Example 17.2-2: Diffusion Through a Nonisothermal Spherical Film

BSL Fig. 17.2-3


Part A
Derive expressions for diffusion through a spherical shell that are analogous to BSL Eq. 17.2-10 (concentration profile) and Eq. 17.2-14 (molar flux).






Part B
Extend these results to describe the diffusion in a nonisothermal film in which the temperature changes with the distance according to:

in which T1 is the temperature at r=r1. Assume as a rough approximation that DAB varies as the 3/2-power of the temperature:

in which DAB1 is the diffusivity at T=T1. Problems of this kind arise in connection with drying of droplets and diffusion through gas films near spherical catalyst pellets.







Numerical Example
Continuing on with the result from Part B, we can give values to the constants to see that these equations do indeed yield reasonable answers.




Matthew A. Hayenga 4/30/98