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Numerical simulation of the coagulation process with different kernels

Paweł Damian Kukliński

Abstract

This thesis begins with a description of some commonly known real-life examples of coagulation systems. Then it outlines the theoretical description of coagulation systems with finite size. It describes the continuous approach, the approach based on the Smoluchowki equation as well as the discrete approach in which time and the sizes of clusters are discrete. Based on combinatorial investigations of the number of ways of the evolution of the system formulas for the mean number of clusters of particular size at a particular time are obtained. These formulas were not known previously in the case of systems with additive and product kernels. The most important part of this thesis are the derivations of the numbers of ways a cluster of mass g can be obtained (it is successfully done for the constant, multiplicative and additive kernel). This problem can be boiled down to a difference equation which can be solved using a generating functions approach. This model was verified with numerical simulations which are described in chapter 4. In chapter 5 the results obtained by theory and simulations are compared to the solutions of the Smoluchowski equation in different instances of time of the evolution of the system. The solutions of Smoluchowski’s equation agrees with simulation only in the early stages of the evolution. This problem is not observed in the combinatorial approach. Hence, the comparison works in its favour. The limitation of the combinatorial approach is discussed as well. It is the gelation point in which a phase transition appears. This thesis contains also graphs showing the uncertainties associated with the theoretical values of the average number of cluster of particular size at a particular time. At the end, some suggestions for possible further research are made.
Diploma type
Engineer's / Bachelor of Science
Diploma type
Engineer's thesis
Author
Paweł Damian Kukliński (FP) Paweł Damian Kukliński,, Faculty of Physics (FP)
Title in Polish
Symulacja numeryczna procesu koagulacji z różnymi mechanizmami scalania
Supervisor
Piotr Fronczak (FP/PCSD) Piotr Fronczak,, Physics of Complex Systems Divison (FP/PCSD)Faculty of Physics (FP)
Michał Łepek (FP/PCSD) Michał Łepek,, Physics of Complex Systems Divison (FP/PCSD)Faculty of Physics (FP)
Certifying unit
Faculty of Physics (FP)
Affiliation unit
Physics of Complex Systems Divison (FP/PCSD)
Study subject / specialization
, Fizyka Techniczna
Language
(pl) Polish
Status
Finished
Defense Date
11-02-2019
Issue date (year)
2019
Reviewers
Michał Łepek (FP/PCSD) Michał Łepek,, Physics of Complex Systems Divison (FP/PCSD)Faculty of Physics (FP) Grzegorz Siudem (FP/PCSD) Grzegorz Siudem,, Physics of Complex Systems Divison (FP/PCSD)Faculty of Physics (FP)
Keywords in Polish
układy koagulacyjne, wielomiany Bella, symulacje numeryczne
Keywords in English
coagulation systems, aggregation, numerical simulations, Smoluchowski equation
Abstract in Polish
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engineering_thesis.pdf
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Identyfikator pracy APD: 27175

Uniform Resource Identifier
https://repo.pw.edu.pl/info/bachelor/WUT84bdef744ac44078952b99258f0c412a/
URN
urn:pw-repo:WUT84bdef744ac44078952b99258f0c412a

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