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;
> plot(eq,n1=0...1e-6);
> fsolve(eq,n1=0...1e-6)*mol/cm^2/s; N1: BS&L found .5523e-6 by assuming the two diffuvities were equal.