Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids

Abstract

When describing the growth of crystal ensembles from metastable solutions or melts, a significant deviation from a spherical shape is often observed. Experimental data show that the shape of growing crystals can often be considered ellipsoidal. The new theoretical models describing the transient nucleation of ellipsoidal particles and their growth with and without fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems are considered. The nonlinear transport (diffusivity) of ellipsoidal crystals in the space of their volumes is taken into account in the Fokker–Planck equation allowing for fluctuating growth rates. The complete analytical solutions of integro-differential models of kinetic and balance equations are found and analysed. Our solutions show that the desupercooling dynamics is several times faster for ellipsoidal crystals as compared to spherical particles. In addition, the crystal-volume distribution function is lower and shifted to larger particle volumes when considering the growth of ellipsoidal crystals. What is more, this function is monotonically increasing to the maximum crystal size in the absence of fluctuations and is a bell-shaped curve when such fluctuations are taken into account. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

The influence of non-stationarity and interphase curvature on the growth dynamics of spherical crystals in a metastable liquid

“…Since various physical processes and phenomena dominate at different stages, these stages of a phase transformation are described by different mathematical models. These include, for example, models of the intermediate stage [11][12][13][14][15][16][17], Ostwald ripening [18][19][20][21][22][23][24], particle coagulation [25][26][27] and disintegration [28][29][30][31][32], as well as models that take into account the simultaneous occurrence of such processes (see, among others, [33][34][35][36]). The vast majority of these models are based on the quasi-stationary growth laws of spherical crystals in metastable melts and solutions.…”

Ostwald ripening in the presence of simultaneous occurrence of various mass transfer mechanisms: an extension of the Lifshitz–Slyozov theory

“…Let us especially emphasize in conclusion that the present theory can be developed to take into account the effects of mass influx and withdrawal of crystals [35][36][37][38][39], the shape of growing particles [40,41], the simultaneous occurrence of bulk and directional phase transformations [42][43][44][45][46], concurrent crystallization and polymerization [47,48] and external stochastic fluctuations [49].…”

Evaporation kinetics of a polydisperse ensemble of drops

“…It should be especially noted that non-stationary effects in particle evaporation rates [25][26][27]39], the Gibbs-Thomson and attachment kinetic effects [35,40,41], the particle shape effects [42][43][44][45][46], as well as the influence of external sources and sinks [10,11,47,48] may also essentially change the evaporation dynamics by analogy with nucleation and crystal growth processes. For a more complete understanding of the question of the influence of these aspects on evaporation dynamics, further development of the theory is required, taking into account the simultaneous action of the above-mentioned effects.…”