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The goal of this research is to understand of the essential microphysical mechanisms that govern the flow of surfactant-laden emulsions in presence of electric fields. We have started a systematic study of drop electro-hydrodynamics. During the first year, we have experimentally investigated drop responses to applied uniform DC electric field and classified the different modes in phase diagrams; we quantified the steady shapes of droplets in electric field. During the second year, the focus was on transient behavior as well as theoretical modeling.

1. Droplet dynamics in an uniform electric field

Drop dynamics in electric fields is a classic problem that continues to surprise researchers. The early studies of viscous droplets in uniform electric fields showed that for weakly conducting media the drop fluid undergoes a toroidal flow and the drop adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. However, recent studies have revealed nonaxisymmetric drop deformation accompanied by rotational flow. Our ongoing experiments have discovered new features such as hysteretic and chaotic dynamics, even under creeping-flow conditions. Strong DC electric fields also induce sustained drop oscillations and are reported to lower the effective emulsion viscosity below that of the matrix fluid. The latter, so called “negative viscosity", effect has been also observed in suspensions and linked to electrorotation of the constituent particles.

We studied the complex rotational dynamics of an individual droplet in uniform DC electric fields. The drop and continuous phase fluids (silicon and castor oil) satisfy the condition for oblate deformation and electrorotation. We measured the drop tilt angle and fluid rotation rate as a function of field strength, drop viscosity and size. We discovered significant deviations from the classic Quincke theoretical model for the electrorotation of a rigid sphere. For example, we found that the critical field strength for onset of electrorotation depends on drop size and viscosity. While for small, high viscosity drops, the threshold field strength for the symmetry--breaking is well approximated by the Quincke criterion, reducing the drop viscosity shifts the onset for rotation to stronger fields. Intriguingly, once rotation has been initiated, the rotation rate for each viscosity ratio agrees with the Quincke theory. We found a power law dependence of the threshold electric field on the viscosity ratio (power -1/4). We have also discovered hysteresis in the transition between axisymmetric oblate and asymmetric tilted drop configuration; the larger the drop and the lower the viscosity, the more pronounced the hysteresis.  Moreover, droplets displayed new dynamics such as tilt-angle hysteresis, chaotic tumbling, shape oscillations.

Our experimental results show that unlike the rigid sphere, drop size and fluid viscosity affect electrorotation. The threshold field for onset of fluid rotation increases with decreasing drop viscosity and size; the viscosity dependence is stronger. These effects can be attributed to charge convection by the straining component of the electrohydrodynamc flow, which weakens the induced dipole and reduces oblate drop deformation. Charge convection may also play role in the observed hysteresis in the transition between axisymmetric and asymmetric drop shapes. Hysteresis implies bistability, which is absent in the simple Quincke model. We are currently developing a theoretical model to quantify this hypothesis.

2. Emulsion electrorheology

During the second year, I have also theoretically analyzed drop dynamics when electric field and shear flow are simultaneously applied. A small--deformation perturbation analysis was developed to describe the effect of an uniform DC electric field on drop deformation and orientation in linear flows and emulsion shear rheology. All media were treated as leaky dielectrics and fluid motion is described by the Stokes equations. The model accounts for charge convection. The one-particle contribution to the emulsion effective stress is obtained from the drop stresslet. Analytical solutions for drop dynamics and emulsion stress under the combined action of shear flow and electric field were derived as regular perturbations in the limits of small capillary number and large viscosity ratio. The analytical results show that application of electric field in a direction perpendicular to the shear flow gives rise to normal stresses and may lead to shear--thickening or –thinning depending on the electric properties of the fluids. The theory highlights the physical mechanisms underlying emulsion response to electric and shear flow fields and can serve to validate numerical simulations.

Outlook:

Drop electrorotation is a rich phenomenon and we hope that our work will stimulate further exploration both theoretically and experimentally. A wider range of values of the fluid physical properties needs to be considered, as well as the effect of adsorbed surfactant at the drop interface. The coupling of the shape and surfactant dynamics is likely to produce novel features in drop electrohydrodynamics.

Impact:

The grant partially supported two MS students. One of them decided to pursue a PhD under my supervision on the topic of electro-hydrodynamics of soft particles. The research resulted in one published paper, two submitted manuscripts, and three contributed talks at the APS-DFD and AIChE annual meetings in 2009.