Non-Fickian diffusion in viscous aerosol particles

Abstract

Slow condensed phase diffusion in organic aerosol particles can impede many chemical and physical processes associated with atmospheric aerosol (e.g., gas-particle equilibrium partitioning). The characteristic times associated with these high viscosity particles are typically modelled using a concentration-dependent diffusivity within a purely Fickian framework. In that model, the medium in which diffusion is taking place is treated as being inviscid as far as mass transport is concerned. In this report, we investigate the validity of assuming that the viscosity is equal to zero by using a transport model that includes viscous pressure gradients. It is found that the effect of viscosity is negligible for particles with radii that are larger than 100 nm, but below that radius, it can delay water uptake and loss by orders of magnitude for physically realistic viscosities. However, if the Stokes–Einstein relation is obeyed, then viscosity can be ignored, even for nanosized particles. In addition to numerical calculations, a dimensionless Deborah number is defined that indicates the significance of Fickian diffusion compared with the rheological response during water transport.