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Optimalizace modelování koloidních suspenzí
Thesis title in Czech: Optimalizace modelování koloidních suspenzí
Thesis title in English: Optimization of colloid suspension modeling
Key words: Termodynamika, částicové modelování, mechanika tekutin, paralelní výpočty
English key words: Thermodynamis, particle modeling, fluid mechanics, parallel computing
Academic year of topic announcement: 2018/2019
Type of assignment: diploma thesis
Thesis language:
Department: Mathematical Institute of Charles University (32-MUUK)
Supervisor: RNDr. Michal Pavelka, Ph.D.
Author:
Advisors: RNDr. Štěpán Roučka, Ph.D.
Guidelines
A purpose of this thesis is to optimize the numerical code developed at the University of Chemistry and Technology in Prague [1] so that more particles can be taken into account and that the total simulated time is longer. As a result, the applicability of the code should be broadened so that wider range of experimental results can be addressed. Moreover, development of a thermodynamic description of such systems could provide invaluable insight into behavior of dispersions. This is crucial for industrial applications, where for example stability of the dispersions plays an important role.

The work should consist of the following steps:
1) Analysis of performance of the code from [1]. Identification of bottlenecks.
2) Optimization of the DEM code by means of parallel computing. In particular, efficient implementation of neighbor particles recognition.
3) Comparison of the new numerical results to experimental data, if possible.
4) Proposal of a free energy functional (or a related potential) for the dispersions compatible with results of the numerical simulations.
References
[1] Kroupa, M., Utilization of discrete element method for modeling of disperse systems, Master thesis, Institute of Chemical Technology, Prague 2013
[2] Kroupa, M., Vonka, M. and Kosek, J., Modeling the Mechanism of Coagulum Formation in Dispersions, Langmuir 30 (2014)
[3] Kroupa, M., Vonka, M., Soos, M. and Kosek, J., Size and Structure of Clusters Formed by Shear Induced Coagulation: Modeling by Discrete Element Method, Langmuir 31 (2015)
[4] Jou, D., Lebon, G. and Casas-Vazquez, J., Extended Irreversible Thermodynamics, Springer 2010
Preliminary scope of work in English
Colloidal dispersion is a mixture of microscopically dispersed insoluble particles in a continuous medium. Such mixtures are ubiquitous in everyday life (milk, beer) and in industrial and technical applications (latex paints).

Colloidal dispersions can be successfully modeled by means of coupled interactions between the dispersed particles and the surrounding fluid. Interaction between the particles can be described by Newtonian mechanics implemented as the Discrete Element Method (DEM). Evolution of the fluid is obtained by using Computational Fluid Dynamics (CFD) implemented as Finite Element Method or Finite Volume Method. Finally, DEM and CFD can be coupled, and one obtains a model describing the whole colloidal dispersion, [1], [2], [3].

Such an approach leads to description of evolution of the dispersions in time, and when letting the simulated system relax to equilibrium or to a steady state, equilibrium-thermodynamic or steady-state-non-equilibrium-thermodynamic properties of the system are obtained. Such properties should be compatible with free energy of the dispersion. In particular, to dependence of the free energy on shear rate in the non-equilibrium case [4].

 
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