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<p>Preface xi</p> <p>List of Symbols xv</p> <p><b>1 Introduction 1</b></p> <p>References 10</p> <p><b>2 Single Degree of Freedom System 13</b></p> <p>2.1 Introduction 13</p> <p>2.2 Governing Equations and Solution for Square Pulse Driving 15</p> <p>2.3 Solution for Ramped Pulse Driving 42</p> <p>2.4 Solution for Exponential Pulse Driving 47</p> <p>2.5 Solution for Harmonic Driving and Fourier Analysis 50</p> <p>2.6 Non-linear Effects Associated with Non-complete Filling of the Nozzle 61</p> <p>References 71</p> <p><b>3 Two Degrees of Freedom System 75</b></p> <p>3.1 Introduction 75</p> <p>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</p> <p>3.2 Governing Equations and Solutions for Square Pulse Driving 98</p> <p>3.3 Solutions for Ramped Pulse Driving 119</p> <p>3.4 Solutions for Exponential Pulse Driving 128</p> <p>3.5 Solution for Harmonic Driving and Fourier Analysis 134</p> <p>3.6 Non-linear Analysis 148</p> <p>References 163</p> <p><b>4 Multi-cavity Helmholtz Resonator Theory 167</b></p> <p>4.1 Introduction 167</p> <p>4.2 Governing Equations 169</p> <p>4.3 Solutions for Ramped Pulse Driving for Low Viscosity Inks 174</p> <p>4.4 Solution for Harmonic Driving and Fourier Analysis 183</p> <p>References 192</p> <p><b>5 Waveguide Theory of Single-nozzle Print Head 193</b></p> <p>5.1 Introduction 193</p> <p>5.2 Long Waveguide Theory 197</p> <p>5.3 Solutions for Ramped Pulse Driving of the Waveguide-type Inkjet Pump 207</p> <p>5.4 Solutions for Harmonic Driving and Fourier Analysis Including the Effect of Damping 221</p> <p>5.5 Non-linear Analysis of the Waveguide Type of Print Head Including Inertia, Viscous, and Surface Tension Effects in the Nozzle 243</p> <p>5.6 Means and Methods to Enhance Fluid Velocity in Nozzle 258</p> <p>References 259</p> <p><b>6 Multi-cavity Waveguide Theory 263</b></p> <p>6.1 Introduction to Multi-cavity Acoustics 263</p> <p>6.2 Analysis of Cross-talk in an Open End/Closed End Linear Array Print Head with Alternately Activated and Non-activated Pumps 266</p> <p>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</p> <p>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</p> <p>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</p> <p>6.6 Analysis of Cross-talk in a Closed End/Closed End Linear Array Print Head with Alternately Activated and Non-activated Pumps 302</p> <p>References 307</p> <p><b>7 Droplet Formation 309</b></p> <p>7.1 Introduction 309</p> <p>7.2 Analysis of Droplet Formation (Positive Pulse) 312</p> <p>7.3 Analysis of Droplet Formation (Negative Pulse) 320</p> <p>7.4 Deceleration Due to Elongational and Surface Tension Effects Prior to Pinching Off 326</p> <p>7.5 Non-linear Two Degrees of Freedom Analysis Including the Effects of Droplet Formation 332</p> <p>7.6 Non-linear Waveguide Theory Including the Effects of Droplet Formation 335</p> <p>References 344</p> <p><b>8 Droplet Flight, Evaporation, Impact, Spreading, Permeation, and Drying 347</b></p> <p>8.1 Introduction 347</p> <p>8.2 Evaporation of a Free-flying Droplet Exposed to Still Air 348</p> <p>8.3 Cooling of a Free-flying Droplet During Flight Through Still Air 353</p> <p>8.4 Deceleration of a Free-flying Droplet due to Air Friction 355</p> <p>8.5 Spreading 357</p> <p>8.6 Permeation into Porous Substrates 389</p> <p>8.7 Evaporation of Dome-shaped Blobs of Fluid 391</p> <p>References 393</p> <p>Appendix A: Solving Algebraic Equations 399</p> <p>A.1 Second-order Algebraic Equation 399</p> <p>A.2 Third-order Algebraic Equation 399</p> <p>A.3 Fourth-order Algebraic Equation 402</p> <p>References 404</p> <p>Appendix B: Fourier Decomposition of a Pulse 407</p> <p>B.1 Pulse with Two Ramps 407</p> <p>B.2 Exponential Pulse 409</p> <p>B.3 Pulse with Three Ramps and Two Stationary Levels 413</p> <p>References 416</p> <p>Appendix C: Toroidal Co-ordinate System 417</p> <p>C.1 Introduction 417</p> <p>C.2 Definition with Respect to Rectangular Co-ordinate System 417</p> <p>C.3 Scale Factors 417</p> <p>C.4 Elementary Line Element 418</p> <p>C.5 Unit Vectors 418</p> <p>C.6 Nabla Operator ∇ 419</p> <p>C.7 Gradient of Scalar 419</p> <p>C.8 Divergence of a Vector Field 419</p> <p>C.9 Dyadic Product ∇v 420</p> <p>C.10 Laplacian of Vector Field ∇. ∇v (∇2v) 421</p> <p>C.11 Indefinite Integrals Involving Hyperbolic Functions 422</p> <p>References 422</p> <p>Index 423</p>

<p><b><i>J. Frits Dijksman</i></b> <i>obtained his master's degree in mechanical engineering at the Technical University of Delft, The Netherlands, in 1973. He finished his PhD within the groups of Professor D. de Jong and Professor W.T. Koiter (Technical University of Delft, The Netherlands, 1978) focusing on the engineering mechanics of leaf spring mechanisms. He worked with Philips Research Laboratories in Eindhoven, The Netherlands, for more than 32 years. After his retirement he continued his work as part time professor at the University of Twente, The Netherlands. The topics include inkjet printing of viscoelastic inks, design of inkjet print heads and printed biosensors. He is now emeritus professor and works as a consultant.</i>

<p>An integral overview of the theory needed to design print heads, authored by an expert with over 30 years' experience in the field of inkjet printing.</p> <p>Clearly structured, the book presents the working principle of a print head in a comprehensive and clear form, right from the start. To begin with, the modelling of piezo-driven drop-on-demand print heads is discussed, building on the theory of mechanical vibrations and acoustics. The design of single-nozzle as well as multi-nozzle print heads is presented, including the importance of various parameters that need to be optimized, such as microfluidic dimensions of the flow path, viscosity, surface tension and nozzle shape. Topics such as refilling the nozzle and the impact of the droplet on the surface of the substrate are equally treated.</p> <p>An essential reference for beginning as well as experienced researchers, from ink developers to mechanical engineers, both in industry and academia.</p>

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