Conclusions

The transpiration boundary condition (2.59) is essential to the analysis of the Stefan diffusion tube, and is used in all the cited studies; several of them also give derivations.

Although many questions have been raised about the validity of the use of the Stefan diffusion tube for the determination of diffusivity coefficients, the results obtained are probably of acceptable accuracy, since, as is easily shown, the evaporation rate predicted by the one-dimensional analysis is asymptotically correct to $O(1)$ as $\varPhi \rightarrow 0$, and most experiments occur with very low values of $\varPhi$. To the best of my knowledge, no upper bound has been placed on the errors caused by finite values of $\varPhi$, though given the symmetry property derived in §2.6.3, it should be at most $O(\varPhi ^2)$ for the overall Sherwood number.

The Stefan diffusion tube is a classical vapour transport problem, and embodies many of the physical phenomena of the present problem. As such, the literature surrounding it has been very useful.