Page 711 - Bird R.B. Transport phenomena

§22.4 Definition of Transfer Coefficients in Two Phases 691

The solubility of O in water at 20°C is 1.38 X 10 3 moles per liter at an oxygen partial
2
pressure of 760 mm Hg, the vapor pressure of water is 17.535 mm Hg, and the total pressure
in the solubility measurements is 777.5 mm Hg. At 20°C, the diffusivity of O 2 in water is
2
2
5
ЯЬ = 2.1 X 10~ cm /s, and in the gas phase the diffusivity for O 2 - N is ЯЬ = 0.2 cm /s.
2
АВ
АС
We can then write
i^ f[ &i .
= ( 2 2 4 1 5 )
Into this we must substitute
1000/18 = 1308 (22.4-16)
(77751760) / (0.08206) (293.5)
= 0.01 (22.4-17)
0.2
3
1.38 X 10" /55.5
760/777.5 (22.4-18)
It follows that

= (1308X0.01X2.54 x 10" ) = 3.32 x 10 (22.4-19)
5
Therefore, only the liquid-phase resistance is significant, and the assumption of penetration
behavior in the gas phase is not critical to the determination of liquid-phase control. It may
also be seen that the dominant factor is the low solubility of oxygen in water. One may gener-
alize and state that absorption or desorption of sparingly soluble gases is almost always liq-
uid-phase controlled. Correction of the gas-phase coefficient for net mass transfer is clearly
not significant, and the correction for the liquid phase is negligible.

EXAMPLE 22.4-2 There are many situations for which the one-phase transfer coefficients are not available for
the boundary conditions of the two-phase mass transfer problem, and it is common practice
Interaction of Phase to use one-phase models in which interfacial boundary conditions are assumed, without re-
Resistances gard to the interaction of the diffusion processes in the two phases. Such a simplification can
introduce significant errors. Test this approximate procedure for the leaching of a solute A
from a solid sphere of В of radius R in an incompletely stirred fluid C, so large in volume that
the bulk fluid concentration of A can be neglected.

SOLUTION The exact description of the leaching process is given by the solution of Fick's second law
written for the concentration of A in the solid in the region 0 < r < R:

(22.4-20)
AB
dt -" idrY dr
r
The boundary and initial conditions are:
B.C.I: atr = 0, c As is finite (22.4-21)
B.C. 2: at r = R, c = mc + b (22.4-22)
As AI
I.C.: at t = 0, c = c (22.4-23)
As 0
The diffusional process on the liquid side of the solid-liquid interface is described in terms of
a mass transfer coefficient, defined by
r^ dC As = k (c - 0) (22.4-24)
dr c Al
in which c (t) is the concentration in the liquid phase adjacent to the interface. The behavior of
Al
the diffusion in the two phases is coupled through Eq. 22.4-22, which describes the equilibrium