This paper describes new and modified numerical techniques for solving the size- and time-dependent aerosol processes of nucleation, coagulation, condensation, dissolution, and reversible chemistry among multiple aerosol particle size distributions and the gas phase and over the entire relative humidity (RH) range. The techniques treat particle number, mole, and volume concentrations, solution and nonsolution densities, and refractive index consistently. Some findings include the following: (1) Coagulation internally mixes particles of different original composition over the entire size distribution. (2) Coagulation internally mixes a greater fraction of larger than smaller particles. (3) Coagulation internally mixes larger particles with more other distributions than it does smaller particles. (4) Coagulation among multiple distributions produces the same summed size distribution as coagulation of a single distribution when the sum of initial distributions is the same in both cases. (5) In a competition for vapor between homogeneous nucleation and condensation, the relative importance of condensation increases with an increasing number of background particles. (6) In the absence of a continuous source of new particles, coagulation, condensation, dissolution, hydration, and chemical reaction internally mix most particles within half a day under moderately polluted conditions. (7) Condensation increases the fractional coating of small more than large particles. (8) The real refractive index of a particle containing electrolytes is higher at low RHs than at high RHs. (9) The difference between total particle and solution real refractive indices increases with decreasing RH. (10) A solution real refractive index generally increases with decreasing particle size.