Results on isothermal stratification of ice particles in ice slurry storage tanks are presented. Furthermore - in an extension - the melting of ice particles by heat fluxes across the boundaries of storage vessels is also taken into consideration. A conservation equation for the ice particles, respectively the ice fraction, is then accompanied by a second basic differential equation, the energy conservation equation. It is identical to the continuous properties model and describes the melting phenomena. To obtain numerical results, a generally accepted physical-properties model of ice slurries had to be generalized. Further main results are the ice fraction distributions of stratification processes.