Multiple-timescale analysis of Taylor dispersion in converging and diverging flows

A multiple-timescale analysis is employed to analyse Taylor-dispersion-like convective-diffusive processes in converging and diverging flows. A long-time asymptotic equation governing the cross-sectionally averaged solute probability density is derived. The form of this equation is shown to be dependent upon the number of spatial dimensions characterizing the duct or 'cone'. The two-dimensional case (non-parallel plates) is shown to be fundamentally different from that for three dimensions (circular cone) in that, in two dimensions, a Taylor dispersion description of the process is possible only for small Peclet numbers or angles of divergence. In contrast, in three dimensions, a Taylor dispersion description is always possible provided sufficient time has passed since the initial introduction of solute into the system. The convective Taylor dispersion coefficients D c for the respective cases of low-Reynolds-number flow between non-parallel plates and in a circular cone are computed and their limiting values, D c 0 , for zero apex angle are shown to be consistent with the known results for Taylor dispersion between parallel plates and in a circular cylinder.