Page 107 - Separation process principles 2

72 Chapter 3 Mass Transfer and Diffusion

Note that ug is zero everywhere, because its molecular-diffusion Table 3.1 Diffusion Volumes from Fuller,
velocity is negated by the molar-mean velocity. Ensley, and Giddings [J. Phys. Chem, 73,
3679-3685 (1969)l for Estimating Binary Gas
(e) The mass-transfer flux for benzene evaporation can be equated
Diffusivity by the Method of Fuller et al. [3]
to the rate of decrease in the moles of liquid benzene per unit cross
section of the beaker. Letting z = distance down from the mouth of Atomic Diffusion Volumes Atomic
the beaker and using (3-35) with Az = z, and Structural Diffusion-Volume Increments
--
C 15.9 F 14.7
H 2.31 C1 21.0
0 6.11 Br 21.9
N 4.54 I 29.8
Separating variables and integrating,
Aromatic ring -18.3 S 22.9
Heterocyclic ring - 18.3

Diffusion Volumes of Simple Molecules
He
The coefficient of the integral on the right-hand side of (6) is
Ne
constant at
Ar

02 16.3 SO2 41.8
From (6), t = 21,530(3) = 64,590 s or 17.94 h, which is a long time Air 19.7
because of the absence of turbulence.

3.2 DIFFUSION COEFFICIENTS

Diffusivities or diffusion coefficients are defined for a binary derived from experimental data:
mixture by (3-3) to (3-5). Measurement of diffusion coeffi-
cients must involve a correction for any bulk flow using
(3-12) and (3-13) with the reference plane being such that
there is no net molar bulk flow.
The binary diffusivities, DAB and DBA, are mutual or
binary diffusion coefficients. Other coefficients include Di, , where DAB is in cm2/s, P is in atm, T is in K,
the diffusivity of i in a multicomponent mixture; Dii, the
self-diffusion coefficient; and the tracer or interdiffusion
coefficient. In this chapter, and throughout this book, the
focus is on the mutual diffusion coefficient, which will be
referred to as the diffusivity or diffusion coefficient.
and Cv summation of atomic and structural diffusion
=
volumes from Table 3.1, which includes diffusion volumes
Diffusivity in Gas Mixtures
of some simple molecules.
As discussed by Poling, Prausnitz, and O'Connell [2], a Experimental values of binary gas diffusivity at 1 atm and
number of theoretical and empirical equations are available near-ambient temperature range from about 0.10 to 10.0 cm2/s.
for estimating the value of DAB = DBA in gases at low Poling, et al. [2] compared (3-36) to experimental data for
to moderate pressures. The theoretical equations, based 5 1 different binary gas mixtures at low pressures over a tem-
on Boltzmann's kinetic theory of gases, the theorem of cor- perature range of 195-1,068 K. The average deviation was
responding states, and a suitable intermolecular energy- only 5.4%, with a maximum deviation of 25%. Only 9 of 69
potential function, as developed by Chapman and Enskog, estimated values deviated from experimental values by more
predict DAB to be inversely proportional to pressure and than 10%. When an experimental diffusivity is available at
almost independent of composition, with a significant in- values of T and P that are different from the desired condi-
crease for increasing temperature. Of greater accuracy and tions, (3-36) indicates that DAB is proportional to T'.~~/P,
ease of use is the following empirical equation of Fuller, which can be used to obtain the desired value. Some repre-
Schettler, and Giddings [3], which retains the form of the sentative experimental values of binary gas diffusivity are
Chapman-Enskog theory but utilizes empirical constants given in Table 3.2.