Diffusion in absorbing media

The problem to be discussed, which arose in connexion with the uptake of moisture by cotton bales, is that of diffusion of one substance through another in the pores of a solid body which may absorb and immobilize some of the diffusing substance. Heat will be evolved by the absorption process, and this will itself diffuse through the medium, and will affect the extent to which the solid can absorb the diffusing substance. We thus have two diffusion processes coupled by the mutual interaction of the diffusing “substances” when they are absorbed by the solid. The pores are envisaged as a continuous network of spaces included in the solid, containing the medium (e.g. air) through which the diffusion takes place. The solid itself may be either discontinuous, as is a bale of cotton fibres, or continuous, like a sponge. For convenience we will refer to the diffusing substance in the pores as the “vapour”, though the theory is not limited to the diffusion of vapours, nor is it necessary to assume pores of larger than molecular dimensions. The essential point is that some of the diffusing substance becomes immobilized, and that heat is given out in the process. Thus the case of a dissolved substance diffusing through a gel would be included, and it is not necessary to suppose the diffusion limited to one phase only. If heat is evolved when vapour is absorbed by the solid, it follows by thermodynamic reasoning that vapour will be set free when heat is immobilized (i.e. disappears). Hence the equations will be symmetrical in form. Equations of the same form would be obtained, neglecting thermal effects, for the diffusion through a porous solid of two substances, each capable of replacing the other in absorption by the solid.