@phdthesis{Pototskyy2005, author = {Pototskyy, Andriy}, title = {Pattern formation in thin one- and two-layer liquid films}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-000000822}, school = {BTU Cottbus - Senftenberg}, year = {2005}, abstract = {This work deals with static and dynamic properties of thin one- and two-layer liquid films. Regarding one-layer films, we study large scale surface deformations of a liquid film unstable due to the Marangoni effect caused by external heating on a smooth and solid substrate. To prevent rupture, a repelling disjoining pressure is included which accounts for the stabilization of a thin precursor film and so prevents the occurrence of completely dry regions. Linear stability analysis, nonlinear stationary solutions, as well as three-dimensional time dependent numerical solutions for horizontal and inclined substrates reveal a rich scenario of possible structures for several realistic liquid parameters. We also propose two methods to control the structuring of unstable thin films of soft matter. The first one is a non-contact method, where an external disturbance can be used to move a single drop, front or hole in a certain direction. The principle is illustrated by incorporating a sonic disturbance in a thin film equation to study the evolution of ultrathin films unstable due to their wetting properties. The second one is based on inhomogeneous templating of the substrate. Here we study the influence of periodic modulation on coarsening in the long time limit. Finally, the fully nonlinear evolution of a 3D system is presented by numerical integration. Further on, we consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both, the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100 nm thickness, or due to temperature-gradient caused Marangoni flows in the heated case. Using a long wave approximation we derive coupled evolution equations for the interface profiles for the general non-isothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag or mixed type. However, in the nonlinear stage of the evolution the mode type and therefore the pattern morphology can change via switching between two different branches of stationary solutions or via coarsening along a single branch.}, subject = {Musterbildung; Fl{\"u}ssigkeitsfilm}, language = {en} }