Modeling and Simulating the Crystallization of Polymers via a Many-Particle System
This paper deals with to the modelling and simulation of the crystallization of polymers in an heterogeneous temperature field. Under realistic parameter ranges, of industrial interest, we face a multiple scale phenomenon since the temperature evolution occurs at a faster time scale with respect to the birth-and-growth process of crystallization. We propose a spatially structured stochastic bith-and-growth model for the crystallization process whose kinetics parameters depend locally upon the temperature field, and nonlocally upon the spatial distribution of the crystalline phase. For a large number of crystals the system can be shown to converge to a classical continuum deterministic model. We report here the results of the numerical simulation of the many particle system, and of the corresponding continuum model.
KeywordsLatent Heat Continuum Model Crystallization Process Nucleation Rate Particle System
Unable to display preview. Download preview PDF.
- 1.V. Capasso, D. Morale, Karl Oelschlaeger, C. Salani, “An interacting particle approach for the crystallization of polymers” Proceedings “La Matematica nelle Scienze della Vita e nelle Applicazioni”, (Agnoli, Fabrizio, Vettori Eds. ), Pitagora Editrice Bologna, 2000.Google Scholar
- 2.M. Burger, V. Capasso, C. Salani, Modeling multi-dimensional crystallization of polymers in interaction with heat transfer., Nonlinear Analysis (2001), In press.Google Scholar
- 3.M. Burger, V. Capasso, A. Micheletti, On the numerical simulation of a stochastic PDE system modelling crystallization of polymers, 2000. In preparation.Google Scholar
- 4.M. Burger, V. Capasso, Mathematical modelling and simulation of non-isothermal crystallization of polymers. Math. Models and Methods in Appl. Sciences (2001), In press.Google Scholar
- 5.G.Eder, H.Janeschitz-Kriegl, Structure Development During Processing: Crystallization, in Materials Science and Technology, Vol.18 (edited by H.Meijer), Verlag Chemie, Weinheim, 1997.Google Scholar
- 6.Morale, D. “Laws of large numbers” for interacting particle systems: from discrete to continuum. An aggregation model., Ph.D. Thesis, Milano, 1999.Google Scholar
- 7.Boi, S., Capasso. V, Morale, D. “Modeling the aggregative behavior of ants of the species Polyergus rufescens.”, Nonlinear Analysis: Real World Applications, I, 2000, p. 163–176.Google Scholar
- 8.K.Oelschläger, Many-Particle Systems and the continuum Description of their Dynamics Habilitationsschrift, Faculty of Mathematics, University of Heidelberg, Germany, 1989.Google Scholar
- 9.C.Salani, Crystallization of polymers with thermal heterogeneities,Thesis for ECMI Diploma, Linz, A.A. 1996/97.Google Scholar
- 10.C. Salani, On the mathematics of polymer crystallization processes: stochastic and deterministic models., Ph.D. Thesis, University of Milano, Italy, 2000.Google Scholar