Theoretical analysis of water diffusivity estimated by Crank's equation

Varied water diffusivities estimated by Crank's 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 Fick's 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 Crank's equation need be further improved.

► Crank's equation is a reason causing the variation of estimated water diffusivity.
► Crank's equation may lead to misinterpretations of water diffusivity.
► Crank's equation is an improper equation to estimate water diffusivity.