Page 696 - Bird R.B. Transport phenomena

676 Chapter 22 Interphase Transport in Nonisothermal Mixtures

§22.2 ANALYTICAL EXPRESSIONS FOR
MASS TRANSFER COEFFICIENTS

In the preceding chapters we obtained a number of analytical solutions for concentra-
tion profiles and for the associated molar fluxes. From these solutions we can now derive
the corresponding mass transfer coefficients. These are usually presented in dimensionless
form in terms of Sherwood numbers. We summarize these analytical expressions here for
use in later sections of this chapter. All of the results given in this section are for systems
with a slightly soluble component A, small diffusivities 4t , and small net mass-transfer
AB
rates, as defined in §§22.1 and 8. It may be helpful at this point to refer to Table 22.2-1,
where the dimensionless groups for heat and mass transfer have been summarized.

Mass Transfer in Falling Films on Plane Surfaces
For the absorption of a slightly soluble gas A into a falling film of pure liquid B, we can
put the result of Eq. 18.5-18 into the form of Eq. 22.1-3 (appropriately modified for molar
concentration units in the manner of Eq. 22.1-11), thus

(22.2-1)
irl

Table 22.2-1 Analogies Among Heat and Mass Transfer at Low Mass-Transfer Rates
Heat transfer Binary mass transfer Binary mass transfer
quantities quantities (isothermal quantities (isothermal
(pure fluids) fluids, molar units) fluids, mass units)
Profiles T 0) A

Diffusivity a = k/pC p ®AB ®AB

Effect of profiles
on density P P \дТ) р P \*хл)р.т * P \dio )
A pJ
Flux q JA = N * + x A (N A + N B ) ) A = n A + a> A (n A + n B )
Transfer rate Q W^o " x A0 (W A0 + W B0 ) U>AO - ^ло(^ло + ^BO)

, ™AO - + W B0 ) W A0 - 0) AQ (W AO 4- w m )
Transfer coefficient Q x A0 (W A0 h
h h
A AT ^Ш А К
A Ao) A
Abx A
Dimensionless groups Re = l o v o p/iJi Re = 1 0 VQP//JL Re = l v p//ji
o o
common to all three Fr = vl/gl 0 Fr = vl/gl 0 Fr = vl/gl 0
correlations
Dimensionless groups Nu = hl /k Sh = kJ 0 /d3b AB Sh = kJ 0 /pGb AB
o
that are different Pr = Sc = Sc = 1л/рЯЬ АВ
Gr = GT X =
Pe = RePr = v C /k Pe = ReSc = I O V O /^AB Pe = ReSc = l v /® AB
l
p
o o
o o
M
/ = ShRe Sc- 1/ 3
Chilton-Colburn D \ 2/ 3
/-factors k x I n
pC p v 0
Notes: (a) The subscript 0 on / and v indicates the characteristic length and velocity respectively, whereas the subscript 0 on the mole
0
0
(or mass) fraction and molar (or mass) flux means "evaluated at the interface." (b) All three of these Grashof numbers can be written as
2
Gr = llpg hp//A , provided that the density change is caused only by a difference of temperature or composition.