Page 328 - Modelling in Transport Phenomena A Conceptual Approach

308 CHAPTER 8. STEADY MICROSCOPIC BALANCES WTHOUT GEN.

8.5.1.2 Evaporation of a spherical drop
A liquid (A) droplet of radius R is suspended in a stagnant gas it3 as shown in Figure
8.35. We want to determine the rate of evaporation under steady conditions.

Figure 8.35 Mass transfer from a spherical drop.

Over a differential volume element of thickness Ar, as shown in Figure 8.35,
the conservation statement for species A, Eq. (8.41), is written as
-
(ANA~)l~ (ANAv)lr+AT = (8.5-19)
Dividing Eq. (8.5-19) by Ar and taking the limit as Ar --+ 0 gives

(8.5-20)

(8.5-21)
Since flux times area gives the molar transfer rate of species A, it^, it is possible
to conclude that
ANA, = constant = I~A (8.5-22)
Note that the area A in J3q. (8.5-22) is perpendicular to the direction of mass flux
and is given by
A = 4m2 (8.5-23)
Since the temperature and the total pressure remain constant, the total molar
concentration, c, in the gas phase is constant. From Table C.9 in Appendix C, the
total molar flux of species d in the r-direction is given by

(8.5-24)

Since species B is stagnant, the molar average velocity is expressed as

(8.5-25)