The composition of atmospheric aerosol particles has been found to influence their micro-physical properties and their interaction with water vapour in the atmosphere. Core-shell models have been used to investigate the relationship between composition, viscosity and equilibration time-scales. These models have traditionally relied on the Fickian laws of diffusion with no explicit account of non-ideal interactions. We introduce the Maxwell-Stefan diffusion framework as an alternative method, which explicitly accounts for non-ideal interactions through activity coefficients. E-folding time is the time it takes for the difference in surface and bulk concentration to change by an exponential factor and was used to investigate the interplay between viscosity and solubility and the effect this has on equilibration time-scales within individual aerosol particles. The e-folding time was estimated after instantaneous increases in relative humidity to binary systems of water and an organic component. At low water mole fractions, viscous effects were found to dominate mixing. However, at high water mole fractions, equilibration times were more sensitive to a range in solubility, shown through the greater variation in e-folding times. This is the first time the Maxwell-Stefan framework has been applied to an atmospheric aerosol core-shell model and shows that there is a complex interplay between the viscous and solubility effects on aerosol composition that requires further investigation.