On diffusion velocity and the mass conservation equation for components

Abstract

The mass migration velocity (absolute velocity) of component i in a multicomponent flow is equal to the convection velocity (frame velocity) plus the diffusion velocity (relative velocity). The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.

In turbulent flow, the mass migration velocity of component i is$\bar v_1^\rho$ (mass-weighted time average velocity). The diffusion velocity ($\bar v_1^\rho - a$) consists of turbulent diffusion velocity ($\bar v_1^\rho - \bar v_1$) and molecular diffusion velocity$\overline {v_1 - a}$ ($\bar v_1$ is the simple time average velocity of component i anda is a certain convection velocity). So, the part of turbulent diffusion velocity is independent of what convection velocity is taken.

In the mass conservation equation for component i, the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes. In turbulent flow, there could be no diffusion terms or a turbulent diffusion term only or both the turbulent and molecular diffusion terms when$\bar v_1^\rho$, or$\bar v_1$, or any velocity other than these two is taken as the convection velocity. The case, in which there could be molecular diffusion only without turbulent diffusion, occurs in laminar flow. The molecular diffusion term always depends on the adoption of convection velocity.

In two-phase flow, the value of the molecular diffusion term is often near or even exceeds that of the turbulent diffusion term, which is quite different from the case in gas mixture flow.