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Regularization of the Ostwald supersaturation model for Liesegang bands.

ABSTRACT: 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.

SUBMITTER: Duley JM

PROVIDER: S-EPMC6735476 | biostudies-literature | 2019 Aug

REPOSITORIES: biostudies-literature

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Regularization of the Ostwald supersaturation model for Liesegang bands.

Duley J M JM Fowler A C AC Moyles I R IR O'Brien S B G SBG

Proceedings. Mathematical, physical, and engineering sciences 20190814 2228

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, ...[more]

PMID: 31534422

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