Page 484 - Modelling in Transport Phenomena A Conceptual Approach

464 CHAPTER 10. UNSTEADY MICROSCOPIC BAL. WITHOUT GEN.

'pable 10.7 Comparison of the exact fiactional uptake values with a short time
solution.

@ Exact Approx.
Eq. (10.3-22) J3q. (10.3-34)
0.1 0.113 0.113
0.2 0.226 0.226
0.3 0.339 0.339
0.4 0.451 0.451
0.5 0.562 0.564
0.6 0.667 0.677
0.7 0.758 0.790
0.8 0.833 0.903
0.9 0.890 1.016
1.0 0.931 1.128

Example 10.8 For a semi-infinite medium, penetration distances for the mo-
mentum and heat transfer are estimated as

s=4&
6t = 4 a
Develop an analogous equation for the mass transfer.

Solution

When s/dm = 2, Eq. (10.3-30) becomes

- cAo = 1 - erf (2) = 0.005
CAI - CA,
indicating that CA N CA,. Therefore, the penetration dis-ance for mass transfer,
6,, is given by
s, = 4JG

10.3.2 Gas Absorption Into a Spherical Droplet
Consider a liquid droplet (23) of radius R surrounded by gas A as shown in Figure
10.5. We are interested in the rate of absorption of species A into the liquid. The
problem will be analyzed with the following assumptions:

1. Convective flux is negligible with respect to the molecular flux, i.e., vl 21 0.
2. The total concentration is constant.