Optimization of particle synthesis

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The economic production of particulate products with exactly pre-defined characteristics is of enormous relevance. Although there are different particle formation routes they may all be described by one class of equations. Therefore, simulation of such processes comprises solution of nonlinear, hyperbolic integro-partial differential equations. This project aims to study this class of equations in order to develop efficient tools for the inverse solution, i.e. determining the optimal process conditions and reactor geometry to achieve a desired product property. This objective is approached by a joint effort of the mathematics and the engineering faculty. Two model-processes are chosen for this study, namely a precipitation process and a highly innovative aerosol process with a nozzle flow allowing for precise control of residence time and temperature and therefore promising to deliver products with unique properties. Since the overall problem is far too complex to be solved in one step a hierarchical sequence of simplified problems has been derived which will be solved consecutively. Model reduction as well as highly innovative mathematical methods (e.g. domain decomposition, second-order optimal-control methods, SQP method) shall be used which have not been applied to similar problems so far. Finally, the simulations will be subject to comparison with experiments.