A Multicomponent Aerosol Dynamics Model (MADM) capable of solving the condensation/evaporation equation of atmospheric aerosols is presented. Condensable species may be organic and/or inorganic. For the inorganic constituents the equilibrium model ISORROPIA is used to predict the physical state of the particle, i.e., whether the aerosol is liquid or solid. The mass transfer equations for the fluxes for solid atmospheric particles are developed. MADM is able to simulate aerosol deliquescence, crystallization, solid to solid phase transitions, and acidity transitions. Aerosols of different sizes can be in different physical states (solid, liquid, or partially solid and partially liquid). Novel constraints on the electroneutrality of the species flux between the gas and aerosol phases are presented for both liquid and solid aerosols. These constraints aid in the stability of the algorithm, yet still allow changes in aerosol acidity. As an example, MADM is used to predict the dynamic response of marine aerosol entering an urban area.