Lattice-Boltzmann modelling of spatial variation in surface tension and wetting effects
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The main focus of the project which is the foundation of the thesis is to study the effects spatial variations in capillary effects have on fluid flow. This requires knowledge of the underlying fluid flow equations, and some sort of numerical method to handle numerical simulations. The first part of this thesis deals with the underlying theory of the methods. Classical fluid theory has a brief introduction, followed by the lattice Boltzmann theory and methods for two phase flow and some basic simulations to demonstrate how the two-phase flow methods work. Papers which have been submitted or presented make up the second part of the thesis. Chapter 1 in the thesis covers classical fluid flow. A particular emphasis is placed on the capillary effects of surface tension, and wetting. The chapter also covers theory on surfactants and their applications. Chapter 2 covers the foundations of the lattice Boltzmann method which I used throughout the project. The methods are a fairly new way of simulating fluid flow, even though it is based on the century old Boltzmann equation. The underlying algorithms are simple, but the simulated flow can be quite complex. Chapter 3 covers how the lattice Boltzmann method deals with more complex flow. This includes multiphase flow and flow with solute components. Variations in surface tension are also covered. Chapter 4 illustrates some of the properties found in the multiphase lattice Boltzmann methods used in this thesis. Chapter 5 is a summary of the work conducted. A short description of the papers included in the second part of this thesis is provided. The chapter also considers further extensions and possible improvements to the work in this thesis.
Paper A: Sigvat K. Stensholt (2010), Simulation of multiphase flows with variable surface tension using the Lattice Boltzmann method. Draft version.Paper B: Sigvat K. Stensholt (2010), Lattice Boltzmann simulations of the motion induced by variable surface tension. Submitted version. Submitted to International Journal on Numerical Analysis & Modeling. Published by Institute for Scientific Computing and Information. Full text not available in BORA.Paper C: Sigvat K. Stensholt (2010), Simulations of the passage of droplets through narrow capillaries using the Lattice Boltzmann method. Submitted version. Submitted to International Journal on Numerical Analysis & Modeling. Published by Institute for Scientific Computing and Information. Full text not available in BORA.Paper D: Sigvat K. Stensholt (2010), Nonideal equation of state in the pseudo-potential lattice Boltzmann methods. Draft version.