Fig. 3: Fitting of SLS hydration data with similarity solution.

a Normalized sodium concentration profiles. The points are from the data reported by Lanford et al.³⁵, and the solid lines are the result of the theoretical calculations using the similarity solution with Eq. (14) with \(\gamma =3.6\) and \({\mathcal{D}}=1\times {10}^{-16}c{m}^{2}/\sec\). The numbers along the top of the plot refer to the length of treatment in days. b Comparison of the 50% depth for the data from Lanford et al. and the similarity solution. The dotted line has a slope of 1, to guide the eyes. c Reproduction of experimental profiles with a sigmoidal shape for 0.16, 1.5, and 13 days of treatment from Fig. 3a, using the similarity solution with Gaussian convolution described by Eq. (20), with the value used for \(\sigma\) in Eq. (29) shown on the plot.