  A straightforward analytical scheme is proposed for computing the long-time,
asymptotic mean velocity and dispersivity (effective diffusivity) of a particle
undergoing a discrete biased random walk on a periodic lattice amongst an array
of immobile, impenetrable obstacles. The results of this Taylor-Aris
dispersion-based theory are exact, at least in an asymptotic sense, and furnish
an analytical alternative to conventional numerical lattice Monte Carlo
simulation techniques. Results obtained for an obstacle-free lattice are
employed to establish generic relationships between the transition
probabilities, lattice size and jump time. As an example, the dispersivity is
computed for a solute moving through an isotropic array of obstacles under the
influence of a finite external field. The calculation scheme is also shown to
agree with existing zero-field results, the latter obtained elsewhere either by
first-passage time analysis or use of the Nernst-Einstein equation in the
zero-field limit. The generality of this scheme permits the study of more
complex lattice structures, in particular trapping geometries.
