Non-Fickian diffusion in viscous aerosol particles

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, even for nanosized particles, viscosity can be ignored. In addition to numerical calculations, a dimensionless Deborah number is defined that indicates the significance of Fickian diffusion compared to the rheological response during water transport.

Analysis of CO2 kinetics in Na,Cs-Rho crystals using the zero length column: a case study for slow systems

Experimental measurements of systems with slow gas transport kinetics are generally considered a relatively easier task when compared to the challenges of measurements of very fast systems. On the other hand, when the transport process goes towards time constants of the order of several hours, not only the measurements, but also the analysis and interpretation of the data offer challenges which make the assessment of the correct time constant of the process non trivial. In this work we used the measurements of CO2 diffusion in Na,Cs-Rho crystals, carried out using the zero length column (ZLC) technique, as a case study for the use of the technique for very slow adsorption processes. The system, which has a time constant of the order of 8 h, shows the importance of using the partial loading approach for the determination of an unambiguous time constant from the analysis of the ZLC desorption curves. The traditional analysis is refined by using the nonlinear ZLC model to take into account the isotherm nonlinearity that results in a concentration dependent diffusivity. Finally, the method proposed by Cavalcante is used to confirm the 3-D diffusion path of the system.

Anomalous Diffusion in Systems with Concentration-Dependent Diffusivity: Exact Solutions and Particle Simulations

We explore the anomalous diffusion that may arise as a result of a concentration dependent diffusivity. The diffusivity is taken to be a power law in the concentration, and from exact analytical solutions we show that the diffusion may be anomalous, or not, depending on the nature of the initial condition. The diffusion exponent has the value of normal diffusion when the initial condition is a step profile, but takes on anomalous values when the initial condition is a spike. Depending on the sign of the exponent in the diffusivity the diffusive behavior will then be either sub-diffusive or super-diffusive. We introduce a particle model that behaves according to the non-linear diffusion equation in the macroscopic limit. This correspondence is demonstrated via kinetic theory, i.e. by means of Chapman-Kolmogorov equation, as well as by direct simulations.