A thermodynamically consistent gradient dynamics model for the evolution of thin layers of liquid mixtures, solutions, and suspensions on solid substrates is presented which is based on a film-height- and mean-concentration-dependent free energy functional. It is able to describe a large variety of structuring processes, including coupled dewetting and decomposition processes. As an example, the model is employed to investigate the dewetting of thin films of liquid mixtures and suspensions under the influence of effective long-range van der Waals forces that depend on solute concentration. The occurring fluxes are discussed, and it is shown that spinodal dewetting may be triggered through the coupling of film height and concentration fluctuations. Fully nonlinear calculations provide the time evolution and resulting steady film height and concentration profiles.

A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such systems at intermediate length scales. This insight allows better understanding of the wrinkling patterns seen in such systems, with which we explain pattern breaking into domains, the properties of domain walls and wrinkle undulation. We compare our predictions with numerical simulations and with experimental observations.

We study equilibrium properties of polymer films and droplets on a solid substrate employing particle-based simulation techniques (molecular dynamics) and a continuum description. Parameter-passing techniques are explored that facilitate a detailed comparison of the two models. In particular, the liquid-vapor, solid-liquid, and solid-vapor interface tensions, and the Derjaguin or disjoining pressure are determined by molecular dynamics simulations. This information is then introduced into continuum descriptions accounting for (i) the full curvature and (ii) a long-wave approximation of the curvature (thin film model). A comparison of the dependence of the contact angle on droplet size indicates that the theories agree well if the contact angles are defined in a compatible manner.

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning.

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