REU Supplement for Collaborative Research: Electrorotational fluid instabilities

Overview: A classic result due to G.I.Taylor is that a weakly conducting drop bearing zero net charge placed in a uniform electric field adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. However, in stronger DC fields a number of intriguing symmetry--breaking instabilities have been experimentally observed by PI Vlahovska's group: drop steady tilt or tumbling, and ribbon-like pattern formation on the surface of a particle-coated drop. PIs’ previous work on electrohydrodynamics suggests that all these instabilities have in common the Quincke effect (the spontaneous rotation of a particle in a uniform DC electric field occurring above a threshold field strength.) However, the numerical and analytical tools needed to analyze these symmetry-breaking phenomena are currently lacking. To fill this void, we propose to develop (i) numerical simulations, based on the there-dimensional Boundary Integral Method, and (ii) analytical models using asymptotic methods, of drop dynamics in an electric fields. Experiments will be designed to guide and validate the computations and analytical results. Intellectual merit: The proposed research is a unifying study of seemingly unrelated electric-field driven instabilities. The proposal integrates theory, computations, and experiment, and transfers knowledge across the fields of fluid mechanics and applied math to systematically investigate electrotational instabilities in fluid systems. The potentially transformative nature of the proposal lies in the unexplained emergent behavior of the system that could inspire new research directions and applications related to complex fluids, instabilities and interfacial flows. With the integration of mathematical modeling, computations, and experiments we anticipate both a much deeper understanding of the underlying physics as well as the discovery of new dynamical regimes and engineering opportunities. Broader impact: In addition to advancing basic knowledge, the research will provide insights on how to harness these electroconvection phenomena for engineering of complex flows or patchy particles with dynamic surface patterns. The visually appealing nature of the experiments will excite students and the general public about electrohydrodynamics and complex systems. The PIs will leverage successful outreach programs at NU and UCSD to translate the relevance and significance of our work to attract students from underrepresented groups in science and engineering. The research advances in science and technology will be broadly disseminated by scientific articles, presentations at conferences, workshops and summer schools.