Nonlinear Droplet Electrohydrodynamics in Stokes Flow Regime

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1132614VlahovskaElectric fields provide a versatile means to control small-scale fluid and particle motion. Recent experiments in the PI's group have discovered unusual droplet behavior such as tumbling, oscillations and chaotic dynamics in response to uniform DC electric fields. The proposed research is motivated by (1) the scientific intrigue of these new nonlinear phenomena occurring under creeping flow conditions and (2) applied interest to exploit them in technologies related to microfluidics and electrorheological materials. The objective of this proposal is to uncover the mechanisms by which interface deformation and charging give rise to nonlinear droplet electrohydrodynamics. To this end, the PI will integrate (1) dynamical systems theory to analyze drop behavior in the small-deformation regime and the transition to chaos; (2) numerical simulations based on the Boundary Integral Method to explore large drop deformations and the collective dynamics of drops; and (3) experiments to guide and test the theoretical analyses and computations.Intellectual merit: The proposed combination of theory, computation and experiment will provide a comprehensive understanding of droplet electrodeformation and electrorheology of emulsions. These are challenging and unexplored problems at the intersection of fluid mechanics, dynamical systems, and soft condensed matter. The potentially transformative nature of the proposal lies in identifying yet unexplained physics that could yield new applications related to microscale flows and complex fluids. The work could become a prototypical physical example of chaotic nonlinear dynamics.Broader impacts: The research outcomes of this proposal are relevant to many natural and industrial processes involving disperse two-phase systems in electric fields, including the break-up of rain droplets in thunderstorms, ink-jet printing, electrohydrodynamic atomization, and separation of emulsified water from oil in the petroleum refining process. More specifically, the research will help advance engineering applications such as microfluidics, where the chaotic particle dynamics can be utilized for in-situ micro-mixing. The project blends physics, applied math, and engineering approaches and thus provides excellent training ground for doctoral and undergraduate students. By means of the synergy between theory and experiment, the project will excite the more experimentally inclined students about theory, and conversely, inspire curiosity in the students who are more focused on theory about the experiments that motivate the mathematical models. The PI will leverage well-established and successful outreach programs at Brown University to attract underrepresented minorities in science and engineering. The research and related advances in science and technology will be broadly disseminated by presentations at meetings, workshops and summer schools. Droplets oscillations, tumbling, and break up are visually appealing effects that naturally excite both general public and science and engineering audiences.