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Mathematical modelling and simulations of the ion transport through confined geometries
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Matejczyk, Bartłomiej (2019) Mathematical modelling and simulations of the ion transport through confined geometries. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3442836~S1
Abstract
In this dissertation, we focus on different aspects of modelling ion transport in confined geometries. The transport of the ions through pores was first investigated in the 19th century for cell membranes. In the last years, there has been a significant increase in research of ion transport in nanoscale devices, such as nanopores, nanowires and many more. Especially synthetic pores have the potential to be used as nanoscale diodes, switches or in DNA sequencing.
In this thesis, we investigate different modelling approaches and discuss their use and validity in various situations. The transport properties of nanoscale pores are strongly determined by the confined geometry as well as surface charges. Depending on the experimental setup considered finite size, electrostatic as well as electrochemical properties have to be resolved on various scales. This leads to a variety of models ranging from microscopic approaches, such as Molecular Dynamics, to macroscopic models like mean field theory. Since finite size effects and fluid dynamics effects should not be neglected in confined geometries various extensions of the Poisson-Nernst-Planck (PNP) system were introduced in the literature such as density functional theory or the coupling to fluid dynamics. Another challenge in ion transport modelling is the multiscale nature of the synthetic nanopores as their length scale is sometimes 104 times larger than their radial dimension.
In the first part of the thesis, we develop a multiscale method that investigates the asymptotic behaviour of the PNP equations for long and narrow nanopores. The significant difference in the radial and lateral length scale allows us to decouple the system and to solve the behaviour in the boundary layers close to the charged pore walls correctly. Two new asymptotic methods were developed to describe the transport problem inside the pore. This asymptotic approximation serves as the basis for the numerical solver. We investigate the quality of the approximations for a variety of pores with different computational experiments. We present comparison of the microscopic quantities such as concentrations and electric potential as well as macroscopic quantities such as current voltage characteristic of exemplary pores. In the second part of the thesis, we compare the simulations of the PNP system with Monte-Carlo methods in the case of ion-channels. We discuss the different modelling assumptions as well as the advantages of both methods. Yet again we present results of the numerical simulations and discuss regimes in which both methods are valid. In the last part, we investigate the optimal control problem for nanopores. Here we want to modify the surface charge of a nanopore to obtain a desired behaviour, such as current-voltage characteristics or rectification behaviour. Two method are derived and implemented as a solution of stated problem.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General) |
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Library of Congress Subject Headings (LCSH): | Nanopores, Ion flow dynamics, Transport theory | ||||
Official Date: | 2019 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Wolfram, Marie-Therese | ||||
Format of File: | |||||
Extent: | xiii, 156 leaves : illustrations, charts | ||||
Language: | eng |
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