Electrohydrodynamic Modeling of Droplet Vibrations under the Influence of Electric Fields

This work focuses on numerical simulations of water droplet deformations under the influence of transient high-voltage electric fields. In the stationary case, the droplet elongates parallel to the electrostatic field. In the transient case, water droplets undergo a complicated oscillatory motion as the electric field and the droplet shape change simultaneously. This multiphysics phenomenon has been the subject of experimental studies but has never been simulated before in the case of a transient electric field. Practical applications of this work include the numerical study of the premature aging of polymer insulators used in power transmission lines and due to water droplets as well as the simulation of industrial processes such as electrowetting and dielectrophoresis. In this thesis, the motion of a single water droplet located on the hydrophobic surface of a silicone rubber insulator is simulated numerically. This is achieved by solving the transient, three-dimensional system composed of the full sets of electro-quasistatics and Navier-Stokes equations. The solution of the coupled system is obtained by using a computational approach based on the finite element method on a moving mesh for the electrical part of the problem and on the finite volume method on a fixed mesh for the fluid mechanical part. The electro-quasistatics finite element solver calculates on a moving curvilinear tetrahedral mesh the electric field, Maxwell stress tensor and electric force density with higher and mixed-element orders. The multiphase flow finite volume solver computes on a fixed Cartesian hexahedral grid the droplet deformation by tracking the evolution of the water-air interface with the volume of fluid method. Both solvers use an independent time integration scheme but are leapfrogged in a synchronized manner to provide a time accurate calculation of the droplet deformations. Several experimental investigations are performed to verify simulation results using a high speed camera. The comparison between simulation and experiment shows good agreement between the numerically computed droplet motion and the recorded video images for both horizontal and vertical applied AC electric fields. The simulation results are analyzed by applying a one-dimensional mechanical model of water droplet deformation based on the linear harmonic oscillator. The standard model which is limited to the steady-state regime is extended to include the transient regime. It is shown that the droplet vibrations occuring at frequencies below the driving frequency are not necessarily due to the accidental charging of the water droplet as it is sometimes suggested in the literature. Rather, they may be caused by underdamped droplet oscillations which originate in the transient regime. This finding is further supported by the fact that their frequencies correspond to the resonance frequencies of the sessile water droplets oscillating freely

Numerical Modeling of Deformation, Oscillation, Spreading and Collision Characteristics of Droplets in an Electric Field

Electric field induced flows, or electrohydrodynamics (EHD), have been promising in many fast-growing technologies, where droplet movement and deformation can be controlled to enhance heat transfer and mass transport. Several complex EHD problems existing in many applications were investigated in this thesis. Firstly, this thesis presents the results of numerical simulations of the deformation, oscillation and breakup of a weakly conducting droplet suspended in an ambient medium with higher conductivity. It is the first time that the deformation of such a droplet was investigated numerically in a 3D configuration. We have determined three types of behavior for the droplets, which are less conducting than ambient fluid: 1) oblate deformation (which can be predicted from the small perturbation theory), 2) oscillatory oblate-prolate deformation and 3) breakup of the droplet. Secondly, a numerical study of droplet oscillation placed on different hydrophobic surfaces under the effect of applied AC voltage including the effect of ambient gas was investigated. The presented algorithm could reproduce droplet oscillations on a surface considering different contact angles. It has been found that the resonance frequency of the water droplet depends on the surface property of the hydrophobic materials and the electrostatic force. Thirdly, a new design of an electrowetting mixer using the rotating electric field was proposed which offers a new method to effectively mix two droplets over a different range of AC frequencies. Two regimes were observed for droplet coalescence: 1) coalescence due to the high droplet deformation, 2) coalescence due to the interaction of electrically induced dipoles. Fourthly, the spreading and retraction control of millimetric water droplets impacting on dry surfaces have been investigated to examine the effect of the surface charge density and electric field intensity. The effect of the surface charge on the spreading of droplets placed gently on surfaces was investigated in the first part. It was found that the maximum spreading diameter increases with an increasing charge. In the second part, the impact of a droplet on a ground electrode was considered. It was also found that in order to keep the maximum diameter after the impact, less charge is needed for surfaces with lower contact angle. Finally, the interaction between two identical charged droplets was investigated numerically. The effects of the impact velocity, drop size ratio and electric charge on the behavior of the combined droplet were investigated. It was shown that two conducting droplets carrying charges of the same polarity under some conditions may be electrically attracted. The formation of charged daughter droplets has been investigated and it was found that the number of the satellite droplets after collision appears to increase with an increase in the droplet charge

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

MULTIPHYSICS ANALYSIS AND OPTIMIZATION OF 3 DIMENSIONAL PRINTING TECHNOLOGY USING NANO FLUIDIC SUSPENSIONS

Fabrication of micro and nano devices is of prime significance to the area of Micro-Electro-Mechanical Systems (MEMS). Attempts have been made to accommodate high performance devices in compact units, thus reducing their overall size. There exist a variety of microfabrication techniques including lithography, chemical vapor deposition, and LIGA that are used today. Manufacturing costs associated with these processes can be prohibitive due to cycle time and the precious material loss that occurs during etching operations. These drawbacks become more significant problem when building curved traces and support structures that most occur in 3D space. To address the problems associated with building 3-dimensional circuits and devices in free space, a unique manufacturing process has been developed. This process utilizes conductive Nano-Particulate Fluid Jets (NPFJ) that are deposited onto a substrate by a Continuous Inkjet (CIJ) printing methodology. In this method, a fluid jet consists of colloidal suspensions of conductors and carrier fluids that are deposited onto a substrate and later sintered at high temperatures to form a homogeneous material. The major contribution of the present research is the investigation, development and optimization of the NPFJ. In this work, a Computational Fluid Dynamics (CFD) model has been developed to simulate the fluid jet and CIJ process. The modified CIJ printing process involves interaction of three domains namely, electrostatics, structural and fluidics. A coupled field analysis of the piezoelectric membrane that exists in the CIJ print head is conducted to establish the perturbation characteristics applied to the fluid. Interaction of the above three domains is captured within a single model using a (FSI) fluid-structural algorithm which staggers between domains until convergence is attained. A Design of Experiments approach was used to determine trends for the drop formations based on various exciting parameters. Results from these simulations have been validated using an ultra-high-speed camera featuring exposure/delay times from 100 nanoseconds at full sensor resolution.The results of present research will give manufacturers the freedom to construct 3D devices and circuits that conform to the desired shapes and sizes of products, rather than being limited to present 2D components such as printed circuit boards

Deformation transients of confined droplets within interacting electric and magnetic field environment

A theoretical exploration and an analytical model for the electro-magneto-hydrodynamics (EMHD) of leaky dielectric liquid droplets, suspended in an immiscible confined fluid domain has been presented. The analytical solution for the system, under small deformation approximation, in creeping flow regime, has been put forward. Study of the droplet deformation suggests that its temporal evolution is exponential, and dependents on the electric and magnetic field interaction. Further, the direction of the applied magnetic field with respect to the electric field decides whether the contribution of magnetic forces opposes or aids the interfacial net electrical force due to the electric field. Validation of the proposed model at the asymptotic limits of vanishing magnetic field show that the model accurately reduces to the case of transient electrohydrodynamic model. We also propose a magnetic discriminating function to quantify the steady-state droplet deformation in the presence of interacting electric and magnetic fields. The change of droplets from spherical shape to prolate, and oblate spheroids, correspond to magnetic discriminating function >0 and <0 regimes, respectively. It is shown that with the aid of low magnitude magnetic field, a substantial augmentation in the deformation parameter, and the associated EMHD circulation within and around the droplet is achieved. The analysis also reveals the deformation lag and specific critical parameters that aid or suppressed this lag behaviour; discussed in terms of relevant non-dimensional parameters.Comment: 61 page

Pore-scale modeling of viscoelastic flow and the effect of polymer elasticity on residual oil saturation

textPolymers used in enhanced oil recovery (EOR) help to control the mobility ratio between oil and aqueous phases and as a result, polymer flooding improves sweep efficiency in reservoirs. However, the conventional wisdom is that polymer flooding does not have considerable effect on pore-level displacement because pressure forces would not be enough to overcome trapping caused by capillary forces. Recently, both coreflood experiments and field data suggest that injecting viscoelastic polymers, such as hydrolyzed polyacrylamide (HPAM), can result in lower residual oil saturation. The hypothesis is that the polymer elasticity provides several pore-level mechanisms for oil mobilization that are generally not significant for purely-viscous fluids. Both experiments and modeling need to be performed to investigate the effect of polymer elasticity on residual oil saturation. Pore-scale modeling and micro-fluidic experiments can be used to investigate pore-level physics, and then used to upscale to the macro-scale. The objective of this work is to understand the effect of polymer elasticity on apparent viscosity and residual oil saturation in porous media. Single- and multi-phase pore-level computational fluid dynamics (CFD) modeling for viscoelastic polymer flow is performed to investigate the dominant mechanisms at the pore level to mobilize trapped oil. Several interesting results are found from the CFD results. First, the elasticity of the polymer results in an increase in normal stress at the pore-level; therefore, the normal stresses exerted on a static oil droplet are significant and not negligible as for a purely-viscous fluid. The CFD results show that viscoelastic fluid exerts additional forces on the oil-phase which may help mobilize trapped oil out of the porous medium. Second, due to the elasticity of polymer, the viscoelastic polymer has some level of pulling effect; while passing above a dead-end pore it can pull out the trapped oil phase and then mobilize it. However, both CFD modeling and micro-fluidic experiments show the pulling-effect is not likely the main mechanism to reduce oil saturation at pore-level. Third, dynamic CFD simulations show less deformation of the oil phase while viscoelastic polymer is displacing fluid compared to purely viscous fluid. It may justify the hypothesis that polymer elasticity resists against snap-off mechanism. As a result, when viscoelastic polymer displaces the oil ganglia, the oil phase does not snap off, and the oil phase remains connected, and therefore easier to move in porous media compared to disconnected oil. For single phase flow, a closed-form flow equation has been developed based on CFD modeling in converging/diverging ducts representative of pore throats. The pore-level equations were substituted into a pore-network model and validated against experimental data. Good agreement is observed. This study reveals important findings about the effect of polymer elasticity to reduce the residual oil saturation; however, more experiments and simulations are recommended to fully-understand the mobilization mechanisms and take advantage of them to optimize the polymer-flooding process in the field.Petroleum and Geosystems Engineerin

Design Of A Piezoelectric Droplet-On-Demand Generator And Simulation Of A Dropped Package On A Concrete Floor Using Ansys

This study at Prairie View A&M University aimed to design a novel droplet generator for microfluidic applications and develop a simulation model to analyze the impact of a free-falling package on the drop tower’s floor. The journey began with an extensive literature review, leading to the discovery of various droplet production methods. The inkjet method was chosen for this application. Controlling droplet size involves manipulating voltage and nozzle parameters and avoiding liquid dripping by applying negative pressure pulses. Incorporating O-rings prevented liquid leakage at component junctions. Multiple iterations refined the droplet generator, culminating in a liquid chamber and a fluid reservoir. The second phase involved developing an Ansys simulation model to assess the impact of a 400 lbs package on a foam bed inside a stainless-steel tank within the drop tower. The objective was to ensure the integrity of the floor, foam, tank, and package. Our literature review guided us to adopt the Two-way Fluid-Structure Interaction method, the Explicit Dynamic method, and the Transient Structural Method for the simulation. While Two-way FSI posed challenges due to computational limitations, we persevered. Explicit Dynamics emerged as the preferred approach for dynamic simulations, involving package velocity determination and foam mechanical property analysis. 3 simulations with varying foam densities and properties were conducted. The initial simulation produced limited data. Subsequent hyper-elastic or viscoelastic foam formulations showed promise despite the package bouncing instead of sinking. Due to Explicit Dynamics limitations, the Ogden foam model was utilized for 2 Expanded Polypropylene foams in Transient Structural. Although the simulation faced difficulties, this study was a valuable learning experience with potential for further exploration. In conclusion, this research at PVAMU led to the creation of an innovative droplet generator and an intricate simulation model. While challenges were encountered, the study lays the foundation for future droplet generation and impact simulation investigations

An interface tracking model for droplet electrocoalescence.

This report describes an Early Career Laboratory Directed Research and Development (LDRD) project to develop an interface tracking model for droplet electrocoalescence. Many fluid-based technologies rely on electrical fields to control the motion of droplets, e.g. microfluidic devices for high-speed droplet sorting, solution separation for chemical detectors, and purification of biodiesel fuel. Precise control over droplets is crucial to these applications. However, electric fields can induce complex and unpredictable fluid dynamics. Recent experiments (Ristenpart et al. 2009) have demonstrated that oppositely charged droplets bounce rather than coalesce in the presence of strong electric fields. A transient aqueous bridge forms between approaching drops prior to pinch-off. This observation applies to many types of fluids, but neither theory nor experiments have been able to offer a satisfactory explanation. Analytic hydrodynamic approximations for interfaces become invalid near coalescence, and therefore detailed numerical simulations are necessary. This is a computationally challenging problem that involves tracking a moving interface and solving complex multi-physics and multi-scale dynamics, which are beyond the capabilities of most state-of-the-art simulations. An interface-tracking model for electro-coalescence can provide a new perspective to a variety of applications in which interfacial physics are coupled with electrodynamics, including electro-osmosis, fabrication of microelectronics, fuel atomization, oil dehydration, nuclear waste reprocessing and solution separation for chemical detectors. We present a conformal decomposition finite element (CDFEM) interface-tracking method for the electrohydrodynamics of two-phase flow to demonstrate electro-coalescence. CDFEM is a sharp interface method that decomposes elements along fluid-fluid boundaries and uses a level set function to represent the interface