The physicochemical changes experienced by organic aerosol particles undergoing dehydration into the surrounding gas phase can be drastic, forcing rapid vitrification of the particle and suppressing internal diffusion. Until recently, experimental studies have concentrated on quantifying diffusional mixing of either water or non-volatile components, while relatively little attention has been paid to the role of semivolatile organic component (SVOC) diffusion and volatilisation in maintaining the equilibrium between the gas and particle phases. Here we present methods to simultaneously investigate diffusivities and volatilities in studies of evolving single ternary aerosol particle size and composition. Analysing particles of ternary composition must account for the multiple chemical species that volatilise in response to a step change in gas phase water activity. In addition, treatments of diffusion in multicomponent mixtures are necessary to represent evolving heterogeneities in particle composition. We find that the contributions to observed size behaviour from volatilisation of water and a SVOC can be decoupled and treated separately. Employing Fickian diffusion modelling, we extract the compositional dependence of the diffusion constant of water and compare the results to recently published parametrisations in binary aerosol particles. The treatment of ideality and activity in each case is discussed, with reference to use in multicomponent core shell models. Meanwhile, the evaporation of an SVOC into an unsaturated gas flow may be treated by Maxwell's equation, with slow diffusional transport manifesting as a suppression in the extracted vapour pressure.