Electrohydrodynamic Manipulation Of Liquid Droplet Emulsions In A Microfluidic Channel

This work specifically aims to provide a fundamental framework, with some experimental validation, for understanding droplet emulsion dynamics in a microfluidic channel with an applied electric field. Electrification of fluids can result in several different modes of electrohydrodynamics (EHD). Several studies to date have provided theoretical, experimental, and numerical results for stationary droplet deformations and some flowing droplet configurations, but none have reported a method by which droplets of different diameters can be separated, binned and routed through the use of electric fields. It is therefore the goal of this work to fill that void and report a comprehensive understanding of how the electric field can affect flowing droplet dynamics. This work deals with two primary models used in electrohydrodynamics: the leaky dielectric model and the perfect dielectric model. The perfect dielectric model assumes that fluids with low conductivities do not react to any effects from the small amount of free charge they contain, and can be assumed as dielectrics, or electrical insulators. The leaky dielectric model suggests that even though the free charge is minimal in fluids with low conductivities, it is still is enough to affect droplet deformations. Finite element numerical results of stationary droplet deformations, implemented using the level set method, compare well both qualitatively (prolate/oblate and vortex directions), and quantitatively with results published by other researchers. Errors of less than 7.5% are found when comparing three-dimensional (3D) numerical results of this study to results predicted by the 3D leaky dielectric model, for a stationary high conductivity drop suspended in a slightly lower conductivity suspending medium. Droplet formations in a T-junction with no applied electric field are adequately predicted numerically using the level set finite element technique, as demonstrated by other researchers and verified in this study. For 3D models, droplet size is within 6%, and droplet production frequency is within 2.4% of experimental values found in the microfluidic Tjunction device. In order to reduce computational complexity, a larger scale model was solved first iii to obtain electrical potential distributions localized at the channel walls for the electrode placement configurations. Droplet deceleration and pinning is demonstrated, both experimentally and numerically, by applying steep gradients of electrical potential to the microchannel walls. As droplets flow over these electrical potential “steps,” they are pinned to the channel walls if the resulting electric forces are large enough to overcome the hydrodynamic forces. A balance between four dimensionless force ratios, the electric Euler number (Eue – ratio of inertial to electric forces), Mason number (M a – ratio of viscous to electric forces), electric pressure (P s – ratio of upstream pressure forces to electric forces), and the electric capillary number (Cae – ratio of electric to capillary forces) are used to quantify the magnitudes of each of these forces required to pin a droplet, and is consistent with a cubic dependency on the drop diameter. For larger drop diameters, effects of hydrodynamic forces become more prominent, and for smaller droplets, a greater electric forces is required due to the proximity of the droplet boundary with reference to the electrified channel wall. Droplet deceleration and pinning can be exploited to route droplets into different branches of a microfluidic T-junction. In addition, using steep electrical potential gradients placed strategically along a microchannel, droplets can even be passively binned by size into separate branches of the microfluidic device. These characteristics have been identified and demonstrated in this work

Numerical modelling of liquid droplet dynamics in microgravity

Microgravity provides ideal experimental conditions for studying highly reactive and under-cooled materials where there is no contact between the sample and the other experimental apparatus. The non-contact conditions allow material properties to be measured from the oscillating liquid droplet response to perturbations. This work investigates the impact of a strong magnetic field on these measurement processes for weakly viscous, electrically conducting droplets. We present numerical results using an axisymmetric model that employs the pseudo-spectral collocation method and a recently developed 3D model. Both numerical models have been developed to solve the equations describing the coupled electromagnetic and fluid flow processes. The models represent the changing surface shape that results from the interaction between forces inside the droplet and the surface tension imposed boundary conditions. The models are used to examine the liquid droplet dynamics in a strong DC magnetic field. In each case the surface shape is decomposed into a superposition of spherical harmonic modes. The oscillation of the individual mode coefficients is then analysed to determine the oscillation frequencies and damping rates that are then compared to the low amplitude solutions predicted by the published analytical asymptotic theory

Topological Defects and Interactions in Nematic Emulsions

Inverse nematic emulsions in which surfactant-coated water droplets are dispersed in a nematic host fluid have distinctive properties that set them apart from dispersions of two isotropic fluids or of nematic droplets in an isotropic fluid. We present a comprehensive theoretical study of the distortions produced in the nematic host by the dispersed droplets and of solvent mediated dipolar interactions between droplets that lead to their experimentally observed chaining. A single droplet in a nematic host acts like a macroscopic hedgehog defect. Global boundary conditions force the nucleation of compensating topological defects in the nematic host. Using variational techniques, we show that in the lowest energy configuration, a single water droplet draws a single hedgehog out of the nematic host to form a tightly bound dipole. Configurations in which the water droplet is encircled by a disclination ring have higher energy. The droplet-dipole induces distortions in the nematic host that lead to an effective dipole-dipole interaction between droplets and hence to chaining.Comment: 17 double column pages prepared by RevTex, 15 eps figures included in text, 2 gif figures for Fig. 1

Finite size effects on kaonic pasta structures

Non-uniform structures of mixed phases at the first-order phase transition to charged kaon condensation are studied using a density functional theory within the relativistic mean field model. Including electric field effects and applying the Gibbs conditions in a proper way, we numerically determine density profiles of nucleons, electrons and condensed kaons. Importance of charge screening effects is elucidated and thereby we show that the Maxwell construction is effectively justified. Surface effect is also studied to figure out its effect on the density profiles

Thickness of the strangelet-crystal crust of a strange star

It has recently been pointed out that if the surface tension of quark matter is low enough, the surface of a strange star will be a crust consisting of a crystal of charged strangelets in a neutralizing background of electrons. This affects the behavior of the surface, and must be taken into account in efforts to observationally rule out strange stars. We calculate the thickness of this ``mixed phase'' crust, taking into account the effects of surface tension and Debye screening of electric charge. Our calculation uses a generic parametrization of the equation of state of quark matter. For a reasonable range of quark matter equations of state, and surface tension of order a few MeV/fm^2, we find that the preferred crystal structure always involves spherical strangelets, not rods or slabs of quark matter. We find that for a star of radius 10 km and mass 1.5 Msolar, the strangelet-crystal crust can be from zero to hundreds of meters thick, the thickness being greater when the strange quark is heavier, and the surface tension is smaller. For smaller quark stars the crust will be even thicker.Comment: 10 pages, LaTe