Velocity molar diffusion

See also Problem 12.12.) The mixture-averaged diffusion coefficient of Eq. 12.176 was derived for use in calculating the molar diffusion velocity J with respect to the molar average velocity V, as in Eq. 12.172. 

Here w, is the mass fraction of component i. We can express the molar diffusion flow J(A, based on the molar average velocity vM... 

On the other hand, we could choose u as the reference velocity and define molar diffusion fluxes relative to it as... 

These are the most commonly encountered sets of fluxes other sets could be defined. We could, for example, define a mass diffusion flux relative to the molar average velocity or a molar diffusion flux relative to the mass average velocity. Still other choices of reference velocity are sometimes used for example, the volume average velocity... 

In a similar way we define the molar diffusion flux relative the velocity m" by... 

To relate the molar diffusion flux relative to the volume average velocity to the molar diffusion flux relative to the molar average reference velocity we use the transformation... 

Molar diffusion flux relative to arbitrary reference velocity... 

In place of the molar diffusion flux with respect to the molar average velocity we may use the diffusion fluxes in the volume average reference velocity frame uY, in which case Fick s law takes the form... 

Starting from the definitions of the molar diffusion fluxes in the molar average velocity reference frame and in volume average velocity reference frame (Table 1.3), verify Eqs. 1.2.20 and 1.2.22. These equations may be written in n — 1 dimensional matrix form as... 

Obtain an equation similar to Eqs. 1.2.20 or 1.2.22 that transforms the molar diffusion flux relative to an arbitrary reference velocity m" to the molar diffusion flux relative to some other arbitrary reference velocity u. Verify that Eqs. 1.2.20 and 1.2.22 are special cases of the general result. 

Molar diffusion flux relative to the mass average reference velocity [mol/m s] Molar turbulent diffusion flux of component i [mol/m s]... 

The molar diffusion flux J, is defined with respect to the molar average velocity,... 

In Section 2.2 bulh the mass diffusive flux relative to the mass average velocity and the molar diffusive flux relative to the molar average velocity were defined ... 

Define the following terms mass-average velocity, molar-average velocity, mass (or molar) flux, and diffusion mass (or molar) flux. 

Ay ss diffusion velocity, m/s Ay molar diffusion velocity, m/s velocity of species A in the y-phase, m/s... 

But this is not all, the same diffusion coefficient D may be used if we use molar quantities in formulation of Pick law for this binary concentration diffusion, cf. (4.562) below. Specifically, using the molar diffusion flow of constituent 1 defined as the corresponding (specific) diffusion flow given above divided by the molar mass Ml of the first constituent (molar quantities are denoted, in addition, by apostrophe e.g. the molar diffusion flow relatively to volume average velocity as... 

The molar diffusion flux relative to the mass average velocity v is... 

Component A diffuses due to the concentration gradient -dc /d. Component B diffuses due to the mean molar velocity v, v = (+ CgVg )lc, like a fish swimming upstream with the same velocity as the flowing water, /y = 0, with regard to a fixed point. 

For the mass balance of component A, diffusion velocity and the corresponding diffusion factor are defined with regard to the mean molar velocity V, defined by the equation... 

---