Coupled dynamics of a thin lubricating film with hydrodynamic instabilities in a conjugated liquid layer

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In the course of the originally funded project DI 1689/1-1, the Bénard-Marangoni (BM) cellular convective instability, driven by a temperature gradient, was generated in a liquid layer. The convection cells cause interfacial deformations of a thin immiscible film placed between the layer and the supporting substrate. The deformations can be fixated if the film fluid is a polymer curable by irradiation with ultraviolet (UV) light. Re-establishing BM convection in a liquid layer placed on such a pre-structured substrate leads to a flow pattern which is exactly identical to the one used to structure the substrate, i.e. the hydrodynamic pattern formed in the fluid volume is 'stored' at its boundary and retrieved from it again. This follow-up proposal aims at elaborating on this principle in more detail. The stability regime of the conjugated liquid layer system will be probed by a weakly non-linear analysis as well as by full numerical simulations. Subsequently, the description of such coupled self-organizing subsystems will be cast in a more generic mathematical framework to identify a class of coupling operators which cause an emergent behavior of the full system. This means that its dynamics (i.e. of the conjugated layers) may be qualitatively different from that of its constituents (i.e. the individual liquid layers). Solidification of the film is not required; the pattern-conserving effect the thin film has on the upper layer remains functional as long as the characteristic time the liquid-liquid interface takes to flatten after a temporary removal of the driving temperature gradient is much larger than the decay time of the convection in the thicker layer. This property will be used to experimentally explore convection-diffusion dynamics of a dissolved/suspended species subjected to BM convection. Storing and retrieving a hydrodynamic pattern from the boundary of a fluid domain may be feasible for a broader class of flow phenomena. To this end, the Faraday instability emerging in a liquid layer upon exposure to vertical vibrations will be experimentally examined when a thin liquid film is placed between the liquid layer and the solid substrate. By contrast to BM convection, the Faraday instability implies linear oscillatory flow, whose shear stress does not necessarily cause a time-averaged deformation of the liquid film. Nevertheless, the presence of the film may render the conjugated system non-linear, so that a time-averaged deformation may be observed. Via solidification by UV light such deformations may be stored at the fluid boundary and analyzed by a profilometer, while its hydrodynamic 'information content' may be retrieved in a subsequent experiment. With this work we intend to establish the fundaments of a new engineering tool allowing not only to tune the stability regimes of certain flows, but also to 'engrave' certain flow characteristics into the domain boundary. We call this novel principle hydrodynamic pattern memory.