scholarly journals Electrohydrodynamics of viscous drops in strong electric fields: numerical simulations

2017 ◽  
Vol 829 ◽  
pp. 127-152 ◽  
Author(s):  
Debasish Das ◽  
David Saintillan
Keyword(s):  
Numerical Simulations ◽  
Electric Fields ◽  
Small Deformation ◽  
Dielectric Liquid ◽  
Uniform Electric Field ◽  
Liquid Drops ◽  
Wide Range ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric

Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviours contingent on field strength and material properties. These phenomena are best described by the Melcher–Taylor leaky dielectric model, which hypothesizes charge accumulation on the drop–fluid interface and prescribes a balance between charge relaxation, the jump in ohmic currents from the bulk and charge convection by the interfacial fluid flow. Most previous numerical simulations based on this model have either neglected interfacial charge convection or restricted themselves to axisymmetric drops. In this work, we develop a three-dimensional boundary element method for the complete leaky dielectric model to systematically study the deformation and dynamics of liquid drops in electric fields. The inclusion of charge convection in our simulations permits us to investigate drops in the Quincke regime, in which experiments have demonstrated a symmetry-breaking bifurcation leading to steady electrorotation. Our simulation results show excellent agreement with existing experimental data and small-deformation theories.

Transient Electrohydrodynamic Manipulation of Particles on the Surface of a Drop

2016 ◽  
Author(s):  
Edison C. Amah ◽  
Ian S. Fischer ◽  
Pushpendra Singh
Keyword(s):  
Electric Field ◽  
Applied Electric Field ◽  
Control Parameter ◽  
Transient Behavior ◽  
Uniform Electric Field ◽  
Electrohydrodynamic Flow ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric

In our previous studies we have shown that particles adsorbed on the surface of a drop can be concentrated at its poles or equator by applying a uniform electric field. This happens even when the applied electric field is uniform; the electric field on the surface of the drop is nonuniform, and so particles adsorbed on the surface are subjected to dielectrophoretic (DEP) forces. In this study, we use leaky dielectric model to model the transient behavior of particles at low electric field frequencies. We show that the frequency of the electric field is an important control parameter that under certain conditions can be used to collect particles at the poles or the equator, and to move them from the poles to the equator. The speed with which particles move on the surface depends on the strength of the electrohydrodynamic flow which diminishes with increasing frequency.

Electrohydrodynamic deformation and interaction of drop pairs

1998 ◽  
Vol 368 ◽  
pp. 359-375 ◽  
Author(s):  
J. C. BAYGENTS ◽  
N. J. RIVETTE ◽  
H. A. STONE
Keyword(s):  
Electric Field ◽  
Local Electric Field ◽  
Uniform Electric Field ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric

The motion of two drops in a uniform electric field is considered using the leaky dielectric model. The drops are assumed to have no native charge and a dielectrophoretic effect favours translation of the drops toward one another. However, circulatory flows that stem from electrohydrodynamic stresses may either act with or against this dielectrophoretic effect. Consequently, both prolate and oblate drop deformations may be generated and significant deformation occurs near drop contact owing to enhancement of the local electric field. For sufficiently widely spaced drops, electrohydrodynamic flows dominate direct electrical interactions so drops may be pushed apart, though closely spaced drops almost always move together as a result of the electrical interaction or deformation.

Numerical Analysis on the Stability Conditions of an Electrohydrodynamic Jet

2020 ◽  
Author(s):  
Sílvio Cândido ◽  
José C. Páscoa
Keyword(s):  
Numerical Model ◽  
Flow Rate ◽  
Applied Voltage ◽  
Taylor Cone ◽  
Fine Grid ◽  
Wide Range ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric ◽  
Multi Phase

Abstract The Taylor cone jet is a well-known electrohydrodynamic flow (EHD), usually produced by applying an external electric field to a capillary liquid. The generation of this kind of flow involves a multi-phase and a multi-physics process and its stability has a specific operation window. This operating window is intrinsically dependent on the flow rate and magnitude of the applied electric voltage. In case high voltages are applied to the jet it can atomize and produce an electrospray. Our work presents a numerical study of the process of atomization of a Taylor cone jet using computational fluid dynamics (CFD). The study intents to assess the limit conditions of operation and the applied voltage needed to stabilize an electrospray. The numerical model was implemented within OpenFOAM, where the multi-phase hydrodynamics equations are solved using a volume-of-fluid (VOF) approach. This method is coupled with the Maxwell equations governing an electrostatic field, in order to incorporate the electric body forces into the incompressible Navier-Stokes equations. The leaky-dielectric model is used and, therefore, the interface between the two phases is subject to the hydrodynamic surface tension and electric stress (Maxwell stress). This allows a leakage of charge though the phase due to ohmic conduction. Thus, the permittivity and conductivity of the phases are taken into consideration. A two-fluid system with relevant electric properties can be categorized as, dielectric-dielectric, dielectric-conducting, and conducting-conducting considering the electrical conductivity and permittivities of the participating phases. Due to the usage of the leaky-dielectric model, it is possible to simulate any of this physical situations. By increasing the applied voltage reaches a value where the cone instability is verified, allowing a discussion on this effect. It is demonstrated that to adequately model the process of atomization a fine grid refinement is needed. The validation of the numerical model is made by comparing against diverse experimental data, for the case of a stable jet. The diameter and velocity of the droplet and the electric current of the jet are the main variables that are compared with previous results. The tests were performed with Heptane. The cone and the jet are strongly affected by the flow rate. The dimensionless diameter, as a function of the dimensionless flow rate, agrees with the scaling laws. The model predicts accurate results over a wide range of flow rates with an accuracy of around 10%. The results are obtained using structured meshes.

The vibration of electrified water drops

1971 ◽  
Vol 322 (1551) ◽  
pp. 523-534 ◽  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Axial Ratio ◽  
Uniform Electric Field ◽  
Interferometric Technique ◽  
Photographic Analysis ◽  
Wide Range ◽  
Water Drops ◽  
Strength And Deformation ◽  
A Charge

Pressure has been used as the principal parameter in calculations of the fundamental vibrational frequencies of spherical drops of radius R , density ρ, and surface tension T carrying a charge Q or uncharged spheroidal drops of axial ratio a / b situated in a uniform electric field of strength E . Freely vibrating charged drops have a frequency f = f 0 ( 1 - Q 2 /16π R 3 T ) ½ , as shown previously by Rayleigh (1882) using energy considerations; f 0 is the vibrational frequency of non-electrified drops (Rayleigh 1879). The fundamental frequency of an uncharged drop in an electric field will decrease with increasing field strength and deformation a / b and will equal zero when E ( R )/ T ) ½ = 1.625 and a / b = 1.86; these critical values correspond to the disintegration conditions derived by Taylor (1964). An interferometric technique involving a laser confirmed the accuracy of the calculations concerned with charged drops. The vibration of water drops of radius around 2 mm was studied over a wide range of temperatures as they fell through electric fields either by suspending them in a vertical wind tunnel or allowing them to fall between a pair of vertical electrodes. Photographic analysis of the vibrations revealed good agreement between theory and experiment over the entire range of conditions studied even though the larger drops were not accurately spheroidal and the amplitude of the vibrations was large.

Electron energy distributions in uniform electric fields and the Townsend ionization coefficient

1958 ◽  
Vol 244 (1237) ◽  
pp. 166-185 ◽  
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Electric Fields ◽  
Cross Sections ◽  
Collision Cross Section ◽  
Present Theory ◽  
Uniform Electric Field ◽  
Ionization Coefficient ◽  
Special Cases ◽  
Wide Range

The second-order differential equation which expresses the equilibrium condition of an electron swarm in a uniform electric field in a gas, the electrons suffering both elastic and inelastic collisions with the gas molecules, is solved by the Jeffreys or W.K.B. method of approximation. The distribution function F(ε) of electrons of energy ε is obtained immediately in a general form involving the elastic and inelastic collision cross-sections and without any restriction on the range of E/p (electric strength/gas pressure) save that introduced in the original differential equation. In almost all applications the approximation is likely to be of high accuracy, and easy to use. Several of the earlier derivations of F(ε) are obtained as special cases. Using the function F(ε) an attempt is made to relate the Townsend ionization coefficient a to the properties of the gas in a more general manner than hitherto, using realistic functions for the collision cross-section. It is finally expressed by the equation α/ p = A exp ( — Bp/E ) in which A and B are functions involving the properties of the gas and the ratio E/p . The important coefficient B is directly related to the form and magnitude of the total inelastic cross-section below the ionization potential and can be evaluated for a particular gas once the cross-section is known experimentally. The present theory shows clearly the influence of E/p on both A and B, a matter which has not been satisfactorily discussed previously. The theory is illustrated by calculations of F (ε) and a/p for hydrogen over a range of E/p from 10 to 1000. The agreement between the calculated results and recent reliable observations of α/ p is surprisingly good considering the nature of the calculations and the wide range of E/p .

Deformation of an encapsulated bubble in steady and oscillatory electric fields

2018 ◽  
Vol 844 ◽  
pp. 567-596 ◽  
Author(s):  
Yunqiao Liu ◽  
Dongdong He ◽  
Xiaobo Gong ◽  
Huaxiong Huang
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Equilibrium Shape ◽  
Bubble Surface ◽  
Axisymmetric Deformation ◽  
Uniform Electric Field ◽  
Bending Rigidity ◽  
Shape Oscillation ◽  
Leaky Dielectric Model ◽  
Interfacial Charge

In this paper, we investigate the dynamics of an encapsulated bubble in steady and oscillatory electric fields theoretically, based on a leaky dielectric model. On the bubble surface, an applied electric field generates a Maxwell stress, in addition to hydrodynamic traction and membrane mechanical stress. Our model also includes the effect of interfacial charge due to the jump of the current and the stretching of the interface. We focus on the axisymmetric deformation of the encapsulated bubble induced by the electric field and carry out our analysis using Legendre polynomials. In our first example, the encapsulating membrane is modelled as a nearly incompressible interface with bending rigidity. Under a steady uniform electric field, the encapsulated bubble resumes an elongated equilibrium shape, dominated by the second- and fourth-order shape modes. The deformed shape agrees well with experimental observations reported in the literature. Our model reveals that the interfacial charge distribution is determined by the magnitude of the shape modes, as well as the permittivity and conductivity of the external and internal fluids. The effects of the electric field on the natural frequency of the oscillating bubble are also shown. For our second example, we considered a bubble encapsulated with a hyperelastic membrane with bending rigidity, subject to an oscillatory electric field. We show that the bubble can modulate its oscillating frequency and reach a stable shape oscillation at an appreciable amplitude.

Small deformation theory for two leaky dielectric drops in a uniform electric field

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190517
Author(s):  
Michael Zabarankin
Keyword(s):  
Electric Field ◽  
Deformation Theory ◽  
Small Deformation ◽  
Dielectric Constants ◽  
Dynamics Simulation ◽  
Uniform Electric Field ◽  
Fluid Viscosity ◽  
Ambient Fluid ◽  
Drop Dynamics ◽  
Leaky Dielectric

A small deformation theory for two non-identical spherical drops freely suspended in an ambient fluid and subjected to a uniform electric field is presented. The three phases are assumed to be leaky dielectric (slightly conducting) viscous incompressible fluids and the nonlinear effects of inertia and surface charge convection are neglected. The deformed shapes of the drops are linearized with respect to the electric capillary number that characterizes the balance between the electric stress and the surface tension. When the two drops are sufficiently far apart, their deformed shapes are predicted by Taylor’s small deformation theory—depending on Taylor’s discriminating function, the drops may become prolate, oblate or remain spherical. When the two drops get closer to each other, in addition to becoming prolate/oblate, they start translating and developing an egg shape. (Since there is no net charge, the centre of mass of the two drops remains stationary.) The extent of each of these ‘modes’ of deformation depends on the distance between the drops’ centres and on drop-to-ambient fluid ratios of electric conductivities, dielectric constants and viscosities. The predictions of the small deformation theory for two drops perfectly agree with the existing results of two-drop dynamics simulation based on a boundary-integral equation approach. Moreover, while previous works observed only three types of behaviour for two identical drops—the drops may either become prolate or oblate and move towards each other or become prolate and move away from each other—the small deformation theory predicts that non-identical drops may, in fact, become oblate and move away from each other when the drop-to-ambient fluid conductivity ratios are reciprocal and the drop-to-ambient fluid viscosity ratios are sufficiently large. The presented theory also readily yields an analytical insight into the interplay among different modes of drop deformation and can be used to guide the selection of the phases’ electromechanical properties for two-drop dynamics simulations.

scholarly journals “Leaky Dielectric” Model for the Suppression of Dynamic $R_{\mathrm{ON}}$ in Carbon-Doped AlGaN/GaN HEMTs

2017 ◽  
Vol 64 (7) ◽  
pp. 2826-2834 ◽  
Author(s):  
Michael J. Uren ◽  
Serge Karboyan ◽  
Indranil Chatterjee ◽  
Alexander Pooth ◽  
Peter Moens ◽  
...  
Keyword(s):  
Carbon Doped ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Gan Hemts ◽  
Leaky Dielectric

The electrostatically forced Faraday instability: theory and experiments

2019 ◽  
Vol 862 ◽  
pp. 696-731 ◽  
Author(s):  
Kevin Ward ◽  
Satoshi Matsumoto ◽  
Ranga Narayanan
Keyword(s):  
Interfacial Instability ◽  
Perfect Conductor ◽  
Dc Voltage ◽  
Fluid Systems ◽  
Instability Theory ◽  
Dielectric Model ◽  
Leaky Dielectric Model ◽  
Leaky Dielectric ◽  
Rigorous Model ◽  
Parametric Frequency

The onset of interfacial instability in two-fluid systems using a viscous, leaky dielectric model is studied. The instability arises as a result of resonance between the parametric frequency of an imposed electric field and the system’s natural frequency. In addition to a rigorous model that uses Floquet instability analysis, where both viscous and charge effects are considered, this study also provides convincing validating experiments. In other results, it is shown that (a) the imposition of a periodic electrostatic potential acts to counter gravity and this countering effect becomes more effective if a DC voltage is also added, (b) a critical DC voltage exists at which the interface becomes unstable such that no parametric frequency is required to completely destabilize the interface and (c) the leaky dielectric model approaches a model for a perfect dielectric/perfect conductor pair as the conductivity ratio becomes large. It is also shown via experiments that parametric resonant instability using electrostatic forcing may be reliably used to estimate interfacial tension to sufficient accuracy.

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