Scaling properties of time-space kinetic mass transport equations and the local equilibrium limit

Abstract

Scaling properties of kinetic mass conservation equations are presented, and their implications investigated for advective and diffusive transport in an isothermal system in a single spatial dimension. It is demonstrated that for a system undergoing pure advection, scaling the kinetic rate constants by a common factor, thereby preserving their ratios, is equivalent to scaling the time and space coordinates of the original solution. Diffusive transport requires that the diffusion coefficient must also be scaled by the reciprocal factor. These results have far reaching consequences on the possible form of solutions of the kinetic mass transport equations. -from Author