Modeling, Analysis and Optimization of Particle Growth, Nucleation and Ripening by the Way of Nonlinear Hyperbolic Integro-Partial Differential Equations

Abstract

We consider the processes of particle nucleation, growth, precipitation and ripening via modeling by nonlinear 1-D hyperbolic partial integro differential equations. The goal of this contribution is to provide a concise predictive forward modeling of the processes including appropriate goal functions and to establish a mathematical theory for the open-loop optimization in this context. Beyond deriving optimality conditions in the synthesis process, we present the application of a fully implicit method for Ostwald ripening of ZnO quantum dots which preserves its numeric stability even with respect to the inherent high sensitivities and wide disparity of scales. FIMOR represents an appropriate method that can be integrated to subordinate optimization studies which enables its future application in the context of continuous particle syntheses and microreaction technology (MRT).