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Title: Finite element analysis of multi-body interactions in membranes and colloidal systems
Author: Hassan, Ghasan F.
Awarding Body: University of Surrey
Current Institution: University of Surrey
Date of Award: 2009
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Colloidal interactions namely hydrodynamic and electrical forces are of a significant practical importance to many industries. Electrostatic interactions are one of the major forces affecting the stability and behaviour of a colloidal system. Thus, studying these interactions and understanding their behaviour will have very useful implications in many areas. The aim of this study is to quantify electrostatic interactions in multi-body colloidal systems using numerical methods to solve the governing equations for electrical potential and surface charge distribution. Finite Element Method combined with error estimation and mesh refinement has been used to provide a flexible numerical solution to the 2D non-linear Poisson-Boltzmann equation in order to obtain the potential distribution, which is used to calculate the free energy of interaction and the electrostatic force for surface potential and surface charge density boundary conditions; for different geometries and settings. The FEM has been used to provide solution to 3D geometries as well. The schemes provide quantifications of the electrostatic interactions which is expected to be very useful in many fields, and to fill some of the void in numerical software vicinity, regards solving the non-linear PBE. This will help to gain more understanding of the nature of multi-body interactions, which is yet to be fully understood. The model has been applied to a number of different study cases, in particular, that of a charged sphere approaching a charged wall, two identical charged spheres, chain of charged spheres, and a chain of spheres inside a chain of rings for the 2D model. The problem of two charged spheres approaching a charged wall and an array of charged spheres have also been solved in the 3D model. The finite element method has proved to be effective in quantifying multi-body electrostatic interactions in 2D geometries and more complex 3D geometries. The 3D code has been first validated by comparison with previous 2D code results where very good agreement were obtained, and then extended to solve 3D cases where no previous solution exists.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available