Supplementary material from "Regularization of the Ostwald supersaturation model for Liesegang bands"
Posted on 2019-07-25 - 15:10
In a previous paper, we analysed the Keller–Rubinow formulation of Ostwald's supersaturation theory for the formation of Liesegang rings or Liesegang bands, and found that the model is ill-posed, in the sense that after the termination of the first crystal front growth, secondary bands form, as in the experiment, but these are numerically found to be a single grid space wide, and thus an artefact of the numerical method. This ill-posedness is due to the discontinuity in the crystal growth rate, which itself reflects the supersaturation threshold inherent in the theory. Here we show that the ill-posedness can be resolved by the inclusion of a relaxation mechanism describing an impurity coverage fraction, which physically enables the transition in heterogeneous nucleation from precipitate-free impurity to precipitate-covered impurity.
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Duley, J. M.; Fowler, A. C.; Moyles, I. R.; O'Brien, S. B. G. (2019). Supplementary material from "Regularization of the Ostwald supersaturation model for Liesegang bands". The Royal Society. Collection. https://doi.org/10.6084/m9.figshare.c.4589429.v1