Dynamic wetting on deforming substrates, elastic sheets, and under evaporation: A study with the boundary element method

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Dynamic wetting of flexible and switchable substrates has many fascinating manifestations and potential for applications. Droplets on thin elastic sheets assume the shape of a lens, which is tunable by tension forces applied to the sheet. This effect can be used to construct micro-optical lenses. Controlling the surface deformations of soft substrates in time allows to move micron-sized droplets, an essential process for lab-on-a-chip devices. The evaporation of droplets covered with light-switchable surfactants offers the possibility to position solutes such as ink pigments on a substrate with subdroplet precision, which is relevant for technological advances in printing.In our project we plan to address these topics in order to achieve a fundamental and thorough understanding. We will use the boundary element method (BEM) to determine the flow field within the droplet and phenomenological expressions such as the Cox-Voinov law to describe the contact-line dynamics. Recently, we have implemented our BEM approach for rigid substrates with spatio-temporal wettability patterns in a computer code, which we will extend to deal with the different topics.First, we will study the directed transport of droplets by traveling-wave deformations on the surface of light-responsive materials and determine conditions of optimal transport. Second, we address dynamic wetting on elastic sheets, which we describe with the two-dimensional elastic Skalak model and the Helfrich Hamiltonian for bending. We perform a thorough study of the lens-shaped droplets under varying tension forces and investigate durotaxis, where the droplet moves to softer parts of the sheet. Third, we will apply tension forces, which vary in time and along the sheet edge to explore the possibility of controlled droplet motion, also using electrowetting. We will collaborate here with P. Huber (Hamburg), who can fabricate elastic nanoporous silicon sheets and plans to perform corresponding experiments. Finally, for rigid substrates we look at evaporating droplets, where the surface tension determined by light-switchable surfactants is locally changed with irradiated light. The resulting Marangoni currents induce vortices within the droplet, which trap solutes and ultimately deposit them on the substrate in designed patterns.