods of Zientara and Freed [J. Phys. Chem. 83, 3333 (1979)] have been used to study the diffusion-controlled kinetics of domain coalescence in order to ultimately consider the time evolution of protein folding. The mean coalescence lifetime for a domain pair has been calculated using the eigenfunction expansion method and finite differences in the solution of a modified form of the Smoluchowski equation. This approach allows for an orientational preference in the domain coalescence process, which has been studied throughout the complete range of reactivities. Three cases of interdomain forces were investigated, one of which represents the shielding of charged domains by ions in solution. As the forces vary from the strongly repulsive to the strongly attractive in these cases, the coalescence lifetime decreases by several orders of magnitude. In addition, a hydration shell model, which provides an activation barrier to coalescence, has been analyzed. The lifetimes resulting from this model were observed to depend strongly on the location and extent of the hydration shell. Anisotropic initial conditions were also incorporated causing, in some cases, non-negligible effects upon the coalescence lifetimes.