Different Forms of Fick's First Law: Table 16.2-1
After executing Table161defs
> dx:=array(1...2); domeg:=array(1...2); To hold differentials of mol and mass fractions
> dx[1]:=diff(x[1],c[1]); Assume that c[1] changes slightly
> domeg[1]:=simplify(diff(omega[1],c[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
> Jstar1:=simplify(Jstar[1]); And this is the definition of the molar flux relative the the mol average velocity
> j1c1:=-simplify(rhotot*DAB*domeg[1]*dc1); Equation C in Table 16.2-1 where dc1 stands for the gradient of c[1]
> Jstar1c1:=-simplify(ctot*DAB*dx[1]*dc1); Equation D in Table 16.2-1
> j1/Jstar1; From the definitions in Tables 16.1-1, 2, 3
> j1c1/Jstar1c1; From the relations given in Table 16.2-1
It is apparent that the two ratios are identical; thus the two definitions of Fick's Law are equivalent