Inverse problem approach to modeling of particulate systems

Modeling of particulate system is complicated by the wide range of mechanisms that affect particles of various sizes. Even when detailed fundamental models are available, they are often intractable for online control. We use an approach intermediate between first principles models and empirical modeling. By treating each of the processes of growth, nucleation, and aggregation as a separate functionality identified within the structure of the population balance, we create a model suited for online control in accuracy, tractability and availability. Express acknowledgment of a distributed framework allows the model to capture a broad range of behavior accurately. Relative simplicity facilitates rapid simulation. We demonstrate the application of an inverse problem technique for identification of growth and nucleation dependences to two examples. The crystallization example shows extraction of size dependent growth and nucleation rates from simulated experimental data. Both rate laws are determined from a single experiment. The emulsion polymerization example shows the use of the technique for model reduction and demonstrates how a growth mechanism change in time can be handled.