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Surfaces exhibiting complex topographies, such as those encountered in biology, give rise to an enormously rich variety of interfacial morphologies of a liquid to which they are exposed. In the present article, we elaborate on some basic mechanisms involved in the statics and dynamics of such morphologies, focusing on a few simple paradigm topographies. We demonstrate that different liquid interface morphologies on the same sample frequently coexist. To exemplify the impact of the dynamics on the final droplet morphology, we discuss the shape instability of filamentous liquid structures in wedge geometries. We finally show that some side effects that may dominate on a larger scale, such as contact line pinning and contact angle hysteresis, seem to play a minor role on the microscopic scale under study. This establishes the validity of simple theoretical concepts of wetting as a starting point for describing liquids at substrate surfaces of high complexity.
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