Theoretical analysis of water diffusivity estimated by Crankʹs equation

Varied water diffusivities estimated by Crankʹs equation have been reported. However, the corresponding theoretical explanation is still not available. Here reported is our effort about this concern. A model combining the Fickʹs second law diffusion with a convective boundary condition on the material surface is solved numerically, and the obtained solution is used to estimate water diffusivity through Crank equation. The result shows that a significant underestimation of water diffusivity occurs due to a failure to account for appropriate boundary, which may imply that Crankʹs equation need be further improved.