Thermodynamics and kinetics of binary nucleation in ideal-gas mixtures

TL;DR

This paper extends the theory of droplet nucleation to binary mixtures, deriving new equations for droplet evolution, thermodynamics, and equilibrium vapor pressure, with numerical examples demonstrating nonisothermal and enrichment effects.

Contribution

It introduces a macroscopic kinetic approach to binary droplet nucleation, generalizes the Kelvin equation, and links thermodynamics with kinetic equations in the (V,x,T) space.

Findings

Existence of nonisothermal and enrichment effects in binary nucleation.

Derived droplet motion equations in (V,x,T) space.

Numerical calculations for o-xylene-m-xylene system.

Abstract

The nonisothermal single-component theory of droplet nucleation (Alekseechkin, 2014) is extended to binary case; the droplet volume V, composition x, and temperature T are the variables of the theory. An approach based on macroscopic kinetics (in contrast to the standard microscopic model of nucleation operating with the probabilities of monomer attachment and detachment) is developed for the droplet evolution and results in the derived droplet motion equations in the space (V,x,T) - equations for V_dot, x_dot, and T_dot. The work W(V,x,T) of the droplet formation is calculated; it is obtained in the vicinity of the saddle point as a quadratic form with diagonal matrix. Also the problem of generalizing the single-component Kelvin equation for the equilibrium vapor pressure to binary case is solved; it is presented here as a problem of integrability of a Pfaffian equation. The equation for is shown to be the first law of thermodynamics for the droplet, which is a consequence of Onsagers reciprocal relations and the linked-fluxes concept. As an example of ideal solution for demonstrative numerical calculations, the o-xylene-m-xylene system is employed. Both nonisothermal and enrichment effects are shown to exist; the mean steady-state overheat of droplets and their mean steady-state enrichment are calculated with the help of the 3D distribution function. The qualitative peculiarities of the nucleation thermodynamics and kinetics in the water-sulfuric acid system are considered in the model of regular solution. It is shown that there is a small kinetic parameter in the theory due to the small amount of the acid in the vapor and, as a consequence, the nucleation process is isothermal.