Projection operator analysis of macrotransport processes

Projection operator methods are used to derive a systematic perturbation expansion scheme that provides formal justification for the otherwise ad hoc arguments underlying generalized Taylor dispersion theory. The latter theory is a coarse-graining procedure for eliminating the internal variables from multidimensional phase-space convective-diffusion-type transport equations in the limit of long times. In addition to rationalizing the otherwise ad hoc Lagrangian moment scheme, projection operator methods are further used to: (i) investigate nonasymptotic effects arising from ‘‘memory’’ of the initial conditions; (ii) establish the existence of higher-order contributions beyond second-order terms in the physical-space spatial gradients. Explicit criteria are developed for when these third- and higher-order non-Gaussian terms may be neglected in the coarse-grained, Taylor dispersion or macrotransport equation.