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

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, c 0 , and a constant surface concentration, c s , at times greater than zero is shown to be of the form\documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\bar c - c_s }}{{c_0 - c_s }} = 1 - \frac{2}{{\sqrt \pi }}\frac{S}{V}\sqrt {Dt} + \frac{{f^{''} (0)}}{2}\left( {\frac{S}{V}} \right)^2 Dt $\end{document} in the neighborhood of time zero, and\documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\bar c - c_s }}{{c_0 - c_s }} = \frac{\alpha }{{\beta ^2 }}\exp \left\{ { - \beta ^2 \left( {\frac{S}{V}} \right)^2 Dt} \right\} $\end{document} 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 β 2 = 1.301. The diffusion coefficient is an Arrhenius‐type function of temperature given by D = D 0 exp {‐ E / RT } where D 0 = 76.8 cm. 2 /sec. and E = 12.20 kcal./mole.