Power-law setting of steady concentration in a binary solution within a droplet at diffusion-controlled or free-molecular regimes of the droplet binary growth in the vapor-gas environment

TL;DR

This paper analytically investigates the power-law time dependence of droplet growth and concentration stabilization in binary vapor condensation under diffusion-controlled and free-molecular regimes, linking parameters to thermodynamic and kinetic factors.

Contribution

It provides analytical expressions for the power-law behavior of droplet radius and concentration in binary condensation regimes, connecting them to vapor properties and thermodynamics.

Findings

Power-law growth of droplet radius after nucleation.

Power-law setting of steady concentration within the droplet.

Parameters linked to vapor thermodynamics and kinetics.

Abstract

The times required for reaching the power-law-in-time growth of the droplet radius after nucleation of a markedly supercritical binary droplet, are found analytically and estimated at diffusion-controlled or free-molecular regimes of isothermal binary vapor condensation. The process of setting steady concentration in the binary solution within the growing droplet at the same regimes of binary condensation has been analyzed. It has been shown that setting the steady droplet concentration has also a power-law character in time. The parameters of the power law are specified for each regime of binary condensation and are linked to thermodynamic and kinetic characteristics of condensing vapors and to the steady concentration established in a binary droplet.