Lattice Boltzmann simulations of the dynamics of thin liquid films

Fluid dynamics is a part of our everyday life. The governing equations describe not only large weather systems on planetary scales (10^6 m) but also reach down to wetting problems on the nanometric scale (10^(-9) m). That a single theory can describe both the movement of atmospheric layers as well as the displacement of the contact line of a droplet with a diameter smaller than a micrometer (10^(-6) m) is highly non trivial and related to the scale invariant nature of flow problems. The lubrication approximation was first thought of by Osborn Reynolds in the 19^th century. He understood that a lubrication layer is essentially a thin layer of fluid between mechanical components. This thin layer offered some novelties which made it possible to simplify the Navier-Stokes equation. From that time onwards the functional formulation of the lubrication approximation, the so-called thin film equation, has shed new light on problems such as wetting, coating and printing to name but a few. Today the thin film equation is used to understand several phenomena in nature and on the other hand to optimize various industrial applications. Insects for example need to have a water-repellent exoskeleton. Due to their size they would not be able to overcome the surface tension of water and therefore could become trapped inside a drop. In agriculture the distribution of pesticides relies on the adhesion between the pesticide's transport fluid and the plant's surface. Having a too low affinity would just wash off the pesticide, however by reducing the surface tension via so-called surfactants it is more likely that the pesticide sticks to the plant. Another application relates to the production of computer chips. The process itself is fairly complex, however at some point the yield on the wafer heavily relies on the homogeneous distribution of photoresist, and therefore on wetting. Over the past six decades numerical methods have become more and more essential to study fluid dynamics. Culminating in a topic of research of its own called computational fluid dynamics (CFD). Not only is it used in an academic environment but also in for entertainment purposes, e.g. computer games and animated movies. One numerical approach among the vast zoo of CFD methods is the lattice Boltzmann method (LBM). Instead of a direct simulation of the fluid's density and velocity the LBM uses a statistical approach based on the Boltzmann equation. We make use of this approach and derive a model that is capable of solving the thin film equation. The starting point is the shallow water lattice Boltzmann method. Interestingly enough with well defined approximations the shallow water dynamics can be recast to the thin film equation. This approach is tested and in agreement with known numerical and experimental results such as instabilities, droplet dynamics and dewetting. Dewetting, i.e. the process when a liquid retracts from a surface, is extensively studied in this thesis. When it comes to dewetting one mostly ignored effect of experiments is the presence of thermal fluctuations. Theoretically this poses a different and more complex problem as the resulting equation is no longer deterministic. The resulting stochastic thin film (STF) equation can however be treated with the here developed LBM. Including fluctuations does in fact accelerate dewetting, which is in agreement with previous studies, but can also lead to novel couplings when the substrates' wettability is heterogeneous. Dewetting can also be addressed using a time and spatially dependent wettability. The priority program SPP 2171 of the German Research Foundation (DFG) aims to deepen our understanding of liquid-substrate interactions. Our contribution to this program is the study of so-called switchable substrates. With simple arguments it is shown that a morphological transition during dewetting can be induced. Instead of several droplets fewer rivulets are present based on the dynamics of the local wettability. Lastly, it should be mentioned that this thesis is of cumulative nature. It encompasses the work of four peer review publications. The first three chapters are intended as a general introduction to the topic, the theory and the numerical method. Introducing, therefore, the concept of a thin liquid film, the governing equations of motion and suitable numerical algorithms to solve them. Following these introductory chapters are the four chapters containing the four peer reviewed articles and one chapter to conclude the thesis.