Flow phenomena at microstructured surfaces

The microstructure of a surface significantly influences its properties on the macroscale. It is for example responsible for the fact that a drop of water rolls down a superhydrophobic surface seemingly without any resistance. In nature, this behavior is known from various plant leafs, where it relies on the entrapment of air in the indentations of the surface. Transferred to technical applications, it could lead to a substantial increase in efficiency. For the development of such specifically tailored surfaces, a fundamental understanding not only of superhydrophobic, but also of similar surfaces is required. Up to now, analytical solutions for the flow along such surfaces have only been known for a limited number of theoretical and idealized cases. In the work presented here, analytical equations are derived that describe the effect of a microgrooved surface on the flow above it in a universal manner. For the first time, its dependency on the involved fluids and on the geometry of the grooves is characterized. To this aim, first, flow over an individual cavity is considered, and its flow field is calculated with complex analysis. The results are transferred to a periodically grooved surface via a superposition technique, so that an explicit, comparatively simple, but very exact analytical equation for the flow field above the surface is obtained. An expression of the same properties for the slip length follows, which is an effective measure for the macroscopic impact of the processes occurring on the microscale. Consequently, it is of considerable practical interest. With the present work, it can for the first time be directly related to the viscosities of the fluids and to the geometry of the grooves. Thereby, a basis is established for the investigation and design of surfaces that are optimized for their particular application, also beyond mere superhydrophobicity. A variety of insights into the functional principles of such flows further contribute to this aim. The findings also lay the foundations for the investigation of numerous further effects. For instance, the influence of slippage on electroosmotic and thermocapillary flow has been characterized. Electroosmotic flow relies on the propulsion of charges that naturally accumulate close to an interface. It can usually be observed in the vicinity of solid walls. A concept has been explored that aims at extending this effect to fluid-fluid interfaces, as they e. g. occur due to the enclosure of air in the indentations of the surface. Apart from numerical simulations, the net effect of a microstructured surface on the flow above it can also be derived for the case of electroosmotic flow. This explicit, analytical, macroscopic boundary condition also reflects well the influence of the details of the surface design. The investigated concept for the usage of superhydrophobic surfaces for electroosmotic flow enables substantial enhancements of the flow velocity. Aspects relevant to the practical realization have been discussed and a corresponding experimental setup has been developed.