An accurate understanding of the equilibration timescale of organic aerosol particles with surrounding water vapor is difficult because of the strong concentration-dependent diffusivities that are present in these systems. We examine this problem along with the closely related problem of the time-dependent radius of a binary aerosol particle during the uptake or loss of water. The governing equations and boundary conditions are discussed and a boundary value problem is formulated and solved. The resulting expressions are applied to water uptake and loss in two systems of atmospheric importance: aqueous-inorganic particles and high-viscosity organic particles. Accuracy is evaluated through a comparison with numerical solutions. For particles whose diffusivity has a strong dependence on water concentration and whose viscosity remains above 1 Pa.s during water uptake or loss, the expression for the characteristic equilibration time is found to be in excellent agreement with numerical results. Moreover, it provides physical insights into mass transport processes.