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.

Numerical Study of Dynamic Behavior of Dielectric Fluid Bubbles Within Diverging, External Electric Fields

2006 ◽  
Author(s):  
Matthew R. Pearson ◽  
Jamal Seyed-Yagoobi
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Numerical Study ◽  
Pool Boiling ◽  
Spherical Shape ◽  
Past Research ◽  
Bubble Surface ◽  
Uniform Electric Field ◽  
Dielectric Fluid ◽  
Uniform Field

Past research in the area of pool boiling within the presence of electric fields has generally focused on the case of uniform field intensity. Any numerical or analytical studies of the effect of non-uniform fields on the motion of bubbles within a dielectric liquid medium have assumed that the bubbles will retain their spherical shape rather than deform. These studies also ignore changes to the electrical field caused by the presence of the bubbles. However, these assumptions are not necessarily accurate as, even in the case of a nominally uniform electric field distribution, bubbles can exhibit considerable physical deformation and the field can become noticeably affected in the vicinity of the bubble. This study explores the effect that a non-uniform electric field can have on vapor bubbles of a dielectric fluid by modeling the physical deformation of the bubble and the alteration of the surrounding field. Numerical results show that the imbalance of electrical stresses at the bubble surface exerts a net dielectrophoretic force on the bubble, propelling the bubble to the vicinity of weakest electric field, thereby enhancing the separation of liquid and vapor phases during pool boiling. However, the proximity of the bubble to one of the electrodes can considerably alter the bubble trajectory due to an attractive force that arises from local distortions of the potential and electric fields. This phenomenon cannot be predicted if bubble deformation and field distortion effects are neglected.

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.

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.

The elongated shape of a dielectric drop deformed by a strong electric field

2010 ◽  
Vol 664 ◽  
pp. 286-296 ◽  
Author(s):  
DOV RHODES ◽  
EHUD YARIV
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Strong Electric Field ◽  
Outer Region ◽  
Spherical Shape ◽  
Problem Formulation ◽  
Boundary Integral ◽  
Uniform Electric Field ◽  
Cross Sectional ◽  
Drop Shape

A dielectric drop is suspended within a dielectric liquid and is exposed to a uniform electric field. Due to polarization forces, the drop deforms from its initial spherical shape, becoming prolate in the field direction. At strong electric fields, the drop elongates significantly, becoming long and slender. For moderate ratios of the permittivities of the drop and surrounding liquid, the drop ends remain rounded. The slender limit was originally analysed by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047) using a singularity representation of the electric field. Here, we revisit it using matched asymptotic expansions. The electric field within the drop is continued into a comparable solution in the ‘inner’ region, at the drop cross-sectional scale, which is itself matched into the singularity representation in the ‘outer’ region, at the drop longitudinal scale. The expansion parameter of the problem is the elongated drop slenderness. In contrast to familiar slender-body analysis, this parameter is not provided by the problem formulation, and must be found throughout the course of the solution. The drop aspect-ratio scaling, with the 6/7-power of the electric field, is identical to that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047). The predicted drop shape is compared with the boundary-integral solutions of Sherwood (J. Fluid Mech., vol. 188, 1988, p. 133). While the agreement is better than that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047), the weak logarithmic decay of the error terms still hinders an accurate calculation. We obtain the leading-order correction to the drop shape, improving the asymptotic approximation.

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.

scholarly journals Mathematical modelling of electrical potential difference in a non-uniform electric field

2020 ◽  
pp. 64-72
Author(s):  
Mustafa Erol ◽  
İldahan Özdeyiş Çolak
Keyword(s):  
Electric Field ◽  
Mathematical Modelling ◽  
Electric Fields ◽  
Electrical Potential ◽  
Potential Difference ◽  
Uniform Electric Field ◽  
Electrical Potential Difference ◽  
Dc Power ◽  
Scalar Products ◽  
Modelling Process

This work offers an unproblematic teaching tool for the instruction of challeng-ing concept of electric potential difference in a non-uniform electric field. Specifically, mathematical modelling process is employed and managed to comprehend and teach exceedingly difficult concepts of uniform and non-uniform electric fields, electrical potential difference, scalar products of vectors and also concept of path integral. In order to accomplish those tasks, initially a basic conducting panel/sheet, that is simply a wet cardboard, is designed as a part of the apparatus, together with a dc power supply, a multi meter and connecting cables. The established method is interesting in the sense that the 3D wet cardboard is novel, very practical and minimal costing, hence the approach offers physics educators fresh teaching routes and opportunities to clarify the puzzling concept of electrical potential difference and further.

Suppression of runaway of electrons in a Lorentz plasma. II. crossed electric and magnetic fields

1970 ◽  
Vol 4 (3) ◽  
pp. 441-450 ◽  
Author(s):  
Barbara Abraham-Shrauner
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Electric Fields ◽  
Cyclotron Frequency ◽  
Collision Frequency ◽  
Uniform Electric Field ◽  
Drift Motion ◽  
Electric And Magnetic Fields ◽  
The Magnetic Field

Suppression of runaway of electrons in a weak, uniform electric field in a fully ionized Lorentz plasma by crossed magnetic and electric fields is analysed. A uniform, constant magnetic field parallel to a constant or harmonically time varying electric field does not alter runaway from that in the absence of the magnetic field. For crossed, constant fields the passage to runaway or to free motion as described by constant drift motion and spiral motion about the magnetic field is lengthened in time for strong magnetic fields. The new ‘runaway’ time scale is roughly the ratio of the cyclotron frequency to the collision frequency squared for cyclotron frequencies much greater than the collision frequency. All ‘runaway’ time scales may be given approximately by t2E Teff where tE is the characteristic time of the electric field and Teff is the ffective collision time as estimated from the appropriate component of the electrical conductivity.

The Effect of Electrostatic Forces on the Distribution of Drops in a Channel

2002 ◽  
Author(s):  
Arturo Ferna´ndez ◽  
Jiacai Lu ◽  
Asghar Esmaeeli ◽  
Gre´tar Tryggvason
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Hydrodynamic Interaction ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Dielectric Fluids ◽  
Wide Range ◽  
Leaky Dielectric Model

Direct numerical simulations are used to examine the effect of electric fields on the behavior of suspension of drops in dielectric fluids. The effect of electric field is modeled using the “leaky dielectric” model, coupled with the full Navier-Stokes equations. The governing equations are solved using a front-tracking/finite volume technique. The interaction of the drops is strongly dependant on the conductivity and the permittivity ratio, but fibration, where drops line up into long columns, takes place over a wide range of these parameters. The hydrodynamic interaction due to fluid circulation induced by the electric field has a strong influence on the drop distribution and the rate of fibration.

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