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Full Description
An integral overview of the theory and design of printheads, authored by an expert with over 30 years' experience in the field of inkjet printing.
Clearly structured, the book presents the design of a printhead in a comprehensive and clear form, right from the start. To begin with, the working principle of piezo-driven drop-on-demand printheads in theory is discussed, building on the theory of mechanical vibrations and acoustics. Then the design of single-nozzle as well as multi-nozzle printheads is presented, including the importance of various parameters that need to be optimized, such as viscosity, surface tension and nozzle shape. Topics such as refilling the nozzle and the impact of the droplet on the surface are equally treated. The text concludes with a unique set of worked-out questions for training purposes as well as case studies and a look at what the future holds.
An essential reference for beginning as well as experienced researchers, from ink developers to mechanical engineers, both in industry and academia.
Contents
Preface xi
List of Symbols xv
1 Introduction 1
References 10
2 Single Degree of Freedom System 13
2.1 Introduction 13
2.2 Governing Equations and Solution for Square Pulse Driving 15
2.3 Solution for Ramped Pulse Driving 42
2.4 Solution for Exponential Pulse Driving 47
2.5 Solution for Harmonic Driving and Fourier Analysis 50
2.6 Non-linear Effects Associated with Non-complete Filling of the Nozzle 61
References 71
3 Two Degrees of Freedom System 75
3.1 Introduction 75
3.1.1 Rayleigh's Method to Determine Approximately the Resonance Frequencies of a Two Degrees of Freedom System for the Case with Surface Tension 79
3.2 Governing Equations and Solutions for Square Pulse Driving 98
3.3 Solutions for Ramped Pulse Driving 119
3.4 Solutions for Exponential Pulse Driving 128
3.5 Solution for Harmonic Driving and Fourier Analysis 134
3.6 Non-linear Analysis 148
References 163
4 Multi-cavity Helmholtz Resonator Theory 167
4.1 Introduction 167
4.2 Governing Equations 169
4.3 Solutions for Ramped Pulse Driving for Low Viscosity Inks 174
4.4 Solution for Harmonic Driving and Fourier Analysis 183
References 192
5 Waveguide Theory of Single-nozzle Print Head 193
5.1 Introduction 193
5.2 Long Waveguide Theory 197
5.3 Solutions for Ramped Pulse Driving of the Waveguide-type Inkjet Pump 207
5.4 Solutions for Harmonic Driving and Fourier Analysis Including the Effect of Damping 221
5.5 Non-linear Analysis of the Waveguide Type of Print Head Including Inertia, Viscous, and Surface Tension Effects in the Nozzle 243
5.6 Means and Methods to Enhance Fluid Velocity in Nozzle 258
References 259
6 Multi-cavity Waveguide Theory 263
6.1 Introduction to Multi-cavity Acoustics 263
6.2 Analysis of Cross-talk in an Open End/Closed End Linear Array Print Head with Alternately Activated and Non-activated Pumps 266
6.3 Analysis of Cross-talk in an Open End/Closed End Linear Array Print Head with Alternately One Pump Activated and Two Pumps Idling 277
6.4 Analysis of Cross-talk in an Open End/Closed End Linear Array Print Head with Alternately One Pump Activated and Three Pumps Idling 285
6.5 Analysis of Cross-talk in an Open End/Closed End Linear Array-shared Wall Shear-mode Print Head with Alternately One Pump Activated and Two Pumps Non-activated 297
6.6 Analysis of Cross-talk in a Closed End/Closed End Linear Array Print Head with Alternately Activated and Non-activated Pumps 302
References 307
7 Droplet Formation 309
7.1 Introduction 309
7.2 Analysis of Droplet Formation (Positive Pulse) 312
7.3 Analysis of Droplet Formation (Negative Pulse) 320
7.4 Deceleration Due to Elongational and Surface Tension Effects Prior to Pinching Off 326
7.5 Non-linear Two Degrees of Freedom Analysis Including the Effects of Droplet Formation 332
7.6 Non-linear Waveguide Theory Including the Effects of Droplet Formation 335
References 344
8 Droplet Flight, Evaporation, Impact, Spreading, Permeation, and Drying 347
8.1 Introduction 347
8.2 Evaporation of a Free-flying Droplet Exposed to Still Air 348
8.3 Cooling of a Free-flying Droplet During Flight Through Still Air 353
8.4 Deceleration of a Free-flying Droplet due to Air Friction 355
8.5 Spreading 357
8.6 Permeation into Porous Substrates 389
8.7 Evaporation of Dome-shaped Blobs of Fluid 391
References 393
Appendix A: Solving Algebraic Equations 399
A.1 Second-order Algebraic Equation 399
A.2 Third-order Algebraic Equation 399
A.3 Fourth-order Algebraic Equation 402
References 404
Appendix B: Fourier Decomposition of a Pulse 407
B.1 Pulse with Two Ramps 407
B.2 Exponential Pulse 409
B.3 Pulse with Three Ramps and Two Stationary Levels 413
References 416
Appendix C: Toroidal Co-ordinate System 417
C.1 Introduction 417
C.2 Definition with Respect to Rectangular Co-ordinate System 417
C.3 Scale Factors 417
C.4 Elementary Line Element 418
C.5 Unit Vectors 418
C.6 Nabla Operator ∇ 419
C.7 Gradient of Scalar 419
C.8 Divergence of a Vector Field 419
C.9 Dyadic Product ∇v 420
C.10 Laplacian of Vector Field ∇. ∇v (∇2v) 421
C.11 Indefinite Integrals Involving Hyperbolic Functions 422
References 422
Index 423
