Optimization of particle synthesis

具有精确预定义特性的颗粒产品的经济生产具有巨大的相关性。虽然有不同的粒子形成路线，但它们都可以用一类方程来描述。因此，这些过程的模拟包括求解非线性的双曲型积分偏微分方程。本项目旨在研究这类方程，以开发有效的反解工具，即确定最佳工艺条件和反应器几何形状，以实现所需的产品性质。这个目标是通过数学系和工程系的共同努力来实现的。本研究选择了两个模型过程，即沉淀过程和高度创新的气溶胶过程，喷嘴流量允许精确控制停留时间和温度，因此有望提供具有独特性能的产品。由于整个问题太过复杂，无法一步解决，因此推导了一个简化问题的层次序列，这些问题将连续解决。模型约简以及高度创新的数学方法（如领域分解、二阶最优控制方法、SQP方法）应使用，这些方法迄今尚未应用于类似问题。最后，将模拟结果与实验结果进行比较。

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.