Equilibration times in viscous and viscoelastic aerosol particles

Abstract

Secondary organic aerosol (SOA) particles in Earth's atmosphere can exist in phase states where mass transport and chemical transformations are greatly impeded. Gas-particle partitioning in both semi-solid and solid (e.g. glassy phase state) SOA particles can be kinetically limited, and these equilibration timescales are often evaluated using a Fickian model with a concentration-dependent diffusivity. Within that framework, particles are considered to be inviscid fluids and thus their rheology is ignored. In this work, rheological properties are not neglected and particle equilibration is investigated using both a viscous model (an incompressible Newtonian fluid) and a viscoelastic model (a Maxwell material). We derive analytic expressions for gas-particle equilibration times in viscous and viscoelastic aerosol particles and compare these times to the well-known Fickian equilibration time. These expressions are then applied to the important example of the equilibration of atmospheric aerosol particles with the surrounding relative humidity (i.e. water uptake and loss). The two systems studied here are aqueous sucrose, which is often used as a surrogate for secondary organic material found in the atmosphere, and aqueous oxidized α-pinene, which is an atmospherically relevant secondary organic material. We show that viscous effects (i) are likely unimportant in single particle experiments, except under very dry conditions, and (ii) can result in water vapor equilibration times of minutes to hours at any altitude in the troposphere for accumulation mode particles.