Page 645 - Bird R.B. Transport phenomena

§20.2 Steady-State Transport in Binary Boundary Layers 625

Continuity + continuity of A:
pv (o) - ш ) dy + r dy - pv (ct) - o) ) (20.2-7)
dx Jn x AK А A o Acx> A0
These equations are extensions of the von Kdrmdn balances of §§4.4 and 12.4 and may be
similarly applied, as shown in Example 20.2-1.
Boundary layer techniques have been of considerable value in developing the the-
ory of high-speed flight, separations processes, chemical reactors, and biological mass
transfer systems. A few of the interesting problems that have been studied are chemical
2
reactions in hypersonic boundary layers, 1 mass transfer from droplets, electrode polar-
3
2
ization in forced convection and free convection, reverse-osmosis water desalination, 4
and interphase transfer in packed-bed reactors and distillation columns. 5
EXAMPLE 20.2-1 An appropriate mass transfer analog to the problem discussed in Example 12.4-1 would be
the flow along a flat plate that contains a species A slightly soluble in the fluid B. The concen-
Diffusion and Chemical tration at the plate surface would be c , the solubility of A in B, and the concentration of A far
A0
Reaction in Isothermal from the plate would be с . In this example we let c = 0 and break the analogy with Exam-
Аж
Ax
Laminar Flow Along a ple 12.4-1 by letting A react with В by an nth order homogeneous reaction, so that R -
A
Soluble Flat Plate -k'"c . The concentration of dissolved A is assumed to be small, so that the physical proper-
A
ties ц, p, and 4t are virtually constant throughout the fluid. We wish to analyze the system,
AB
sketched in Fig. 20.2-1, by the von Karman method.
SOLUTION We begin by postulating forms for the velocity and concentration profiles. To minimize the
algebra and still illustrate the method, we select simple functions (clearly one can suggest
more realistic functions):
У_
8 у < 8{x)
у > 5W (20.2-8)

C
A0 O c У ^ 8 M (20.2-9)
C
у > 5 (x)
^ = 0 f
8(x)
Fluid
approaches
with
velocity
v
Fig. 20.2-1. Assumed velocity and con-
centration profiles for the laminar bound-
ary layer with homogeneous chemical
reaction.

2
V. G. Levich, Physicochemical Hydrodynamics, 2nd edition (English translation), Prentice-Hall,
Englewood Cliffs, NJ. (1962).
3
С R. Wilke, C. W. Tobias, and M. Eisenberg, Chem. Eng. Prog., 49, 663-674 (1953).
4
W. N. Gill, D. Zeh, and C. Tien, Ind. Eng. Chem. Fund., 4,433-439 (1965); ibid., 5, 367-370 (1966).
See also P. L. T. Brian, ibid., 4, 439-445 (1965).
5
J. P. Sefrensen and W. E. Stewart, Chem. Eng. Sci., 29, 833-837 (1974); W. E. Stewart and
D. L. Weidman, ibid., 45, 2155-2160 (1990); Т. С Young and W. E. Stewart, AIChE Journal, 38, 592-602,
1302 (1992).