The theory of dispersion of chemically active solutes in a rectilinear flow field: The vector problem

In this paper and its sequel we seek an understanding of diffusion and reaction processes in multicomponent systems under convective conditions. To do this, we construct dispersion approximations to c, the solution of the vector convective diffusion equation, and to its transverse average, . Dispersion coefficients are not the direct route to dispersion approximations in the vector problem. Yet constant long time dispersion coefficients exist and imply a rearrangement of the Hermite expansion of . We deduce the rearrangement and introduce useful approximations thereto.