Page 138 - Separation process principles 2

3.6 Models for Mass Transfer at a Fluid-Fluid Interface 103

(e.g., constant wall temperature and uniform heat flux) at Churchill-Zajic equation:
low-to-moderate Prandtl numbers.
Using mass-transfer analogs,
For calculation of convective mass-transfer coefficients,
kc, for turbulent flow of gases and liquids in straight, (3-184) gives Ns,, = 0.850
smooth, circular tubes, it is recommended that the (3-185) gives NShl = 94
Churchill-Zajic equation be employed by applying the
(3-186) gives NSh, = 1686
analogy between heat and mass transfer. Thus, as illustrated
(3-183) gives NSh = 1680
in the following example, in (3-183) to (3-186), from
Table 3.13, the Sherwood number, NShr is substituted for the From Table 3.13,
Nusselt number, NN,; and the Schmidt number, Ns,, is sub-
stituted for the Prandtl number, NW

which is an acceptable 92% of the experimental value.

Linton and Sherwood [49] conducted experiments on the dissolv-
ing of cast tubes of cinnamic acid (A) into water (B) flowing 3.6 MODELS FOR MASS TRANSFER AT
through the tubes in turbulent flow. In one run, with a 5.23-cm-i.d. A FLUID-FLUID INTERFACE
tube, NRe = 35,800, and Ns, = 1,450, they measured a Stanton
number for mass transfer, NstM, of 0.000035 1. Compare this exper- In the three previous sections, diffusion and mass transfer
imental value with predictions by the Reynolds, Chilton-Colburn, within solids and fluids were considered, where the interface
and Friend-Metzner analogies, and by the more theoretically-based was a smooth solid surface. Of greater interest in separation
Churchill-Zajic equation. processes is mass transfer across an interface between a gas
and a liquid or between two liquid phases. Such interfaces
SOLUTION exist in absorption, distillation, extraction, and stripping.
At fluid-fluid interfaces, turbulence may persist to the inter-
From either (3-174) or (3-182), the Fanning friction factor is
face. The following theoretical models have been devel-
0.00576.
oped to describe mass transfer between a fluid and such an
Reynolds analogy: interface.
From (3-162), NstM = $ = 0.0057612 = 0.00288, which, as ex-
pected, is in poor agreement with the experimental value because Film Theory
the effect of Schmidt number is ignored.
A simple theoretical model for turbulent mass transfer to
Chilton-Colburn analogy: or from a fluid-phase boundary was suggested in 1904 by

From (3-165), Nernst [58], who postulated that the entire resistance to mass
transfer in a given turbulent phase is in a thin, stagnant re-
gion of that phase at the interface, called a film. This film is
similar to the laminar sublayer that forms when a fluid flows
which is 64% of the experimental value. in the turbulent regime parallel to a flat plate. This is shown
schematically in Figure 3.18a for the case of a gas-liquid in-
Friend-Metzner analogy: terface, where the gas is pure component A, which diffuses
From (3-173), NstM = 0.0000350, which is almost identical to the into nonvolatile liquid B. Thus, a process of absorption of A
experimental value. into liquid B takes place, without desorption of B into

Gas

Interfacial
region
Figure 3.18 Theories for mass
transfer from a fluid-fluid inter-
face into a liquid: (a) film theory;
(b) penetration and surface- i
renewal theories. I