CONVECTIVE DIFFUSION OF WATER IN SWELLING GELATIN LAYERS

The literature concerning the swell of gelatin layers immersed in wate r is reviewed. It is shown that all of the published swell equations a re effectively special cases of a general empirical rate equation. In an attempt to establish mechanism, a hypothetical scheme is proposed i nvolving a concentration-dependent intrinsic diffusion coefficient, a linear adsorption isotherm relating the free and sorbed water concentr ations, a constant ratio of final swell to dry thickness, and a propor tionality between the local swell and the sorbed water concentration. It is shown for this hypothetical scheme that the convective one-dimen sional diffusion equation can be linearized and solved exactly for the appropriate boundary and initial conditions. It is also shown that th e general solution takes a particularly simple form for moderately lon g times after immersion. Experimental swell data are then used to dedu ce values for the intrinsic diffusion coefficient which compare favour ably with the self-diffusion coefficient of water. It is also shown th at an exact solution to the associated problem of desorption of water from the fully swollen layer can be obtained by a simple rearrangement of the boundary and initial conditions.