Unsteady-State Diffusion Through a Porous Solid

1 Unsteady-State Diffusion Through a Porous Solid 

This problem illustrates the solution approach to a one-dimensional, nonsteady-state, diffusional problem, as demonstrated in the simulation examples, DRY and ENZDYN. The system is represented in Fig. 4.2. Water diffuses through a porous solid, to the surface, where it evaporates into the atmosphere. It is required to determine the water concentration profile in the solid, under drying conditions. The quantity of water is limited and, therefore, the solid will eventually dry out and the drying rate will reduce to zero. 

The movement of water through a solid, such as wood, in the absence of chemical reaction, is described by the following time-dependent diffusional equation. 

Thus at steady state the concentration gradient is constant. 

Note that since there are two independent variables of both length and time, the defining equation is written in terms of the partial differentials, 3C/dt and 3C/dZ, whereas at steady state only one independent variable, length, is involved and the ordinary derivative function is used. In reality the above diffusion equation results from a combination of an unsteady-state mass balance, based on a small differential element of solid length dZ, combined with Pick s Law of diffusion. 

Note that since there are two independent variables of both length and time, the defining equation is written in terms of the partial differentials, dC/dt anddC/dZ, whereas at steady state only one independent variable, length, is 

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Figure 4.2. Unsteady-state diffusion through a porous solid.

Unsteady-State Diffusion through a Porous Solid... 

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