Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth

Abstract

In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting, evaporation/condensation or epitaxial growth, respectively. We highlight similarities and differences of the three systems based on the observation that in certain limits all of them may be described using models of similar form, i.e., time evolution equations for the film thickness profile. Those equations represent gradient dynamics characterized by mobility functions and an underlying energy functional. Two basic steps of mathematical analysis are used to compare the different system. First, we discuss the linear stability of homogeneous steady states, i.e., flat films; and second the systematics of non-trivial steady states, i.e., drop/hole states for dewetting films and quantum dot states in epitaxial growth, respectively. Our aim is to illustrate that the underlying solution structure might be very complex as in the case of epitaxial growth but can be better understood when comparing to the much simpler results for the dewetting liquid film. We furthermore show that the numerical continuation techniques employed can shed some light on this structure in a more convenient way than time-stepping methods. Finally we discuss that the usage of the employed general formulation does not only relate seemingly not related physical systems mathematically, but does as well allow to discuss model extensions in a more unified way.

References in corpus (15)

• Disjoining Potential and Spreading of Thin Liquid Layers in the Diffuse Interface Model Coupled to Hydrodynamics
• Morphology changes in the evolution of liquid two-layer films
• Alternative pathways of dewetting for a thin two-layer film of soft matter
• Coarsening Dynamics of Crystalline Thin Films
• Long-wave theory of bounded two-layer films with a free liquid-liquid interface: Short- and long-time evolution
• Drops on an inclined heterogeneous substrate: onset of sliding motion
• Self-propelled running droplets on solid substrates driven by chemical reactions
• Morphological phase transitions of thin fluid films on chemically structured substrates
• Front instabilities in evaporatively dewetting nanofluids
• Dewetting of thin films on heterogeneous substrates: Pinning vs. coarsening
• Asymptotic theory for a moving droplet driven by a wettability gradient
• Coarsening Dynamics of a One-Dimensional Driven Cahn-Hilliard System
• Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states
• Liquid transport generated by a flashing field-induced wettability ratchet
• Coarsening process in one-dimensional surface growth models

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