Revised Model for Molecular Diffusion and Advection

Abstract

Molecular diffusion of fluid constituents currently is most frequently defined as a flux relative to the mean flux. Different interpretations of “mean flux” exist in the literature; usually it refers to the mass average flux of a solution as a whole. The flux of constituents relative to the mean flux must sum to zero, and consequently diffusion, as currently defined, does not exist in a fluid consisting of a single constituent. Diffusion, as understood by the pioneers, applied to the flux of a single-species fluid as well as the flux of a constituent in a fluid mixture. The purpose of this study was to show that the current definition of diffusion is illogical because “mean flux” is not independent of diffusive flux. Defining diffusion as a flux proportional to a gradient of kinetic energy is consistent with diffusive flux as understood by the early investigators of diffusion, provided the kinetic energy gradients of a particular molecular species are correctly identified. For example, diffusive fluxes of ideal gas constituents are proportional to their partial pressure gradients, and diffusive flux of pure liquid water is proportional to its vapor pressure gradient. Advection is defined here as a volume flux (of a solution as a whole) in response to a pressure gradient and a body force. We evaluate the total flux of a solution as a whole as the vector sum of advection and diffusive fluxes of all constituents.