Analytical expression for gas-particle equilibration time scale and its numerical evaluation

We have derived a time scale τ_eq that describes the characteristic time for a single compound i with a saturation vapour concentration C_eff,i to reach thermodynamic equilibrium between the gas and particle phases. The equilibration process was assumed to take place via gas-phase diffusion and absorption into a liquid-like phase present in the particles. It was further shown that τ_eq combines two previously derived and often applied time scales τ_a and τ_s that account for the changes in the gas and particle phase concentrations of i resulting from the equilibration, respectively. The validity of τ_eq was tested by comparing its predictions against results from a numerical model that explicitly simulates the transfer of i between the gas and particle phases. By conducting a large number of simulations where the values of the key input parameters were varied randomly, it was found out that τ_eq yields highly accurate results when i is a semi-volatile compound in the sense that the ratio of total (gas and particle phases) concentration of i to the saturation vapour concentration of i, μ, is below unity. On the other hand, the comparison of analytical and numerical time scales revealed that using τ_a or τ_s alone to calculate the equilibration time scale may lead to considerable errors. It was further shown that τ_eq tends to overpredict the equilibration time when i behaves as a non-volatile compound in a sense that μ > 1. Despite its simplicity, the time scale derived here has useful applications. First, it can be used to assess if semi-volatile compounds reach thermodynamic equilibrium during dynamic experiments that involve changes in the compound volatility. Second, the time scale can be used in modeling of secondary organic aerosol (SOA) to check whether SOA forming compounds equilibrate over a certain time interval.