Vapor Transport of a Volatile Solvent for a Multicomponent Aerosol Droplet

TL;DR

This paper derives analytical formulas to evaluate vapor transport in multicomponent droplets, revealing unique acceleration-deceleration behaviors and conditions for growth or shrinkage depending on vapor pressure and composition.

Contribution

It introduces a quasi-steady-state analytical model for multicomponent droplet vapor transport, highlighting the effects of nonvolatile cosolvent on evaporation and condensation dynamics.

Findings

Acceleration-deceleration reversal in droplet size change.

Conditions where the acceleration phase may disappear.

Predictions of droplet growth or shrinkage based on vapor pressure.

Abstract

This work presents analytical formulas derived for evaluating vapor transport of a volatile solvent for an isolated multicomponent droplet in a quiescent environment, based on quasi-steady-state approximation. Among multiple solvent components, only one component is considered to be much more volatile than the rest such that other components are assumed to be nonvolatile remaining unchanged in the droplet during the process of (single-component) volatile solvent evaporation or condensation. For evaporating droplet, the droplet size often initially decreases following the familiar "d^2 law" at an accelerated rate. But toward the end, the rate of droplet size change diminishes due to the presence of nonvolatile cosolvent. Such an acceleration-deceleration reversal behavior is unique for evaporating multicomponent droplet, while the droplet of pure solvent has an accelerated rate of size change all the way through the end. This reversal behavior is also reflected in the droplet surface temperature evolution as "S-shaped" curves. However, a closer mathematical examination of conditions for acceleration-deceleration reversal indicates that the acceleration phase may disappear when the amount of nonvolatile cosolvent is relatively small and ambient vapor pressure is relatively high. Because the net effect of adding nonvolatile cosolvent is to reduce the mole fraction of the volatile solvent such that the saturation vapor pressure is lowered, vapor condensation onto the multicomponent droplet is predicted to occur when the ambient vapor pressure is subsaturated with respect to that for the pure volatile solvent. In this case, the droplet will grow asymptotically toward a finite size. But when the ambient vapor pressure becomes supersaturated with respect to that for the pure volatile solvent, the condensation growth of droplet can continue indefinitely without bound.