A kinetic model for heterogeneous condensation of vapor on an insoluble spherical particle

Abstract

A kinetic model is developed to describe the heterogeneous condensation of vapor on an insoluble spherical particle. This new model considers two mechanisms of cluster growth: direct addition of water molecules from the vapor and surface diffusion of adsorbed water molecules on the particle. The effect of line tension is also included in the model. For the first time, the exact expression of evaporation coefficient is derived for heterogeneous condensation of vapor on an insoluble spherical particle by using the detailed balance. The obtained expression of evaporation coefficient is proved to be also correct in the homogeneous condensation and the heterogeneous condensation on a planar solid surface. The contributions of the two mechanisms to heterogeneous condensation including the effect of line tension are evaluated and analysed. It is found that the cluster growth via surface diffusion of adsorbed water molecules on the particle is more important than the direct addition from the vapor. As an example of our model applications, the growth rate of the cap shaped droplet on the insoluble spherical particle is derived. Our evaluation shows that the growth rate of droplet in heterogeneous condensation is larger than that in homogeneous condensation. These results indicate that an explicit kinetic model is benefit to the study of heterogeneous condensation on an insoluble spherical particle.

A modified expression for the steady-state heterogeneous nucleation rate

“…The microscopic contact angle θ n is different from the macroscopic contact angle θ 1 , and takes the form (Hienola et al, 2007) as a function of the line tension τ. The function is known as the modified Dupre-Young equation (Kalikmanov, 2012;Luo et al, 2014) which can be solved by an iterative method.…”

“…The subscript 'n' denotes the parameter of the cluster containing n molecules hereafter. The detailed formulas are described in Luo et al (2014).…”

“…Our derivation is based on our new kinetic model (Luo et al, 2014) which will be introduced briefly here. In the kinetic model for nucleation, the cluster is assumed to gain or lose only single molecule, and cluster-cluster interactions are neglected.…”

“…Kotake and Glass (1979) considered another mechanism of cluster growth, surface diffusion, in the heterogeneous nucleation besides the mechanism of cluster growth, direct addition, within Volmer's theory. Girshick and Chiu (1990) proposed a self-consistent expression for the equilibrium number density of clusters which was subsequently used in the derivation of the SHNR (Kozisek, Demo, & Nesladek, 1998;Luo, Fan, Qin, Gui, & Liu, 2014). Lazaridis (1993) investigated the effect of the three-phase-contact line tension on the heterogeneous nucleation.…”

“…In this paper, we shall use our new kinetic model (Luo et al, 2014) to derive a modified expression for the SHNR on an insoluble spherical particle. In our derivation, three factors including the two mechanisms of cluster growth, the selfconsistent expression for the equilibrium number density of clusters, and the effect of line tension, which have been widely but also separately used in previous expressions, are comprehensively considered.…”