Page 424 - Modelling in Transport Phenomena A Conceptual Approach
P. 424
404 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.
where erf(x) is the error function defined by
2 "
erf(x) = - 1 e-U2du (9.5-130)
J;;
Macroscopic equation
Integration of the governing equation, Eq. (9.5-108), over the volume of the system
gives the macroscopic equation as
Evaluation of the integrations yields
Net molar rate of species A Molar rate of species A entering
entering into the liquid into the liquid through interface
Note that Eq. (9.5-132) is the macroscopic inventory rate equation for the mass of
species A by considering the falling liquid film as a system. The use of Eq. (9.5-
129) in Eq. (9.5-132) gives the rate of moles of species A absorbed in the liquid
The rate of moles of species A absorbed by the liquid can be expressed in terms of
the average mass transfer coefficient as
Since ln(1 + x) N x for small values of x, the term in the denominator of Eq.
(9.5134) can be approximated as
(9.5-135)
