Expressions for the mass flux 

(a) Show how to transform the left side of Eq. 24.2-8 into the left side of Eq. 24.2-9. First rewrite the former as follows: 

Rewrite the second term as a sum over all 13, and then add a term to compensate for the modification of the sum. Note that this change has introduced into the sum a term containing D_aa, which was not defined because it was not needed. Now, we are at liberty to define D_aa in any way we choose, and the choice we make is this choice enables us to obtain the left side of Eq.24.2-9, and also the auxiliary relation given after Eq. 24.2-9 is, in fact, just Eq. 24C.1-3 above.

(b) Next repeat the above derivation by replacing v_β by [v_β + (DT_β/p_β) ∆ in T], and verify that both the diffusion terms and the thermal diffusion terms of Eq. 24.2-8 may be transformed into the corresponding terms in Eq. 24.2-9.

XaXB XB (v, V) %3D , (v, - e B+a B- B+a XB XB = 0 D Xa or a B=1 B+a B=1 all B 2