Hydrodynamic interactions in colloidal crystals (I). General theory for simple and compound lattices

A new method is presented for low-Reynolds-number flow problems involving periodic arrays of spherical particles. The method is based on an exact technique to calculate quasi-static hydrodynamic interactions between a finite number of spheres immersed in an unbounded Newtonian fluid. This technique is applied to an infinite system defined by periodic cells containing an arbitrary configuration of N rigid spheres. The N spheres may be differently sized. Using the translational symmetry of the periodic cells, the set of equations representing all hydrodynamic interactions in the infinite array, is decoupled. The set of decoupled equations resembles that for an isolated group of N particles.