A study of diffusion in solids of arbitrary shape, with application to the drying of the wheat kernel

Abstract

A general mathematical approach to the rigorous treatment of experimental data on nonstationary‐state diffusion in solids of complex shape is developed. The general solution for a uniform initial concentration, c₀, and a constant surface concentration, c_s, at times greater than zero is shown to be of the form in the neighborhood of time zero, and in the neighborhood of time infinity, where c is the average concentration at time t; S and V are the surface area and volume of the solid, respectively; D is the diffusion coefficient; and f″ (0), α, and β are constants dependent on solid shape. The vacuum drying of wheat has been studied, and it is shown that, for the wheat kernel, f″ (0) = 0.588, α = 0.862; and β² = 1.301. The diffusion coefficient is an Arrhenius‐type function of temperature given by D = D₀ exp {‐E/RT} where D₀ = 76.8 cm.²/sec. and E = 12.20 kcal./mole.