Different Forms of Fick's First Law in a Biinary System: Table 17.8-2
After executing Table17defs.mws with ncom=2
>  dx:=array(1...2); domeg:=array(1...2); To hold differentials of mol and mass fractions
>  dx[1]:=simplify(diff(x[1],c[1])); Assume that c[1] changes slightly: here is the change in x[1].

>  domeg[1]:=simplify(diff(omega[1],c[1])); Here is the change in omega[1].

>  j1:=simplify(j[1]); Here is the basic definition of the js ( mass flux relative to the mass average velocity) in terms of the velocities of the species. This was set in table17defs.mws.

>  Jstar1:=simplify(Jstar[1]); And this is the definition of the molar flux relative to the mol average velocity

>  j1c1:=-simplify(rhotot*DAB*domeg[1]*dc1); Equation A in Table 17.8-2 where dc1 stands for the gradient of c[1]

>  Jstar1c1:=-simplify(ctot*DAB*dx[1]*dc1); Equation B in Table 17.8-2

>  j1/Jstar1; From the definitions in table17defs.mws

>  j1c1/Jstar1c1; From the relations given in table17defs.mws

>  simplify(%-j1/Jstar1);

It is apparent that the two ratios are identical; thus the two definitions of Fick's Law are equivalent