Definitions of Concentrations and Velocities

The concentrations of the species in a multicomponent system can be expressed in various forms. Four of these forms, which are the most fl equently used, are the following. Mass concentration, pi, is the mass of species i per unit volume of the solution. Similarly, molar concentration, Ci, is the number of moles of species i per unit volume of the solution. Mass fraction, , , is the mass of species i divided by the total mass of the solution. Finaliy, the mole fraction, Xi, is the number of moles of species i divided by the total number of moles of the solution. The total mass and molar concentrations are p and C, respectively, so that ,- and Xi are given as 

The species in a diffusing mixture move with different velocities. If v,- is the velocity of the ith species with respect to a fixed coordinate system, then the mass average bulk velocity, v, is defined as 

TABLE 4.1 Definitions for Concentrations in Binary Systems TABLE 4.2 Definitions for Velocities in Binary Systems 

Va = velocity of species A relative to fixed coordinates Va — V = diffusion velocity of species A relative to v Va — V = diffusion velocity of species A relative to v Va — V = diffusion velocity of species A relative to v V = mass average velocity 

Finally, the volume average bulk velocity, v, is defined as 

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