Simulation of discontinuous population balance equation with integral constraint of growth rate expression

An effective method based on the concept of continuous characteristics is developed to solve the continuous population equation with integral constraint of growth rate expression. This method can also be extended to solve a general form of a first order partial differential equation. A typical example of a class II MSMPR crystallization process at transient state is modelled and analyzed. The system which possesses originally a discontinuous population density function is transformed into a continuous one by appropriate treatment of the initial condition. The partial differential equation of the continuous population density function is solved by the shifted Legendre polynomials approximation and moments method simultaneously. The original discontinuous population density function is then transformed back from the calculated continuous one by the system characteristics. Very satisfactory computational results are obtained.