Page 699 - Bird R.B. Transport phenomena

§22.3 Correlation of Binary Transfer Coefficients in One Phase 679

Mass Transfer in the Neighborhood of a Rotating Disk
For a disk of diameter D coated with a slightly soluble material A rotating with angular
velocity П in a large region of liquid B, the mass flux at the surface of the disk is inde-
pendent of position. According to Eq. 19D.4-7 we have

N A0 = 0.6201 „i/6 (c A0 - 0) - (22.2-13)

This may be expressed in terms of the Sherwood number as

/Ш 1 / 2 р 1 / 6 \
Sh = = 0.620 = 0.620
m 1/3 1/6
\ 2) д /
= 0.620 Re Sc 1/3 (22.2-14)
1/2
Here the characteristic velocity in the Reynolds number is chosen to be Dft.

§22.3 CORRELATION OF BINARY TRANSFER
COEFFICIENTS IN ONE PHASE
In this section we show that correlations for binary mass transfer coefficients at low
mass-transfer rates can be obtained directly from their heat transfer analogs simply by a
change of notation. These correspondences are quite useful, and many heat transfer cor-
relations have, in fact, been obtained from their mass transfer analogs.
To illustrate the background of these useful analogies and the conditions under
which they apply, we begin by presenting the diffusional analog of the dimensional
analysis given in §14.3. Consider the steadily driven, laminar or turbulent isothermal
flow of a liquid solution of A in B, in the tube shown in Fig. 22.3-1. The fluid enters the
tube at z = 0 with velocity uniform out to very near the wall and with a uniform inlet
composition x AV From z = 0 to z = L, the tube wall is coated with a solid solution of
A and B, which dissolves slowly and maintains the interfacial liquid composition con-
stant at x . For the moment we assume that the physical properties p, jx, c, and %b are
AQ
AB
constant.
The mass transfer situation just described is mathematically analogous to the heat
transfer situation described at the beginning of §14.3. To emphasize the analogy, we pre-
sent the equations for the two systems together. Thus the rate of heat addition by con-
duction between 1 and 2 in Fig. 14.3-1 and the molar rate of addition of species A by

Nozzle

Fluid enters
with uniform
composition x A]

I Soluble coating on wall maintains ( Velocity of dissolved A
I constant liquid composition x A0 \ and В away from wall is
next to wall surface assumed to be small

Fig. 22.3-1. Mass transfer in a pipe with a soluble wall.