Electric Fields in Composite Dielectrics and their Applications (eBook)

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