Section 18.8 Diffusion in a Three-component System
> restart;
> n:=3;N:=array(1..n,[N1,0,0]);
> x:=array(1..n,[1-x2(z)-x3(z),x2(z),x3(z)]);delx:=array(1...n,[diff(x1(z),z),diff(x2(z),z),diff(x3(z),z)]);
> cDif:=array(1..n,1..n);
> des:=array(1...n);
> for i from 1 to n do
> des[i]:=delx[i]-sum((x[i]*N[j]-x[j]*N[i])/cDif[i,j],j=1...n); The Stefan-Maxwell equations: 17.9-1
> od;
Compare delx[2] and delx[3] with equations 18.8-2,3
> s2:=dsolve({des[2],x2(L)=x2L},x2(z));
> assign(s2);x2:=unapply(x2(z),z);
> s3:=dsolve({des[3],x3(L)=x3L},x3(z));
> assign(s3);x3:=unapply(x3(z),z);
> x1:=unapply(x[1],z); eq. 18.8-8
> eq:=x1(0)-x10; eq. 18.8-9
> c:=3.46e-5*mol/cm^3;
> D12:=.364*cm^2/s;D13:=.357*cm^2/s;
> cDif[2,1]:=c*D12;cDif[3,1]:=c*D13;
> eq;
> x10:=.449;L:=11.2*cm;x2L:=0.75;x3L:=.15;
> eq;
> N1:=n1*mol/cm^2/s;eq;
![[Maple Math]](images/sec1882.gif)
> plot(eq,n1=0...1e-6);
![[Maple Plot]](images/sec1883.gif)
> fsolve(eq,n1=0...1e-6)*mol/cm^2/s; N1: BS&L found .5523e-6 by assuming the two diffuvities were equal.
![[Maple Math]](images/sec1884.gif)