Analytical calculation of time lag of homogeneous nucleation

Abstract

At the very first stage of solidification (or condensation) the clusters of a product phase are formed within a metastable parent phase via nucleation. One of the important and experimentally observable characteristics of this process is the so-called time lag corresponding to the moment at which the steady-state is established in the mother phase (supersaturated vapour, undercooled melt). By the use of a method, based on the boundary layer theory combined with the Green function technique, this quantity is determined in approximate analytical form. The dependences of the time lag on temperature, interfacial energy and on the kinetic barrier of nucleation are also presented. The accuracy of our approach is demonstrated by comparison with purely numerical simulations as well as with experimental data and previous analytical solutions.