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 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.

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.

Three-dimensional analysis of the steady-state shape and small-amplitude oscillation of a bubble in uniform and non-uniform electric fields

1999 ◽  
Vol 384 ◽  
pp. 59-91 ◽  
Author(s):  
S. M. LEE ◽  
I. S. KANG
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Indirect Effect ◽  
Oscillation Frequency ◽  
Small Amplitude ◽  
Free Oscillation ◽  
Three Dimensional ◽  
Spherical Shape ◽  
Uniform Electric Field ◽  
Small Amplitude Oscillation

A three-dimensional analysis is performed to investigate the effects of an electric field on the steady deformation and small-amplitude oscillation of a bubble in dielectric liquid. To deal with a general class of electric fields, an electric field near the bubble is approximately represented by the sum of a uniform field and a linear field. Analytical results have been obtained for steady deformation and modification of oscillation frequency by using the domain perturbation method with the angular momentum operator approach.It has been found that, to the first order, the steady shape of a bubble in an arbitrary electric field can be represented by a linear combination of a finite number of spherical harmonics Yml, where 0[les ]l[les ]4 and [mid ]m[mid ][les ]l. For the oscillation about the deformed steady shape, the overall frequency modification from the value of free oscillation about a spherical shape is obtained by considering two contributions separately: (i) that due to the deformed steady shape (indirect effect), and (ii) that due to the direct effect of an electric field. Both the direct and indirect effects of an electric field split the (2l+1)-fold degenerate frequency of Yml modes, in the case of free oscillation about a spherical shape, into different frequencies that depend on m. However, when the average is taken over the (2l+1) values of m, the frequency splitting due to the indirect effect via the deformed steady shape preserves the average value, while the splitting due to the direct effect of an electric field does not.The oscillation characteristics of a bubble in a uniform electric field under the negligible compressibility assumption are compared with those of a conducting drop in a uniform electric field. For axisymmetric oscillation modes, deforming the steady shape into a prolate spheroid has the same effect of decreasing the oscillation frequency in both the drop and the bubble. However, the electric field has different effects on the oscillation about a spherical shape. The oscillation frequency increases with the increase of electric field in the case of a bubble, while it decreases in the case of a drop. This fundamental difference comes from the fact that the electric field outside the bubble exerts a suppressive surface force while the electric field outside the conducting drop exerts a pulling force on the surface.

Numerical Study of Dielectric Fluid Bubble Behavior Within Diverging External Electric Fields

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Matthew R. Pearson ◽  
Jamal Seyed-Yagoobi
Keyword(s):  
Mathematical Model ◽  
Electric Field ◽  
Electric Fields ◽  
Numerical Study ◽  
Electrode Spacing ◽  
Small Scale ◽  
Arbitrary Distribution ◽  
Dielectric Fluid ◽  
Reciprocal Effect ◽  
Bubble Deformation

A three-dimensional mathematical model is presented that models bubble deformation of a dielectric fluid due to the presence of a nonuniform electric field and calculates the net dielectrophoretic force that is exerted by the electric field on the bubble. The study includes the development of a method of predicting the shape of a bubble based on the arbitrary distribution of stresses over its surface without requiring an axisymmetric configuration. The reciprocal effect of the bubble’s presence on the electric field is also incorporated into the model, and dimensional analysis is used to obtain a single key parameter that governs the bubble deformation phenomenon. Numerical implementation of the mathematical model shows that the bubble deformation can be significant. Furthermore, bubble deformation and electric field distortion can have significant effects on the dielectrophoretic behavior of bubbles in nonuniform fields, especially within small-scale devices where the bubble size and electrode spacing are similar in magnitude.

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.

Control of Dielectric Fluid Flow Distribution in Micro-Tubes With EHD Conduction Pumping: Numerical Study

2011 ◽  
Author(s):  
Miad Yazdani ◽  
Jamal Seyed-Yagoobi
Keyword(s):  
Fluid Flow ◽  
Electric Field ◽  
Conduction Mechanism ◽  
Numerical Study ◽  
Fluid Motion ◽  
Flow Distribution ◽  
Operating Conditions ◽  
Dielectric Fluid ◽  
Total Flow ◽  
Flow Through

The control of fluid flow distribution in micro-scale tubes is numerically investigated. The flow distribution control is achieved via electric conduction mechanism. In electrohydrodynamic (EHD) conduction pumping, when an electric field is applied to a fluid, dissociation and recombination of electrolytic species produces heterocharge layers in the vicinity of electrodes. Attraction between electrodes and heterocharge layers induces a fluid motion and a net flow is generated if the electrodes are asymmetric. The numerical domain comprises a 2-D manifold attached to two bifurcated tubes with one of the tubes equipped with a bank of uniquely designed EHD-conduction electrodes. In the absence of electric field, the total flow supplied at the manifold’s inlet is equally distributed among the tubes. The EHD-conduction, however, operates as a mechanism to manipulate the flow distribution to allow the flow through one branch surpasses the counterpart of the other branch. Its performance is evaluated under various operating conditions.

Optimization of the electric field calculation for a rod-shaped conductor in a uniform electric field

2019 ◽  
Vol 30 (05) ◽  
pp. 1950039 ◽  
Author(s):  
Juan Wu ◽  
Xin Gao ◽  
Yikai Ma
Keyword(s):  
Electric Field ◽  
Traditional Method ◽  
Uniform Electric Field ◽  
Image Method ◽  
Field Calculation ◽  
Uniform Field ◽  
Multiple Image ◽  
Improve Calculation ◽  
Conducting Spheres ◽  
Electric Field Calculation

A rod-shaped conductor in a uniform electric field is analyzed based on finite difference method. Most induction charges distribute at the two hemisphere ends, which is similar with two connected conducting spheres in a uniform field. Therefore, the boundary potentials are calculated by multiple image method for the system with two connected conducting spheres. Comparing the results from our method with those from traditional method with constant boundary potentials, our method can improve calculation evidently. Results prove that this method is available and credible, and it can give electric field with high precision.

In situinvestigation of the non-linear optical crystal rubidium titanyl arsenate, RbTiOAsO4, under applied electric field using X-ray imaging

2007 ◽  
Vol 40 (3) ◽  
pp. 505-512 ◽  
Author(s):  
D. Walker ◽  
P. A. Thomas ◽  
P. Pernot-Rejmánková ◽  
J. Baruchel
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Surface Region ◽  
Uniform Field ◽  
Linear Optics ◽  
Near Surface ◽  
X Ray ◽  
Non Linear ◽  
Linear Optical ◽  
Section Topography

Recent work on the non-linear optical single-crystal rubidium titanyl arsenate (RbTiOAsO4, RTA) has shown that it exhibits behaviour consistent with a ferroelectric semiconductor under large applied electric fields, with the development of a non-uniform field in the near-surface region. To confirm aspects of the proposed model, the behaviour of 001 slices of initially single-domain RTA, patterned with periodic Ag electrodes of spacing 38 µm, as for periodic poling in non-linear optics, were investigated using synchrotron X-ray section topography with the electric field appliedin situwhile under X-ray illumination at the ID19 topography beamline of the ESRF, Grenoble. The results of white-beam section topography as both a function of crystal to film distance, and under DC voltage are reported, confirming that there is a bending of the planes in the near-surface region. The strain in the near-surface region was examined directly using high-resolution monochromatic X-ray section topography. This revealed an extensive strain of 3 (±1) × 10−4at 1 kV, indicating that the electrostrictive coefficient, γ3333, in RTA is positive in sign.

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