Page 485 - Modelling in Transport Phenomena A Conceptual Approach

10.3. MASS TRANSPORT 465

Figure 10.5 Gas absorption into a droplet.

Since CA = CA(T), Table C.9 in Appendix C indicates that the only non-zero molar
flux component is NA, and it is given by

NA, = J;, = -?)AB - (10.3-35)
dCA
dr
For a spherical differential volume element of thickness AT, as shown in Figure
10.5, Eq. (10.3-1) is expressed in the form

lr 8
NA, 47rr2 - NA, Ir+A,. 4~(r + Ar)2 = - [4?rr2Ar (CA - CA,)] (10.3-36)
at
Dividing Eq. (20.3-36) by 47rAr and taking the limit as AT + 0 gives

(10.3-37)

(10.3-38)

Substitution of Eq. (10.3-35) into Eq. (10.3-38) gives the governing differential
equation for the concentration of species A as

(10.3-39)

The initial and the boundary conditions associated with Eq. (10.3-39) are

at t =O CA =CA, (10.3-40)
acA
at r=O -- - 0 (10.%41)
&
at r = R CA = C> (10.3-42)
where c> is the equilibrium solubility of species A in liquid B.