Professor Martin Taylor Publications: Books

INDUSTRIAL ELECTROSTATICS: Fundamentals and Measurements

D.M.Taylor

School of Electronic Engineering and Computer Systems
University of Wales, Bangor

P.E.Secker

Electronic Engineering Group, Department of Physics
Keele University

RESEARCH STUDIES PRESS LTD

JOHN WILEY AND SONS INC

Editorial Foreword

The previous twelve titles in this series have described various aspects of electrostatics, all of which, in one way or another, have relied on the use and understanding of a number of electrostatic phenomena and different measurement techniques. In this monograph, the origin of electrostatic phenomena as well as fundamental parameters such as resistivity, electric field, potential, charge etc. are discussed and techniques for measuring these parameters described in detail. Throughout an emphasis is placed on relating each new topic to industrial situations.

The authors not only describe methods of measurement but also clearly identify potential errors in otherwise seemingly simple techniques. This, combined with useful discussions relating to the interpretation of data, makes this monograph not only a useful companion to other titles in the series but also an extremely valuable reference in its own right.

Whether for teaching, for research or for industrial applications, following the guidance given by the authors will ensure that any measurement made on an electrostatic system will be a meaningful one.

J.F.Hughes
S.C.Johnson Professor of New Technologies
Southhampton, March 1994

Contents

Editorial Foreword (Xi)

1 INTRODUCTION Page1

1.1 Industrial Problems caused by Static Electricity 1

1.2 Applications of Static Electricity 4

1.3 Insulators 12

1.4 Standards 12

1.5 Concluding Remarks 14

2 BASIC ELECTROSTATIC THEORY Page 16

2.1 Electrostatic Charges 17

2.2 Forces Between Charges 17

2.2.1 Coulomb`s Law 18

2.3 Electric Field 19

2.3.1 Electric Field of a Point Charge 20

2.3.2 Flux Density (Displacement) 20

2.3.3 Electric Field of an Infinite Sheet of Charge 21

2.3.4 Electric Field of a Volume of Charge 21

2.3.4.1 Gauss` Theorem 24

2.3.4.2 Electric Fields in Spherical Containers 25

2.3.4.3 Electric Field in a Pipe 26

2.4 Potential 28

2.4.1 Potential of a Point Charge 28

2.4.2 Potential of an Infinite Sheet of Charge 29

2.4.3 Equipotentials 30

2.5 Fields and Potentials Associated with a Volume Charge 30

2.6 Boundries of Dielectrics 33

2.6.1 General Rules at Dielectric Interfaces 34

(a) Electric Fields Normal to the Interface 34

(b) Electric Fields Parrallel to an Interface 35

(c) Interfacial Charges 36

2.6.2 Image charges 36

(a) Image Charges in Conducting Surfaces 36

(b) Image Charges in Dielectric Surfaces 38

2.6.3 Method of Images 40

(a) Line Charge Parrallel to an Earthed Plane 40

(b) Sheet of Charge Parallel to an Earthed Plane 41

(c) Image of a Charged Sheet Tangential to an Earthed Roller 42

2.7 Capacitance 43

2.7.1 Parallel-Plate capacitor 44

2.7.2 Cylindrical and Spherical Capacitors 45

(a) Coaxial Cylinders 46

(b) Parrallel Cylinders 47

(c) Cylinder and a Plane 48

(d) Concentric Spheres 49

(e) Sphere and a plane 50

2.7.3 Other types of Capacitances 52

2.7.4 Addition of Capacitances 52

(a) Parallel combination of Capacitors 52

(b) Series Combination of Capacitors 53

2.7.5 Energy Stored in a Capacitor 53

2.8 Independant and Dependant Electrostatic Parameters 55

2.9 Insulating Materials 57

2.9.1 Relative Permittivity (Dielectric Constant) 57

2.9.2 Volume Resistivity 59

2.9.3 Surface Resistivity 60

2.9.4 Relaxation Time 60

2.9.5 Transparency to Electric Flux 63

2.9.6 Breakdown Strength 64

2.10 Equivalent Circuit of an Electrostatic System 64

3 INITIATION OF ELECTROSTATIC PHENOMENA Page 67

3.1 Charging of Liquids in a Pipeline Flow 68

3.1.1 The Double-Layer 68

3.1.2 The Streaming Current 73

3.1.2.1 Streaming Current in Long Pipes 74

3.1.2.2 Effect of Flow Velocity 76

3.1.2.3 Effect of Pipe Length 77

3.1.2.4 Effect of Liquid Conductivity 78

3.1.2.5 Outlet Effects 79

3.1.3 Streaming Current in Transformers 80

3.1.4 Electrification of Polymers During Extrusion 81

3.1.5 Streaming Current in Insulating Pipes 81

3.1.6 Other Related Electrification Mechanisms in Liquids 82

3.2 Contact and Frictional Charging of solids 82

3.2.1 Models Based on Electron Transfer 85

3.2.1.1 Metal-Metal Contact 85

3.2.1.2 Metal-Insulator Contact 87

(a) Surface States 91

(b) Nature of Surface States 93

3.2.1.3 Insulator-Insulator Contacts 95

3.2.2 Triboelectrification 96

3.2.3 Ion Transfer 96

3.2.4 Role of Back-Discharges and Back-Tunnelling in Tribocharging 98

3.2.5 Tricharging Limits in Industrial processes 100

(a) Insulating Sheet 100

(b) Spherical Particles 102

3.2.6 Tribocharging in Industry 103

(a) Applications 103

(b) Hazards and Problems 103

3.3 Charging by Induction 104

3.3.1 Ink-Jet Printers 106

3.3.2 Atomisation 107

3.3.3 Induction Charging of Personnel 109

3.4 Corona Charging 110

3.4.1 The Corona Discharge 110

3.4.1.1 Corona Threshold Voltage 112

3.4.1.2 Current-Voltage Characteristic of a Corona 114

3.4.1.3 Current Density of a Corona 115

3.4.2 Corona Charging of Airborne Particles 116

3.4.2.1 Limiting Charge 116

3.4.2.2 Charging Time Constant 118

3.4.2.3 Bipolar Charging 120

3.4.2.4 Diffusion Charging 121

3.4.2.5 Back-Ionisation 121

3.4.3 Charging of Insulating Sheets 122

3.4.4 Static Eliminators 124

3.4.5 Nature of Corona Ions 124

3.5 Other Sources of Static 125

4 MEASUREMENT OF ELECTRIC FIELD Page 129

4.1 Introduction 129

4.1.1 Measurement Philosophy 130

4.2 The Induction Probe 130

4.2.1 Effects of Atmospheric Currents on Field Measurement.

4.3 The Field Mill 136

4.3.1 Detecting Electric Field Polarity 139

4.3.2 Field Penetration through Apertures 143

4.3.3 Making Field Mill Measurements 144

4.3.4 Field Mill Applications 148

4.4 Vibrating Probe Field Meter 152

4.5 Other Field Detection Techniques 153

4.5.1 The Ballistic Probe 153

4.5.2 The Charged Particle Probe 155

4.5.3 Electro-Optical Effects 155

5 MEASUREMENT OF VOLTAGE Page 159

5.1 Introduction 159

5.2 Voltmeters Exploiting Electrostatic Force Effects 159

5.3 Field Mill Voltmeter 167

5.4 Voltage Dividers 170

5.4.1 Direct Voltage Dividers 171

5.4.2 Alternating Voltage Dividers 175

5.4.3 Dividers for Impulse and Step-Function Voltages 177

5.5 Spark Gaps 179

5.6 Other Techniques for Voltage Measurement 182

6 MEASUREMENT OF CHARGE Page 185

6.1 Charged Particles 185

6.2 Charged Surfaces 193

6.2.1 Achieving Good Spatial Resolution in Surface Charge Measurements 196

6.3 Charge Distributed Throughout a Volume 201

6.3.1 Space-Charge Measurements in a Gaseous Medium 203

6.3.2 Space-Charge Measurement in Liquid 204

6.3.3 Volume Charge Density in Solid Materials 205

6.4 Concluding Comments 207

7 RESISTANCE AND CHARGE DECAY Page 210

7.1 Introduction 210

7.2 Bonding to Ground 211

7.2.1 Practical Monitoring of Earth Bonding 211

7.2.1.1 Antistatic Boots 211

7.2.1.2 Buried Conductors 212

7.2.1.3 Work-Pieces on Conveyors 214

7.3 Characterisation of Process Materials 215

7.3.1 Volume Resistivity 215

7.3.1.1 Volume Resistivity of Solids 216

7.3.1.2 Volume Resistivity of Liquids 217

7.3.1.3 Volume Resistivity of Powders 218

7.3.1.4 General Considerations 220

7.3.2 Surface Resistivity 221

7.3.2.1 General Considerations 222

7.3.3 Charge Decay Measurements 223

7.3.3.1 Liquids 223

7.3.3.2 Films and Laminates 224

7.3.3.3 On-Line Surface-Charge-Decay Gauge 228

7.3.3.4 General Considerations 230

8 ELECTROSTATIC DISCHARGES (ESD) Page 232

8.1 Electrical Breakdown in Air 232

8.1.1 Townsend -Process 232

8.1.2 Townsend -Process 233

8.2 Types of Electrical Discharge 234

8.2.1 Spark Discharge 235

8.2.2 Brush Discharge 236

8.2.3 Corona Discharge 238

8.2.4 Propagating Brush Discharge 238

8.2.5 Cone Discharges 240

8.3 Simulating Spark Discharges 242

8.3.1 Minimum Ignition Energy 242

8.3.1.1 Incendivity of Electrostatic Discharges 242

(a) Spark Discharge 242

(b) Brush Dischrage 243

(c) Corona Discharge 244

(d) Propagating Brush Discharge 245

(e) Cone Discharge 245

8.3.1.2 Measuring the MIE of a Gas/Air mixture 245

8.3.1.3 Measuring the MIE of a Dust/Air Mixture 247

8.3.2 Human Body Model 250

8.4 Monitoring Spark Discharges 253

8.4.1 Radio Frequency Detection 253

8.4.2 Measuring the Current Flow in Electrostatic Discharges 256

8.5 Concluding Remarks 261

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