Section 21.3 Binary Mass-Transfer coefficients in Two Phases

> restart;

> eq11:=NA0=kx*(xA0-xAb)+xA0*(NA0+NB0); The nomenclature from eq. 21.1-11 is easier to type than that from eq. 21.1-10.

> NB0:=0;

> eq11; We will need an equation like this for each of the phases.

> eqliq:=NAliq=kx*(xA0-xAb)+xA0*NAliq;

> eqgas:=NAgas=ky*(yA0-yAb)+yA0*NAgas;

> N1:=solve(eqliq,NAliq); The flux from the interface to the liquid.

> N2:=solve(eqgas,NAgas); The flux from the interface to the gas.

> eqkk:=N1+N2=0; The net flow to the interface must be zero.

> eqkk:=N1=-N2; Another way of showing this realtion.

> eqkk:=N2/N1=-1; One more.

> eqkk:=kx/ky*N2/N1=-kx/ky; Mulitply both sides of that last equation by kx/ky to get:

> eqkk:=(1-yA0)/(1-xA0)*kx/ky*N2/N1=-(1-yA0)/(1-xA0)*kx/ky; Now multiply both sides by (1-yA0)/(1-xA0).

> simplify(%); Close to eq. 21.3-4.

> eqOVA:=NAgas=Ky*(yAe-yAb)+yAe*NAgas; Using an "over-all mass transfer" coefficient in the gas phase: Ky. Note that yAe=f(xAb).

> N3:=solve(eqOVA,NAgas);

> 1/N3; Starting to put this in a form that could lead to eq. 21.3-8.

> lhs8:=simplify((yAe-yAb)/N3); This is the Left Hand Side of eq. 21.3-8.

> eq7:=yAe-yAb=my*(xAb-xA0)+yA0-yAb; eq. 21.3-7. my is the slope found by: (yAe-yA0)/(xAb-xA0).

> eq7/Ns; The LHS of this is the same as lhs8.

> my*(xA0-xAb)/N1; Remember that N1 = - N3, so this is the first term on the RHS of eq7/Ns.

> simplify((yA0-yAb)/N2); This is the 2nd term on the RHS of eq7/Ns.

> rhs8:=my*(xA0-xAb)/N1+%; This is the RHS of eq7/Ns.

> eq8:=lhs8=rhs8; Thus we finally get eq. 21.3-8.

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