Electric 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.

Project Report

Intellectrual merit: This project studied the behavior of liquid drops in electric fields. Our experiments discovered novel features in the drop electrohydrodynamics: in a uniform DC electric field, a droplet deforms into an ellipsoid which can assume a steady tilted orientation relative to the applied field, see Figure A, or undergo irregular rotational motions, illustrated in Figure B. If drop viscosity is high, the ellipsoid tumbles, see Figure B.b, while randomly reversing the direction of rotation. A low-viscosity drop however can undergo additional deformation while rotating, see Figure B.a. Our theoretical models showed that the mechanism underlying the peculiar drop dynamics is Quincke rotation: the spontaneous spinning of a dielectric sphere that occurs above a threshold electric field. The Quincke rotor is one of the few physical realizations of a Lorenz chaotic system. Our research highlighted that drop deformability leads to even richer chaotic dynamics. Broader impact: The information from this project will be useful to scientists and engineers to design and process novel materials such as emulsions with tunable structure and viscosity, and develop new approaches for mixing in microfluidic applications. The complex behavior of an isolated deformable rotating drop hints upon even more interesting dynamics in a collection of drops, i.e., an emulsion. Active emulsions are a system of tremendous interest, whose emergent behavior is just starting to be explored. The award trained one PhD and one undergraduate student, and partially supported three post-docs. The results were published in five papers and broadly disseminated in the fluid dynamics, nonlinear physics, and applied math communities. Figure (detailed caption): A. Sketches illustrating drop shape and flow streamlines in a uniform direct current (DC) electric field with increasing strength: (a). The drop is spherical in the absence of electric field. (b). Weak fields induce pure straining flow and axisymmetric oblate deformation. (c). In strong fields, the flow acquires a rotational component and the drop is tilted with respect to the applied field direction. B. Examples of unsteady drop behavior in a uniform DC electric field. a) Viscosity ratio v=1, field strength E=9.9kV/cm, drop radius a=1.8mm. b) v=14, E=9.7kV/cm, a=3.0mm. Experimental system is silicon oil drop suspended in castor oil. c) Evolution of the aspect ratio in real time and in time-delay plots with dt=1/3s (inset) for drop with viscosity ratio v = 1.

Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
Brown University
United States
Zip Code