The objective of this Faculty Early Career Development (CAREER) Program award is to investigate and understand the physical origin and quantify the dynamics of self-sustained motions, singularity formation, and topological changes of complex fluid interfaces in the context of Marangoni effects driven by surface-active substances (surfactants). Achieving these objectives will require developing new theoretical tools in order to identify the conditions for the occurrence of surfactant-driven instabilities and resulting self-induced dynamical motions, and uncover the role of interfacial singularities in sustaining such motions. The proposed research will lead to the elaboration of new geometrically inspired theoretical methods based on the synergy of dynamical systems, differential geometry, geometric flows, and singularity theories. If successful, this research program will also help one to understand the interplay between singularity and instability phenomena and thus allow one to make progress on Arnold's problem of combining Cartan's and singularity theories.
Self-sustained motions of interfaces are at the basis of all motors in living organisms. Revealing and artificially creating such functions is important both from the fundamental and practical points of view, e.g. in the development of artificial cells. Addressing these questions will advance new fields in science and engineering. In particular, the proposed research program will enhance the theoretical basis for understanding mechanisms of certain types of biological motors at meso- and macroscopic scales and for creating biological functions artificially. Since complex interfaces are ubiquitous, the outcome of this research program should provide ideas for the most efficient designs in numerous applications of surfactants with desired functions ranging from engineering to biology. At the dissemination level, the studied phenomena provide a great opportunity to introduce people to science and technology at varying degrees of complexity and to encourage scientific training. Graduate, undergraduate, and regional high-school students will benefit not only through classroom instruction, but will also receive firsthand research experience.
Self-sustained motions of interfaces are at the basis of all motors in living organisms. Revealing and artificially creating such functions is important both from the fundamental and practical points of view. The research supported by this award was aimed at elucidating the physical origin and quantifying the dynamics of self-sustained motions, singularity formation, and topological changes of fluid interfaces. With the help of analytical and experimental methods, we made progress on each of these tasks. General interfacial singularities, occurring both in time and space, were studied and resolved in the context of water impact phenomena and chemically-driven interfacial flows. The effects of surface tension variation on the flow topology were analyzed experimentally in the context of coating flows, which revealed bifurcation phenomena responsible for thickening of the coating film. We also developed a new theoretical framework to analyze stability on time-dependent domains, which include interfacial systems exhibiting patterns of singular structures such as the ones formed on liquid rims discovered in our experiments. Overall, during the grant period, we made progress on understanding the underlying physics responsible for the existence of various types of interfacial singularities, their interrelation to instabilities and role in sustaining interfacial motions. Two graduate and a few undergraduate students were trained and partially supported with this award.
