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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.

Drop behavior in strong electric fields

We have completed an experimental study on the electro-hydrodynamics of a surfactant-free drop. In the second year, we will focus on theoretical modeling and experimental investigation of surfactant-covered drops.

A drop with different physical properties than the surrounding fluid polarizes when placed in a uniform electric field. As a result, the electric stress changes discontinuously at the interface and deforms the drop.  In addition, electric field acting on induced free surface charges creates a tangential stress, not present in the case of perfect dielectrics, which drags the fluids into motion.

In weak electric fields, the suspending fluid undergoes axisymmetric extensional flow, which was explained by the leaky dielectric model introduced by G.I. Taylor.  He showed that the surface charge distribution and direction of surface fluid motion depend on the charging response of the fluids. If the charging time of the drop fluid is shorter than the suspending liquid, the interface charge distribution is dominated by charges brought from the interior fluid and the induced dipole moment is aligned with the electric field.  In this case, charges at the poles are attracted by the electrodes, pulling the drop into a prolate shape.  If the charging response of the suspending fluid is faster than the interior fluid, the charging of the interface is dominated by the exterior medium and the drop dipole is reversed; it is directed oppositely to the applied electric field.  In this charge configuration, the drop can become either prolate or oblate.  

In strong electric fields, the flow pattern changes to rotation and drop deformation is no longer axisymmetric.  The electro-rotation behavior of drops is analogous to the spontaneous spinning of a rigid sphere in a uniform electrostatic field, reported by Quincke in 1896.  For rotation to occur, the suspending fluid and sphere must be slightly conducting dielectrics and have the induced dipole moment of the sphere oriented in opposite direction of the applied field.  This configuration becomes unstable above a critical strength of the electric field.  A perturbation in the dipole alignment induces physical rotation of the sphere.  The charge distribution rotates with the sphere, however, the exterior fluid simultaneously recharges the interface.  The balance between rotation and interface charging results in an oblique dipole orientation.  The rate of rotation and threshold electric field are determined from angular momentum conservation.   

To observe drop behavior in electric fields, we have constructed a fluid chamber from plexiglass with brass plates as electrodes.  A camera with a magnifying lens was positioned above the chamber to recorded drop images.  To produce strong electric fields, a high voltage DC amplifier was utilized.  Using castor oil as the continuous fluid for all experiments, silicone oil drops were injected to obtain oblate deformation and water drops to obtain prolate deformation.

Drop deformation was measured at weak fields for both prolate and oblate shapes and compared to Taylor's model.  The results showed close agreement with theory for small capillary numbers, Ca<0.3.  Increasing the field strength resulted in drop breakup in the case of prolate drops.  Oblate drops, however, first adopted a steady oblique orientation accompanied by fluid rotation and only at very strong field broke up.  We measured the critical electric field, rotation rate, and tilt angle in order to quantify drop electrorotation and compared the experimental data with the Quincke model for a rigid sphere.

The critical electric field strength for drop rotation was determined for different drop sizes and drop viscosities.  The experiment showed that decreasing the drop/matrix viscosity ratio increased the critical electric field.  The higher critical field for low viscosity drops can be attributed to the greater rate of energy dissipation associated with a higher strain rate for the fluid motion in this case.  Small viscous drops, which remain mostly spherical, experienced a critical field strength similar to the critical field predicted by Quincke rotation theory.   For a given viscosity ratio, larger drops were found to have a slightly lower critical electric field, which is explained by the greater perturbation to the electric field created by the non-spherical deformed drop.  The effect of drop size was less significant compared to that of the viscosity ratio.  Once rotation was induced, the characteristics defining this behavior, oblique orientation with respect to the electric field and rotation rate, were examined at increasing electric field strength.  Low viscosity drops were found to rapidly transition to a large tilt angle while high viscosity drop exhibited a gradual transition.  At higher field strengths, the tilt angle for all viscosity drops continued to slowly increase.  Hysteresis was discovered in the angle measurement for larger drop sizes.  The rotation rate for small drop was measured by seeding aluminum particles in the drop and measuring the rotation period of particles near the interface.  The experiment showed that once rotation was initiated, the rotation rate is well approximated by the Quincke rotation theory for a rigid sphere. 

Surfactant-induced drift of a drop in Poiseuille flow

Cross-streamline drop migration leads to non-uniform emulsion microstructure, which affects flow resistance in pipes.  In Stokes flows, symmetry considerations dictate that a neutrally-buoyant spherical particle will not migrate laterally with respect to the flow direction. We showed that a loss of symmetry due to flow-induced surfactant redistribution leads to cross-stream drift of a spherical drop in Poiseuille flow.  We derived analytical expressions for the migration velocity in the limit of small non-uniformities in the surfactant distribution, corresponding to weak-flow conditions or a high-viscosity drop. The analysis predicts that the direction of migration is always towards the flow centerline in contrast to a surfactant-free deformable drop, for which the direction of migration depends on viscosity ratio.

Impact

The grant supported one MS student (Paul Salipante), who decided to pursue a PhD under my supervision on the topic of electro-hydrodynamics of soft particles. The research resulted in one submitted manuscript, and two manuscripts are in preparation.