Toward a Molecular Theory of Homogeneous Bubble Nucleation: I. Equilibrium Embryo Definition

Abstract

We propose an equilibrium embryo definition for homogeneous bubble nucleation within the pure component superheated Lennard-Jones liquid. The suggested embryo definition serves as an improvement to a previous (n,v) embryo model (Uline and Corti 2007). In that model, the constrained equilibrium between the bubble and the surrounding superheated liquid was maintained by placing n particles within a spherical volume v, without concern for the redundant counting of configurations and the relevance of the model to the dynamics of a nucleation process. To eliminate this redundancy, while only considering those embryos that should most likely appear at a transitional state, we now define the volume of the embryo via the use of a shell particle and only include n particles inside the volume that are deemed to be "vapor-like". The underlying free energy surface of formation of the new (n,v) embryo model is generated via Monte Carlo simulation and also approximately by a suggested density functional theory method. The resulting surface implies that small and locally confined regions of near-zero density serve as precursors initiating homogeneous bubble nucleation. Furthermore, the nonredundant counting of the embryo configurations yields a well-defined and sharp conduit in the free energy surface that directs the initially formed embryos toward the critical nucleus. We discuss how the suggested equilibrium embryo model aids in both the identification of the transitional configurations and calculation of the average number density of the critical nuclei within the superheated liquid phase, which is the focus of the companion paper (DOI 10.1021/jp404151h).

Simple improvements to classical bubble nucleation models

“…Previous studies have investigated the minimum work for a bubble formation with two variables, taking into account bubble compressibility [41][42][43][44][45][46]. Here we use the two variables r and P g .…”

“…In bubble nucleation, additional detail in the treatment of the process is required, in comparison to droplet nucleation, because of the variable vapor pressure and density in bubbles as they grow [41][42][43][44][45][46]. The vapor pressure in bubbles varies as they grow and has a significant effect on their growth rates and on the pre-exponential factor in the CNT formula for the nucleation rate.…”

Detecting vapour bubbles in simulations of metastable water

“…b) Authors to whom correspondence should be addressed. Electronic addresses: christoph.dellago@univie.ac.at and cvaleriani@quim.ucm.es super-heated fluid has been recently studied in simple liquids (Lennard-Jones) using either the volume of the largest bubble as a local order parameter [6][7][8] or the density as a global one. 9 In recent work, Meadley and Escobedo 10 demonstrated that when comparing the nucleation free energy barrier obtained with the volume of the largest bubble to the one computed using the global density, the largest bubble volume is a better reaction coordinate than the density; it correlates more strongly with committor probabilities.…”

Effect of entropy on the nucleation of cavitation bubbles in water under tension

“…The largest one of these volumes is the preliminary volume ξ which we use to track the progress of the nucleation process. Note that a number of suitable bubble detection procedures have been suggested in the literature [28][29][30][31], which can all be used to obtain the preliminary volume ξ of the largest bubble in the system. In the second step, we calibrate the bubble volume v such that it corresponds to the average change in system volume due to the presence of such a bubble:…”