Nucleation, growth and ageing scenarios in closed systems I: A unified mathematical framework for precipitation, condensation and crystallization

We propose a theoretical approach of nucleation, growth and ageing processes, relevant for precipitation in solution, vapor condensation and crystallization in a simple melt. It is based on the classical nucleation theory, on a size-dependent (algebraic) growth law allowing growth, resorption and ripening of particles (or droplets) simultaneously, and on conservation laws akin to a thermodynamically closed system. Compared to popular population balance models, it explicitly keeps track of the time evolution of any   particle nucleated in the system. This yields a thorough knowledge of the particle population, which not only allows the crystal size distribution to be computed as a by-product, but permits a deeper understanding of the dynamics of these disequilibrated systems. The evolution of the system is followed through the time dependence of a control parameter S(t)S(t), and the changes in the instantaneous particle population. The model yields a set of highly non-linear coupled equations, which, aside from the initial conditions, are functions of only three irreducible dimensionless parameters. This assures that a common general scenario exists for the dynamics of these systems, as shown in the following paper in this issue.