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Zjednodušené nerovnovážně termodynamické modelování polymerních pěn
Thesis title in Czech: Zjednodušené nerovnovážně termodynamické modelování polymerních pěn
Thesis title in English: Simplified non-equilibrium thermodynamic modeling of polymeric foams
Key words: Nerovnovážná termodynamika, fázová separace, difuze, polymerní směs
English key words: Non-equilibrium thermodynamics, phase separation, diffusion, polymer mixture
Academic year of topic announcement: 2018/2019
Type of assignment: Bachelor's thesis
Thesis language:
Department: Mathematical Institute of Charles University (32-MUUK)
Supervisor: RNDr. Michal Pavelka, Ph.D.
Advisors: prof. Ing. František Maršík, DrSc.
The work should consist of the following steps:
1) Review of the current state of knowledge.
1) Non-equilibrium thermodynamic [2,3] reformulation of the Maxwell-Stefan Cahn-Hilliard model from [4]. Dependence of the diffusion coefficients on the state variables can be simplified.
2) Analysis of solutions to the model in 1D: Construction of the phase diagram - spinodal and binodal curves. Estimate of thickness of the phase interface. Linear stability analysis, estimate of the fastest growing perturbation.
3) Weak formulation of the evolution equations should be solved in time numerically (by finite element method within the FeniCS framework), showing for example Ostwald ripening, and the results should be compared to the analytical results and, if possible, to experiments carried out at the University of Chemistry and Technology in Prague (Juraj Kosek's group).
[1] M. Vonka, A. Nistor, A. Rygl, M. Toulec and J. Kosek, Morphology model for polymer foams formed by thermally induced phase separation, Chemical Engineering Journal 284 (2016), 357-371
[2] S. R. de Groot and P. Mazur, Non-equilibrium thermodynamics, Dover 1984
[3] G. Lebon, D. Jou and J. Casas-Vázquez, Understanding Non-equilibrium Thermodynamics, Springer 2008
[4] M. Voclová, Improved description of transport in Cahn-Hilliard model of morphology evolution, Master thesis, University of Chemistry and Technology, Prague 2016
Preliminary scope of work in English
Polymeric foams (e.g. extruded polystyrene foam) are widely used as thermal insulators, sound insulators or impact absorbers. Such foams can be created from polymer solutions by phase separation. A promising way to trigger the phase separation is spinodal decomposition induced by cooling down the mixture below the critical point [1].

The goal of the thesis is to develop a thermodynamically consistent isothermal model of a mixture of a polymer and a solvent undergoing spinodal decomposition and to analyze solutions to the model.

The thesis could result in deeper understanding of the foam formation, and it should provide sound thermodynamic basis for modeling of the process.
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