1 ACA nP At

where ACa = CA(XA2 — XA1) is the concentration increase of the diffusing substance A in the upper container 1 during time At. Substituting equation 65 into equation 25 gives



Solving for DAB and accounting for the logarithmic mean of the molecular fractions gives


Diffusivity in Liquids

When measuring diffusivity in liquids, it is important to be aware that DAB depends on the concentration of the diffusing substance in solution. Constant DAB is only an approximation and may be used in cases of very dilute solutions where only small changes in the concentration occur. It should also be noted that D^ indicates the diffusivity of A through B, and it is different from DBA (diffusivity of B through A). For gases, DAB = DBA. A simple method to determine D^ when A diffuses through B is shown in Figure 5. Two large containers, 1 and 2, are connected by a long capillary tube with diameter 2r and length Y. A dilute solution (of A in B) in container 2 has an initial concentration CA2() and is slightly more concentrated than CAlfj in

Thus the diffusivity £>¿5 depends on the diffusion tube constant Y/nr2 and the logarithmic meanX„lln of the molecular fraction in solution.

Diffusivity in Solids

When a solid slab with some initial moisture content is brought into an airstream, the moisture inside the solid slab will diffuse through the bulk of the solid and evaporate from its surfaces. Assuming that the slab has a thickness much smaller than its length and width, the one-dimensional Fick's second law (equation 46) can be applied. If the system is maintained at equilibrium and both surface moisture contents are equal, the initial and boundary conditions for the system can be written as at t = 0, C = C0, for 0 < y < Y at y = 0, C = Ce, for t > 0 at y = Y, C = Ce, for t > 0

Equation 46 can be solved for the conditions of equation 68 (4) to give

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