Influence of initial conditions on homogeneous nucleation kinetics in a closed system

Abstract

The formation of nuclei of a new phase from the supersaturated mother phase in a closed system is studied. The depletion of the mother phase due to phase transition is taken into account. Basic kinetic equations describing such process are solved numerically to determine the number density of nuclei of newly forming phase and nucleation rate. It is shown that in contrary to the standard nucleation model, when the depletion of the mother phase is not taken into account, the initial size distribution of the clusters affects considerably the nucleation process at higher supersaturations. Our model starts with the equilibrium size distribution of clusters up to various cluster sizes in the undercritical region. At lower supersaturation the formation of nuclei is similar to the standard model because of the low depletion of the mother phase. At higher supersaturation, the depletion of the mother phase plays an important role and some extremal value appears at the size distribution of nuclei, which is not observed in the standard model. The extremum in the size distribution is not a consequence of the coalescence process itself, but it is caused rather by the depletion of the mother phase during the phase transformation.

Atmospheric Cluster Dynamics Code: a flexible method for solution of the birth-death equations

“…Several studies have explored particle formation through nucleation in a confined system, i.e. where the monomer concentration is depleted during the course of the event (Kožíšek et al, 2004;Kožíšek and Demo, 2005;Kožíšek et al, 2006). Efforts have also been made to solve the BDE for various systems using approximate methods instead of explicit solution of the system of differential equations (see, for example, Rao and McMurry (1989); Girshick and Chiu (1990); Koutzenogii et al (1996); Chesnokov and Krasnoperov (2007) and references therein), in order to reduce the total number of equations to something manageable.…”

Size distribution of nuclei formed by homogeneous nucleation in closed systems

“…(18) and (19) express that the initial size distribution of clusters (at t = 0) is equal to the equilibrium one up to the size i 0 . It was shown (Koíšek & Demo, 2005) that it is appropriate to chose i 0 ≈ i * /2. If nucleation process starts from monomers (i 0 = 1), the depletion of the supersaturation in closed system is too high-for details see Koíšek and Demo (2005).…”

“…We have already studied (Koíšek & Demo, 2005Koíšek, Demo, & Sveshnikov, 2006) nucleation in closed systems including depletion of the mother phase. It was shown (Koíšek & Demo, 2005) that in a closed system the initial size distribution of clusters influences formation of nuclei much more than in standard theory of nucleation with constant supersaturation does.…”

“…It was shown (Koíšek & Demo, 2005) that in a closed system the initial size distribution of clusters influences formation of nuclei much more than in standard theory of nucleation with constant supersaturation does. At low initial supersaturation, depletion of the mother phase (decrease in supersaturation) is low and the standard model describes satisfactorily the formation of nuclei (Koíšek & Demo, 2007).…”

Modified Rachford‐Rice equations including interfacial contributions and their application to the nucleation process

“…In this work, a detailed description of the peculiarities of closed systems is not intended, because several authors have already performed such developments. 21,22 Thermodynamic Potential for IsothermalIsochoric-Closed Systems…”