Session T18: Drops: Electric Field Effects

Metamorphosis of Trilobite-like Drops on a Surface: Electrically-driven Fingering

         The experimental evidence reveals that sessile drops on a dielectric horizontal substrate subjected to sub-critical in-plane electric field acquire steady-state configurations where a balance between the pulling-outwards electric Maxwell stresses and the restoring surface tension has been attained. On the other hand, the experiments show that in super-critical electric field the Maxwell stresses become dominant and not only stretch the drop as a whole, but also trigger growth of multiple fingers crawling towards electrodes on both sides of the drop. This makes the drops with fingers stretched along the electric field lines similar to some trilobites known from their imprints in petrified sediments studied in paleontology. It is shown experimentally and theoretically that fingers are triggered during the encounters of the spreading drop outlines with minor surface imperfections. Such surface defects (existing originally or pre-notched on purpose) result in fingers which can grow being directed by the electric-field lines. The present work details multiple experimental observations of the trilobite-like fingering and also provides a theoretical framework for this novel type of fingering.   

Electrohydrodynamics of Lenticular Drops and Equatorial Streaming

As a result of their ability to induce stresses at fluid interfaces, electric fields can deform drops into shapes exhibiting pointed or sharp features. When exposed to a strong electric field, perfectly conducting drops immersed in perfectly insulating surroundings deform into prolate shapes and eventually develop spindle-like profiles capped by conical tips. The radius of curvature at the tip of the cone tends to zero, giving rise to the conic cusping singularity (Zubarev 2001). Were the drop not a perfect conductor and instead more conducting than its surroundings, the conical ends are destabilized at a finite value of the tip curvature and the instability engenders tip-streaming where fine jets issue from the conical tips (Collins et al. 2008, 2013). However, if the surroundings were more conducting, permittive, and viscous than the drop, the drop deforms into an oblate shape and adopts a lenticular profile at high field strengths (Brosseau and Vlahovska 2017, Wagoner et al. 2020, Marin 2020). At the incipience of instability, the equatorial cross section of the drop superficially resembles a wedge. In this talk, we examine the physics of the destabilization of the wedge and the equatorial streaming---the emission of a liquid sheet---from the unstable drop.   

Not Participating

The interaction of fluids and electric fields is at the heart of natural phenomena such as disintegration of raindrops in thunderstorms and applications such as crude oil demulsification and electrosprays. While an isolated drop in applied electric fields has been extensively studied, the behavior of many drops is largely unexplored. Even the pair-wise drop interactions have received scant attention and existing models are limited to axisymmetric and two-dimensional geometries. In three dimensions, the electrohydrodynamic interactions can be quite complex and non-trivial. For example, in an applied uniform electric field, instead of chaining along the field direction, drops can initially attract in the direction of the field and move towards each other, but then separate in the transverse direction [1]. Using a combination of numerical simulations based on a boundary integral formulation and an analytical theory assuming small drop deformations, we study the dynamics of a drop pair in an applied uniform electric field at arbitrary orientation of their line-of-centers relative to the applied field direction. For identical drops covered with insoluble surfactant [2], we find that the surfactant weakens the electrohydrodynamic flow and thus dielectrophoretic interactions play more prominent role in the dynamics of surfactant-covered drops compared to clean drops. If drop conductivity is the same as the suspending fluid, a nondiffusing surfactant can arrest the drops' relative motion thereby effectively preventing coalescence. Drop dissimilarity can also have profound effect on the pair dynamics. While identical drops tend to align with the field, drops with different permittivity and conductivity can move their line-of-centers away from the applied field direction and the drops orient perpendicularly to the field.

 

    

Electrostatic Control of Extruded Ink Drops and Jets for Nozzle-Based 3D Printing Applications

Nozzle-based three-dimensional (3D) printing technologies, which build a model by depositing materials layer-by-layer, are handicapped by low throughput and different geometric restrictions, which limit where the nozzle can print and how sensitive the prints are to distortions. Here, we introduce additional electrode/s of different configurations, to the printhead, generating an electric field between added electrode/s and printing nozzle. The resulting Coulomb forces manipulate the extruded ink facilitating desirable improvements of the printing process (e.g., higher translational speeds, thinner trace widths, improved deposition on rough surfaces, pre-charge low-volume droplets for enhanced placement, and creation of trace lines and films from discrete drops via electrocoalescence).  Using the predictions of the electrohydrodynamic theory of Direct Ink Writing (DIW) processes proposed in this work, electrode configurations were retrofitted to both a DIW/Drop-on-Demand printer. This relatively simple integration of the electrode to the printhead allowed successful prints with characteristics not found elsewhere. The ability to precisely manipulate extruded materials is essential in additive manufacturing and these results divulge a plethora of design opportunities and ink control in 3D printing processes.   

Not Participating

The effective removal of water from oilfield emulsions is crucial in the petroleum industry. The response of emulsion drops to electric fields has been exploited to accelerate the demulsification process. While previous studies have demonstrated different profound dynamics emulsion drops can exhibit under electric fields, many of them assumed the drop interface to be clean. In more realistic situations, crude oil-water interfaces are populated with absorbed crude oil components such as asphaltenes and resins. These complex interfaces hence display interfacial rheological behaviors that may not be captured by a single value of interfacial tension. In this talk, we report our progress in examining the electrohydrodynamic response of drops with more complex interfaces.   

Aerosol beam profile manipulation to improve particle density outside the aerodynamic lens stack

Charged droplets can be used to manipulate the trajectory of an aerosolized particle beam outside the aerodynamic lens stack. In this simulation study, the Uppsala injector particle beam trajectory is optimized for improving the SNR of the diffraction pattern for XFEL single-particle imaging. Data of droplet size, frequency, position, and velocity distribution are ascertained in Bielecki et. al., 2019 and Hankte et. al., 2018 using Rayleigh scattering microscopy. The aerosolized particle trajectories are integrated from its forces and particle count is aggregated on a bin to generate a discrete map of the particle density profile. This profile is optimized by manipulating an electric field outside the accelerating nozzle of the Aerodynamic Lens Stack (ALS). As such the acceleration of the particles is a function of aerodynamic drag ascertained from Bielecki et. al., 2019, electric field forces from the charged plate are computed using finite element methods and N-Body Coulomb repulsion is computed using Barnes-hut approximation. Under such conditions, the simulation indicates the slowdown of particles increases the particle density at a point dependent on the strength of the electric field by almost 10x in simulation.   

Evolution and Shape of 2D Stokesian Drops Under the Action of Surface Tension and Electric Field: Linear and Nonlinear Theory and Experiment

The creeping-flow theory of two-dimensional ionic-conductor drops under the action of surface tension and the sub-critical (in terms of the electric Bond number) electric field imposed in the substrate plane is developed. The experimental data are acquired for drops impacted or softly deposited on dielectric surfaces of different wettability. The comparison with the theory reveals that it can accurately describe steady-state drop shape on non-wettable substrate. Such a drop is sufficiently raised above the substrate, which diminishes the three-dimensional effects making the two-dimensional description relevant. It is demonstrated how the sub-critical electric field deforms the initially circular drops until an elongated steady-state configuration is reached. The surface tension tends to round off the non-circular drops stretched by the electric Maxwell stresses imposed by the electrodes. A more pronounced substrate wettability leads to more elongated steady-state configurations observed experimentally than those predicted by the two-dimensional theory. In the super-critical electric fields the electrical stretching of drops predicted by the present linearized two-dimensional theory results in splitting into two separate droplets. This scenario is corroborated by the predictions of the fully nonlinear results, and the experimental results on a substrate with slip.   

Improving electrocoalescer performance using temporally varying periodic electric field

One of the cleanest and low energy-intensive techniques used to separate water in oil emulsions in the petroleum industry is electrocoalescence. In electrocoalescence, the electric field is applied across the emulsion, and it induces polarization on droplets. Due to this polarization, the droplets attract and approach each other and coalesce to form larger droplets which then separate under gravity in a reasonable time. An electrocoalescer essentially works on the phenomena of electrocoalescence. Enhancing the performance of an electrocoalescer includes the ability to dehydrate the emulsion in a shorter time, that is increase the kinetics of separation while keeping the operation safe (without sparking). The work proposes the enhancement of separation based on temporally varying periodic electric field and demonstrates it rigorously through several experiments and analysis. These include optimizing and designing the electrical waveform and then demonstrating the faster rate of kinetics by comparing the performance with conventional practices. The technique is established through experiments on oil with dispersed water as deionized water or brine.   

Effect of the relative magnitude of conductivity and permittivity ratio on compound droplet dynamics under transverse electric field and shear flow

The dynamics of a two-dimensional compound droplet are investigated under the combined influence of transverse electric field and shear flow. Governing electrohydrodynamic equations are solved employing phase filed based interface capturing technique. Simulations are performed for selected values of conductivity ratio and permittivity ratio. Droplet motion is steered by electrical force experienced by the charge accumulated on the droplet interface. The interplay of Electric forces and viscous forces depends on the relative magnitude of conductivity ratio and permittivity ratio. Delays or advancement of droplet elongation and breakup are controlled by electric field strength.   

Dynamics of a sessile droplet under periodic and steady electric fields

The electrohydrodynamics of a sessile droplet under the influence of periodic and steady electric fields in microgravity conditions is theoretically investigated using an inertial lubrication model. Previous studies revealed that a spherical droplet with unequal conductivity and permittivity ratios exhibits distinct dynamics under periodic and equivalent steady forcing in the root-mean-square sense. However, it is unclear what happens for sessile droplets, which we address here for the first time. The equivalence between periodic and steady forcing is shown to be governed by the interfacial charge build-up, which further depends on the competition between the charge relaxation and forcing timescales. A circulation-deformation map is introduced for the sessile droplet that acts as a guideline to achieve electric field-induced wetting or dewetting as the case maybe. We also demonstrate that a droplet may be rendered either more or less wetting solely by tuning the forcing frequency.   

Not Participating

Controlling coalescence is crucial for reliable manipulation of droplets in microfluidic applications. Here, we present a method that allows to suppress the coalescence of droplets moving on a liquid-infused surface in an efficient and predictable manner. The method relies on the mutual electrostatic interaction between the droplets induced by a homogeneous external electric field normal to the substrate. In addition to experiments in which droplet trajectories are recorded, detailed numerical computations of the repulsive electrostatic force are performed. The experiments and numerical computations show excellent quantitative agreement. Furthermore, we propose a semi-analytical model based on interacting dipoles, which predicts the relation between repulsion force, applied electric field strength, droplet volumes and separation distance with decent accuracy. Besides coalescence control, our setup allows for taking minute samples from droplet arrays if the electric field exceeds a certain threshold such that tip-streaming occurs.