Takuma / Techaumnat Electric Fields in Composite Dielectrics and their Applications

1. Auflage 2010
ISBN: 978-90-481-9392-9
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 178 Seiten

An accurate quantitative picture of electric field distribution is essential in many electrical and electronic applications. In composite dielectric configurations composed of multiple dielectrics, anomalous or unexpected behavior of electric fields may appear when a solid dielectric is in contact with a conductor or another solid dielectric. The electric field near the contact point may become higher than the original field not only in the surrounding medium but also in the solid dielectric. Theoretically it may become infinitely high, depending on the contact angle. Although these characteristics are very important in a variety of applications, they have been clarified only recently using analytical and numerical calculation methods, and this is the first book to cover these new findings. Electric Fields in Composite Dielectrics and Their Applications describes the fundamental characteristics and practical applications of electric fields in composite dielectrics. The focus is on the field distribution (and the resultant force when appropriate) near points of contact. Applications include insulation design of high-voltage equipment with solid insulating supports, utilization of electrostatic force on dielectric particles in electrophotography and electrorheological fluids, and others. Electric Fields in Composite Dielectrics and Their Applications also explains the calculation methods used to analyze electric fields in composite dielectrics.

Autoren/Hrsg.

Takuma, Tadasu

Techaumnat, Boonchai

Inhaltsverzeichnis

1;Preface;6
2;Acknowledgements;8
3;Contents;10
4;Chapter 1: Basic Properties of Electric Fields in Composite Dielectrics;16
4.1;1.1 Background;16
4.2;1.2 Fundamentals of Composite Dielectric Fields;17
4.2.1;1.2.1 Governing Equations;17
4.2.2;1.2.2 Boundary Conditions;18
4.3;1.3 Effect of Conduction;19
4.3.1;1.3.1 Basic Equations;19
4.3.2;1.3.2 Boundary Conditions;20
4.3.3;1.3.3 Classification Based on the Effect of Volume Conduction;22
4.4;1.4 Outline of Field Behavior near a Contact Point;22
4.4.1;1.4.1 Contact Angle;22
4.4.2;1.4.2 Typical Examples for Contact Angle a = 90;24
4.4.2.1;1.4.2.1 Axisymmetric (AS) Cases;24
4.4.2.2;1.4.2.2 Two-dimensional (2D) Cases;26
4.5;1.5 Outline of the Chapters;26
4.6;References;29
5;Chapter 2: Electric Field Behavior for a Finite Contact Angle;30
5.1;2.1 Analytical Treatment;31
5.1.1;2.1.1 Basic Field Behavior;31
5.1.2;2.1.2 Minimum and Maximum Values of m in 2D Cases;32
5.1.3;2.1.3 Wedge-like Dielectric Interface Without a Contacting Plane Conductor;33
5.1.4;2.1.4 Axisymmetric (AS) Case;34
5.2;2.2 Numerical Treatment;35
5.2.1;2.2.1 Dielectric Interface Between Parallel Plane Conductors;35
5.2.2;2.2.2 Other Configurations;37
5.2.3;2.2.3 Effect of Right-Angled Contact (Curved Edge);37
5.3;2.3 Effect of Volume and Surface Conduction;39
5.3.1;2.3.1 Complex Expressions for Fields;39
5.3.2;2.3.2 Basic Characteristics;39
5.3.3;2.3.3 Effect of Volume Conduction;40
5.3.4;2.3.4 Effect of Surface Conduction;41
5.3.5;2.3.5 Approximate Evaluation of the Effect of Surface Conduction;42
5.4;References;43
6;Chapter 3: Electric Field for a Zero Contact Angle (Smooth Contact);45
6.1;3.1 Stressed Conductor in Contact with a Solid Dielectric;46
6.1.1;3.1.1 Field Strength at a Point of Contact;46
6.1.2;3.1.2 Field Behavior near the Point of Contact;47
6.1.3;3.1.3 Conductor Separated from a Dielectric Plane;49
6.2;3.2 Uncharged Spherical Conductor Under a Uniform Field;50
6.2.1;3.2.1 Expression for Contact-Point Field;50
6.2.2;3.2.2 Comparison of Contact-Point Fields;51
6.2.3;3.2.3 Approximate Expression;52
6.3;3.3 Stressed Conductor on a Solid Dielectric of Finite Thickness;52
6.3.1;3.3.1 Field Strength at a Contact Point;52
6.3.2;3.3.2 Approximate Treatment Based on Series Capacitance;54
6.3.3;3.3.3 Field Behavior for Small D/R;55
6.4;3.4 Other Basic Configurations;58
6.4.1;3.4.1 Dielectric Cylinder Under a Uniform Field;58
6.4.2;3.4.2 Other Simple Configurations;59
6.4.3;3.4.3 Approximate Expressions of the Contact-Point Field for a Zero Contact Angle;61
6.4.4;3.4.4 Summary of the Contact-Point Field for a Zero Contact Angle;62
6.5;3.5 Effect of Volume and Surface Conduction;64
6.5.1;3.5.1 Solid Dielectric Cylinder with Volume Conduction Under a Uniform Field;64
6.5.2;3.5.2 Other Configurations with Volume Conduction;66
6.5.2.1;3.5.2.1 Point and Line Contact;66
6.5.2.2;3.5.2.2 Surface Contact;68
6.5.3;3.5.3 Effect of Surface Conduction;69
6.5.3.1;3.5.3.1 Lower Conductivity;69
6.5.3.2;3.5.3.2 Higher Conductivity;70
6.5.4;3.5.4 Approximate Treatment for Surface Conduction;71
6.5.4.1;3.5.4.1 Limiting Field Distribution for High Conductivity;71
6.5.4.2;3.5.4.2 Approximate Evaluation of the Effect of Surface Conduction;73
6.6;References;74
7;Chapter 4: Electric Field Behavior for the Common Contact of Three Dielectrics;75
7.1;4.1 Contact of Straight Dielectric Interfaces;75
7.1.1;4.1.1 Basic Field Behavior;75
7.1.2;4.1.2 Applications of the Equations for n;76
7.1.2.1;4.1.2.1 Two Dielectrics Without a Conductor;77
7.1.2.2;4.1.2.2 Two Dielectrics in Contact with a Conductor;77
7.1.2.3;4.1.2.3 Three Dielectrics with the Same Angle;77
7.2;4.2 Perpendicular Contact of a Solid Dielectric with Another Solid;78
7.2.1;4.2.1 Equation for Determining n;78
7.2.2;4.2.2 Applications of Eq.4.7;79
7.3;4.3 Numerical Analysis of Field Behavior;80
7.3.1;4.3.1 Computation of n;80
7.3.2;4.3.2 Contact with a Curved Interface;82
7.4;References;84
8;Chapter 5: Electric Field in High-Voltage Equipment;85
8.1;5.1 Finite Contact Angle: Prevention of Field Singularity near a Contact Point;85
8.1.1;5.1.1 Field Distribution of a Disc-type Spacer in Coaxial Structures;85
8.1.2;5.1.2 Optimization of Field Distribution or Spacer Shape;87
8.2;5.2 Zero Contact Angle in Gas-Insulated Equipment;89
8.2.1;5.2.1 Basic Field Behavior at a Point of Contact;89
8.2.2;5.2.2 Field Behavior in a Flange Structure;90
8.2.3;5.2.3 Field Behavior for a Supporting Rod;92
8.2.4;5.2.4 Other Studies;93
8.3;5.3 Common Contact of Three Dielectrics;95
8.3.1;5.3.1 Solid Dielectric Supporting Another Solid Dielectric;95
8.3.2;5.3.2 Oblique Solid Surface with a Rounded Edge;95
8.4;5.4 Application to High-Field-Emission Devices;98
8.4.1;5.4.1 Metal Edge on a Plane Electrode;98
8.4.2;5.4.2 General Cases with Two Dielectrics and a Conductor;99
8.5;References;100
9;Chapter 6: Electric Field and Force in Electrorheological Fluid: A System of Multiple Particles;101
9.1;6.1 Equivalent Dipole Expression;101
9.1.1;6.1.1 Dielectric Sphere Under a Uniform Field;101
9.1.2;6.1.2 Multiple Particles;102
9.2;6.2 Particles Lined Up Parallel to an Applied Field;104
9.2.1;6.2.1 Contact-Point Field;104
9.2.2;6.2.2 Approximate Formula for the Contact-Point Field Strength;105
9.3;6.3 Particle Chain Tilted to the Field Direction;106
9.3.1;6.3.1 Chain of Two Particles;106
9.3.2;6.3.2 Isolated Chain of Multiple Particles;107
9.3.3;6.3.3 Two-Particle Chain in Contact with a Plane Electrode;108
9.3.4;6.3.4 Two-Particle Chain Between Parallel Plane Electrodes;110
9.4;6.4 Two-Particle Chain Between Parallel Plane Electrodeswith the Minimum Separation;111
9.4.1;6.4.1 Scope of the Section;111
9.4.2;6.4.2 Electric Field Distribution;112
9.4.3;6.4.3 DEP Force;114
9.4.4;6.4.4 Approximation of the Maximal Horizontal Force;116
9.5;6.5 Nonhomogeneous Particles;118
9.5.1;6.5.1 Particles with a Surface Film;118
9.5.2;6.5.2 Calculation Method;119
9.5.3;6.5.3 Apparent Conductivity;119
9.6;References;122
10;Chapter 7: Electric Field and Force on Toners in Electrophotography;124
10.1;7.1 Fundamental Characteristics;125
10.1.1;7.1.1 Fundamentals of the Adhesive Force;125
10.1.2;7.1.2 Nonuniform Charging Models;126
10.1.3;7.1.3 Field Calculation;127
10.2;7.2 Charged Dielectric Particle on a Conductor;129
10.2.1;7.2.1 General Expression of Electrostatic Force;129
10.2.2;7.2.2 Adhesion in the Absence of an External Field;130
10.2.3;7.2.3 Discrete Charge Distribution;132
10.2.4;7.2.4 Electrostatic Force Versus VE;133
10.2.5;7.2.5 VE for Detachment;134
10.3;7.3 Charged Dielectric Particle on a Dielectric Barrier;135
10.3.1;7.3.1 Configuration for Study;135
10.3.2;7.3.2 Adhesion in the Absence of an External Field;136
10.3.3;7.3.3 Detachment by an Applied Field;137
10.4;References;138
11;Chapter 8: Analytical Calculation Methods;140
11.1;8.1 Variable-Separation Method for Straight Dielectric Interfaces;140
11.1.1;8.1.1 Dielectric Interface in Contact with a Plane Conductor;141
11.1.2;8.1.2 Solution of Exponent n;142
11.1.3;8.1.3 Two Dielectrics Without a Contacting Conductor;143
11.1.4;8.1.4 Axisymmetric Case;144
11.1.5;8.1.5 Configurations with Three Dielectrics;145
11.2;8.2 Iterative Image Charge Method;147
11.2.1;8.2.1 Conducting Sphere on a Solid Dielectric Plane;148
11.2.2;8.2.2 Conducting Cylinder on a Solid Dielectric Plane;149
11.2.3;8.2.3 Conducting Sphere or Cylinder Separated from a Dielectric Plane;150
11.3;8.3 Uncharged Conducting Sphere Under a Uniform Field on a Dielectric Plane;151
11.3.1;8.3.1 Image Charges;151
11.3.2;8.3.2 Procedure of Image Charge Location;153
11.3.2.1;8.3.2.1 First Set of Images;153
11.3.2.2;8.3.2.2 Second Set of Images;154
11.3.2.3;8.3.2.3 Third Set of Images;154
11.4;8.4 Re-expansion Method for a System of Particles;156
11.4.1;8.4.1 Principle;156
11.4.2;8.4.2 Image Schemes;159
11.4.2.1;8.4.2.1 Grounded Plane;159
11.4.2.2;8.4.2.2 Dielectric Plane;159
11.4.2.3;8.4.2.3 Conducting Sphere;160
11.4.2.4;8.4.2.4 Dielectric Sphere;161
11.4.2.5;8.4.2.5 Sphere with a Surface Film;161
11.4.3;8.4.3 Iterative Calculation Procedure;162
11.4.4;8.4.4 Two Spherical Particles;163
11.4.5;8.4.5 Conducting Particle and a Plane Electrode with a Dielectric Barrier;165
11.5;References;168
12;Chapter 9: Numerical Calculation Methods;170
12.1;9.1 General Remarks;170
12.2;9.2 Charge Simulation Method (CSM);172
12.2.1;9.2.1 Basic Principle;172
12.2.2;9.2.2 Composite Dielectric Cases;173
12.2.3;9.2.3 b-Method: CSM Using Fictitious Charges Inside Surrounding Boundaries Only;174
12.2.4;9.2.4 Mixed (Capacitive-Resistive) Fields;175
12.2.4.1;9.2.4.1 Complex CSM for ac steady fields;175
12.2.4.2;9.2.4.2 CSM for fields including volume conduction;175
12.2.4.3;9.2.4.3 CSM for fields including surface conduction;176
12.2.5;9.2.5 Example of Boundary Division;177
12.3;9.3 Surface Charge Method (SCM);178
12.3.1;9.3.1 Basic Principle;178
12.3.2;9.3.2 Some Improvements;180
12.3.2.1;9.3.2.1 Simulation of Rounded Surface Profiles;180
12.3.2.2;9.3.2.2 Expression of Surface Charge Density;180
12.3.2.3;9.3.2.3 Formulation of Boundary Conditions;181
12.4;9.4 Boundary Element Method (BEM);181
12.4.1;9.4.1 Basic Equations;181
12.4.2;9.4.2 Composite Dielectric Cases;183
12.4.3;9.4.3 Infinite Domain with an External Field;184
12.4.4;9.4.4 Dielectric Interface with Surface Conduction;185
12.4.5;9.4.5 Example of Boundary Division;186
12.5;References;186
13;Index;188