scholarly journals Total Internal Reflection in a Hybrid Nematic Cell Submitted to Weak Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Carlos I. Mendoza ◽  
Juan Adrian Reyes
Keyword(s):  
Electric Fields ◽  
Elastic Energy ◽  
Total Internal Reflection ◽  
Strong Influence ◽  
Uniform Electric Field ◽  
Penetration Length ◽  
Director Field ◽  
Anchoring Energy ◽  
Weak Boundary Conditions ◽  
Energy Dependent

We calculate the trajectory of a monochromatic optical beam propagating in a planar-homeotropic hybrid nematic crystal cell submitted to weak anchoring conditions. We apply a uniform electric field perpendicular to the cell to control the trajectories for various values of the anchoring elastic energy. We have found that the anchoring energy has a strong influence on the ray penetration length and trajectory. Our calculations are consistent with a previously found Frederick’s type transition only present for weak anchoring in which electric fields above an anchoring-energy dependent critical field align completely the director field.

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.

Superior electrostrictive strain achieved under low electric fields in relaxor ferroelectric polymers

2019 ◽  
Vol 7 (10) ◽  
pp. 5201-5208 ◽  
Author(s):  
Zhicheng Zhang ◽  
Xiao Wang ◽  
Shaobo Tan ◽  
Qing Wang
Keyword(s):  
Energy Density ◽  
Energy Conversion ◽  
Electric Fields ◽  
Elastic Energy ◽  
Energy Conversion Efficiency ◽  
Relaxor Ferroelectric ◽  
Ferroelectric Polymers ◽  
Elastic Energy Density ◽  
Electromechanical Responses ◽  
Electromechanical Performance

A relaxor ferroelectric polymer exhibits record electromechanical performance, including the largest electrostrain of −13.4%, the highest elastic energy density of 3.1 J cm−3 and the best energy conversion efficiency of 0.5, among the known ferroelectric polymers. Notably, the excellent electromechanical responses are realized under much lower fields than those of ferroelectric polymers.

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.

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 .

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.

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.

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