Page 698 - Bird R.B. Transport phenomena

678 Chapter 22 Interphase Transport in Nonisothermal Mixtures

For the creeping flow around a solid sphere with a slightly soluble coating that dis-
solves into the approaching fluid, we may modify the result in Eq. 12.4-34 to get
(Зтг) 2/3 Ы у _
в х
' " 2 «Гф
Ли а 8 7
This result may be rewritten in terms of the Sherwood number as
(Зтг) 2/3 Ц
2 7 / 3 Г ф У \ ^ )\Р®лв)
= 0.991 (ReSc) 1/3 (22.2-8)
As in the preceding subsection we have ReSc to the \-power for the gas-liquid system
and ReSc to the \-power for the liquid-solid system.
Both Eq. 22.2-6 and Eq. 22.2-8 are valid only for creeping flow. However, they are
not valid in the limit that Re goes to zero. As we know from Problem 10B.1 and Eq. 14.4-
5, if there is no flow past the solid sphere or the spherical bubble, Sh m = 2. It has been
found that a satisfactory description of the mass transfer all the way down to Re = 0 can
be obtained by using the simple superpositions: Sh m = 2 + 0.6415(ReSc) 1/2 and Sh =
w
1/3
2 + 0.991 (ReSc) in lieu of Eqs. 22.2-6 and 8.
Mass Transfer in Steady, Nonseparated Boundary
Layers on Arbitrarily Shaped Objects
For systems with a fluid-fluid interface and no velocity gradient at the interface, we
found the mass flux at the surface to be given by Eq. 20.3-14:

w г/ (сло0)^, Ас л (22.2-9)
|ос
h h\v dx
Jo x s
The local Sherwood number is

^ L ^ У&± (22.2-10)

l
in which the constant, 1/VTT, is equal to 0.5642 and Re = v p//ji.
o
o
Similarly for systems with fluid-solid interfaces and a velocity gradient at the inter-
face, the mass flux expression is given in Eq. 20.3-26 as
_ o) = vo \ r (22 2-11)
\ dx
z
The analogous Sherwood number expression is

(22.2-1

/
where the numerical coefficient has the value 0.5384. In these equations and v are a
0
0
characteristic length and a characteristic velocity that can be chosen after the shape of
the body has been defined. Here again we see that the \-power on ReSc appears in the
fluid-fluid system, and the \-power on ReSc appears in the fluid-solid system—
regardless of the shape. The radicands of the Sherwood number expressions are
dimensionless.