A rigorous theory of Brownian particle flow and dispersion phenomena in spatially periodic structures is presented within the context of generalized Taylor dispersion theory. The analysis expands upon a prior work, which was limited to transport within the continuous phase, to include convective and diffusive transport of the tracer particle within the interior of the discontinuous phase, as well as surface adsorption and transport along the phase boundary separating the discontinuous and continuous phases. Incorporated within the generalization are considerations of tracer particles of non-zero size, and situations wherein external forces act upon the tracer, the novel effect of each being to cause the tracer to move with a different velocity from that of the fluid in which it is suspended. Applications to various chromatographic separation phenomena are cited. Extensions of the analysis to heat-transfer problems and to situations involving homogeneous, first-order chemical reactions are also made. Both Eulerian and Lagrangian interpretations of the tracer transport phenomena are given.