Coupled dynamics of a thin lubricating film with hydrodynamic instabilities in a conjugated liquid layer
Final Report Abstract
In this project, mainly two types of activities were pursued. The first activity was concerned with electric-field driven instabilities in systems of two superposed immiscible liquid layers. The liquids are immiscible aqueous polymer solutions. Fluorescently stained DNA molecules were adsorbed at the interface. This was done by first dissolving the molecules in one of the phases, followed by applying a DC electric field. Below a threshold field strength, the molecules migrate to the liquid-liquid interface but are not able to cross it. While the DNA molecules are adsorbed at the liquid-liquid interface, patterns in the concentration field emerge, especially filamental structures. These patterns go hand in hand with convection cells and are caused by the electroosmotic flow due to the space charge region around the DNA molecules. A theoretical model for the pattern formation based on a linear stability analysis was developed. The model predicts that first all modes are stable, but at a specific point in time, they get destabilized. The theoretical results agree well with experimental data. The model predictions for the emergence of spatial scales obtained in the linear regime appear to remain valid even in the non-linear regime. It can be hypothesized that such a model framework can also be applied to other pattern formation processes described by non-linear integro-differential equations. The second activity was focused on the Faraday instability in systems of two superposed immiscible liquid layers, where the lower layer is much thinner than the upper one. Briefly, a thin liquid layer is superposed by a much thicker one, and the system is excited by oscillating the supporting surface in vertical direction. A corresponding experimental setup was established, and a theoretical framework based on Floquet theory was developed. The theory predicts that the instability in two layer-systems can be qualitatively different from the singlelayer instability. That is, in the two-layer system the subharmonic mode can be the first one to become unstable. The theoretical predictions for the onset of instability agree well with experimental results, thus corroborating the validity of the theory. In the experiments it was found that in an unstable two-layer system a steady-state deformation of the liquid-liquid interface is obtained, i.e. the lower liquid accumulates in certain regions. This is a non-linear effect not captured by the theory. This effect can be used to implement a principle termed Hydrodynamic Pattern Memory: The hydrodynamic memory is inscribed in the deformations of the liquid-liquid interface. A subsequent excitation of the two-layer system reproduces exactly the same cellular pattern.
Publications
- Faraday instability of a liquid layer on a lubrication film, Journal of Fluid Mechanics 879 (2019), 422-447
S. Zhao, M. Dietzel, and S. Hardt
(See online at https://doi.org/10.1017/jfm.2019.684) - Electric-field-induced pattern formation in layers of DNA molecules at the interface between two immiscible liquids, Physical Review Letters 124 (2020), 064501
S. Hardt, J. Hartmann, S. Zhao, and A. Bandopadhyay
(See online at https://doi.org/10.1103/PhysRevLett.124.064501)
