Master Equation Approach to Gypsum Needle Crystallization
Résumé
We write and solve a master equation which governs the stochastic growth of interacting gypsum needles. Needle blocking by steric hindrance is reproduced in an effective way. The comparison of the results with submicrometric simulations enables us to choose a small number of fitting parameters to optimize the master equation approach. The stochastic description qualitatively predicts the main features of the dynamics, including the transition toward incomplete dissolution of plaster for increasing values of the number of nuclei per plaster grain. The master equation quantitatively reproduces some morphological properties of the final material, such as mean value and standard deviation of the probability distribution of needle length.