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9.2 Gas-Liquid Systems 251
In this case, the solution of equation 9.2-39 with boundary conditions 9.2-31a and
9.2-33b is
(9.2-46)
From equation 9.2-46, using equation 9.2-43, we obtain an expression for NA (z = 0),
which also represents (- rA), since all reaction takes place in the liquid film:
and, on elimination of c& by means of equations 9.2-3 and -8 to take the gas-film resis-
tance into account, as in Section 9.2.3.4.1,
(9.2-48)
Comparison of equation 9.2-48 with 9.2-27 shows that, for this case, the enhancement
factor is
E = Ha/ tanh(Ha) (9.2-49)
9.2.3.4.3. Fast second-order reaction in IiquidJilm only. For a reaction that is second-
order, first-order with respect to each of A and B, we have
(9.230)
In this case, an exact analytical solution of the continuity equations for A and B does
not exist. An approximate solution has been developed by Van Krevelen and Hoftijzer
(1948) in terms of E. Results of a numerical solution could be fitted approximately by
the implicit relation
E = $/tanh$ (9.2-51)
where
(9.2-52)
Ei is the enhancement factor for an instantaneous reaction (see problem 9-ll(c)):
