Multidimensional population balance modelling

In this thesis, the numerical solution of two dimensional Population Balance Equation (PBE) for breakage is studied by Markov Chains Method. PBE is a well-known partial integro differential equation which used in various branches of applied sciences such as: chemical engineering, pharmaceutical industry and aerosol technology. This equation describes the rate of change in Particle Property Distribution (PPD). Moreover, the analytical solutions of PBEs are limited only for some specific functions. Therefore, numerical methods are important in order to find an approximated solution for PBEs. In this study, the two dimensional breakage equation is discretized with assuming particle size and energy as two different particle properties. However, Markovian structure is applied to breakage and selection functions. The results are compared with the previous works and the effectiveness of proposed method is shown.