Modelling of dynamical effects related to the wettability and capillarity of simple and complex liquids

This Thesis explores physical phenomena characteristic for thin liquid films and small droplets of simple and complex liquids on solid substrates for which wettability and capillarity control their statical and dynamical properties. We start by discussing the general concepts of wettability and capillarity and introduce the common mathematical framework of the lubrication approximation for studies of thin liquid films and small contact angle drops. We demonstrate the derivation of the generic equation describing the evolution of a film of simple liquid from the Navier-Stokes equations. We show how this model can be further extended to incorporate various effects relevant to the case of complex liquids. The results described in the Thesis comprise three projects with the common main theme of the influence of wettability and capillarity on the statics and dynamics of the studied systems, namely (i) Evaporating sessile droplets fed through the solid substrate - a geometry that allows us to discuss steady states of the system and their role in the time evolution of freely evaporating droplets without influx in an isothermal case; (ii) The influence of a solute--dependent wettability on the stability, static and dynamical properties of thin films and drops of non-volatile mixtures, suspensions and solutions; (iii) A parameter-passing scheme between particle-based Molecular Dynamics simulations and the continuum lubrication model which allows us to discuss equilibrium properties of small polymeric droplets. We present the physical questions arising in the three systems and discuss approaches and results as well as possible extensions.