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

  • Michael Gröschel
  • Wolfgang Peukert
  • Günter LeugeringEmail author
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)


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).


Nonlinear integro-partial differential equation Particle synthesis Particle growth Ostwald ripening Numerical simulation Optimization 

Mathematics Subject Classification (2010).

Primary 99Z99 Secondary 00A00 



The authors acknowledge the work of the PhD-candidates A. Keimer, L. Pflug, J. Semmler and M. Walther, in particular, with respect to the numerical solutions and R. Wagner for the studies on Si formation (experiment and population balance modeling), Doris Segets and Martin Hartig for the studies with ZnO quantum dots. The authors would like to thank the German Research Council (DFG) for their financial support within the priority programs SPP 1679 (PE427/25) and SPP 1253 (LE595/23), for support within the DFG-Cluster of Excellence “Engineering of Advanced Materials” ( at the University of Erlangen-Nuremberg as well as for funding within the framework of the Elite Network of Bavaria: Identification, Optimization and Control with Applications in Modern Technologies.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Michael Gröschel
    • 1
  • Wolfgang Peukert
    • 2
  • Günter Leugering
    • 1
    Email author
  1. 1.Institute of Applied Mathematics 2Friedrich-Alexander University Erlangen-NürnbergErlangenGermany
  2. 2.Institute of Particle TechnologyFriedrich-Alexander University Erlangen-NürnbergErlangenGermany

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