Fluctuations and patterns in ultrathin fluid films

Abstract

Self-organization processes, in which some form of collective behavior arises from local interactions in a physical system, are promising mechanisms in the context of manufacturing at ultra small scales, where processing techniques are technically challenging. In many cases, the approach is to induce self-organization or self-assembly phenomena on the system surface |which indeed acquires an increased importance at small scales because of the enhanced surface-to-volume ratio| as a result of which a desired surface morphology is achieved, with different properties depending on its intended application. In this thesis, we consider two important examples of self-organization processes which take place at the surfaces of many small non-equilibrium systems. One of them, kinetic roughening, reflects the dominance of fluctuations in the surface morphology, with strong correlations which are quite similar to those of an equilibrium system at a continuous phase transition. The second, opposite self-organization process is the formation of ordered patterns. In the thesis, we will deal with the control of the level and type of various surface properties, like roughness and other, and the conditions for the emergence of a varying degree of spatial order in patterns via spontaneous physical processes. We work in the context of ultrathin fluid films on solid substrates, focusing on the role of the physical effects that become relevant at these very small scales -but not so much at larger scales-, while other loose their relevance. One of these aspects is the thermal noise. The other one is the interaction between the uid surface and the substrate, that play a key role in the two reference physical systems we are going to study: an ultrathin fluid film falling down an inclined plane |where the dynamics of the fluid surface follows the celebrated Kuramoto-Sivashinsky (KS) equation -and a ferrofluid ultrathin film under a magnetic field. Both kinetic roughening and pattern formation usually exhibit some kinds of universal behavior. The universality classes in the kinetic roughening processes that occur in several approximations of the KS equation are widely studied in this thesis. These universality classes are characterized by both how the fluctuations scale with space and time and how these fluctuations are statistically distributed. We will deal with the emergence of symmetries in the fluctuation distributions that are unexpected considering the bare microscopic interactions; the non-trivial relation between the universality class of closely related models; with a novel physical mechanism that induces the transition between different universality (sub)classes as the system temperature and hence the dominant nature of the fluctuations (chaotic or stochastic) changes, and finally with some anomalous kinetic roughening processes in the limit of vanishing viscosity and surface tension. Finally, on the other hand, the formation of highly ordered patterns is assessed in the context of ultrathin ferrofluid films under a magnetic field, due to the spontaneous physical break-up of the film into drops. The conditions under which higher levels of order are achieved will be described. This is intended as a proof-of-concept, previous step that could encourage experiments being performed for this type of systems.