A physical box model simulating the aerosol particle evolution along air mass trajectories is developed to provide a tool for interpreting the local observations of stratospheric aerosols (i.e., polar stratospheric clouds). The model calculates the composition and the size distributions of H2SO4/H2O and HNO3/H2SO4/H2O liquid droplets. The parameterization of the physical processes affecting the dynamics of HNO3 and H2SO4 solid hydrates and ice particle size distributions is also included, but not used. This work is restricted to some speculations about the liquid to solid transition, according to existing theories. The evolution of liquid particles is simulated taking into account nucleation, diffusive condensation/evaporation and coagulation. This paper reports the physical and numerical details of the model, which are discussed within the framework of the current understanding of the stratospheric aerosol physics. Performance and limitations of the model are discussed on the basis of the evolution of particle size, and composition along synthetic air mass thermal histories. Size distributions and size-dependent acid weight fractions of the liquid stratospheric aerosols consisting of HNO3/H2SO4/H2O are calculated in the cases of air mass thermal histories with different cooling rates and with rapid temperature fluctuations.