Diffusivity and Mass Transport Nomenclature

Transport of mass or diffusion of mass takes place in a fluid mixture of two or more species whenever there is a spatial gradient in the proportion of the mixture, that is, a concentration gradient. Consider a two-component or binary system, for example, a glass of water into which a drop of colored dye is injected. As is known from experience, the dye will diffuse outward from the point of injection where the concentration is highest compared to the other portions of the water where there is no dye. The transport of dye molecules is equal and opposite to the transport of the water molecules, and after a sufficient time, an equilibrium state is achieved with a uniform mixture of dye and water. In a solution or mixture, there are a variety of ways of defining concentration. The two basic concentration units used are mass concentration and molar concentration. Let a solution be made up of i number of species. The concentration parameters can be expressed in a variety of ways as follows  

Quantities of interest for diffusive transport are mass flux and molar flux  

There are a number of definitions of the average velocity characterizing the bulk motion of a multicomponent system, where each species is moving at a different speed. Often, the solvent velocity is used as a reference velocity. Another reference velocity is the mass average velocity defined as 

In equations (4.15) and (4.16), the terms inside the summation represent the individual mass and molar fluxes of each species f with respect to fixed coordinates, respectively. 

In flow systems, the mass and molar fluxes with each species motion in reference to the mass average and molar average velocities are written as 

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