The dynamics of the piezo inkjet printhead operation

The operation of a piezo inkjet printhead involves a chain of processes in many physical domains at different length scales. The final goal is the formation of droplets of all kinds of fluids with any desired volume, velocity, and a reliability as high as possible. The physics behind the chain of processes comprise the two-way coupling from the electrical to the mechanical domain through the piezoelectric actuator, where an electrical signal is transformed into a mechanical deformation of the printhead structure. The next two steps are the coupling to the acoustic domain inside the ink channels, and the coupling to the fluid dynamic domain, i.e. the drop formation process. The dynamics of the printhead structure are coupled via the acoustics to the drop formation process in the nozzle. Furthermore, wetting of the nozzle plate and air bubbles can have a negative influence on the printhead performance. The five topics (actuation, channel acoustics, drop formation, wetting, and air bubbles) are reviewed in this paper. This research connects the product developments for many emerging new industrial applications of the inkjet technology to the fundamental physical phenomena underlying the printhead operation.

[1]  D. Bonn,et al.  Drop formation by thermal fluctuations at an ultralow surface tension. , 2006, Physical review letters.

[2]  A. Marmur Wetting on Real Surfaces , 1999, Journal of Imaging Science and Technology.

[3]  H. Fernholz Boundary Layer Theory , 2001 .

[4]  K. Ferrara,et al.  The natural frequency of nonlinear oscillation of ultrasound contrast agents in microvessels. , 2007, Ultrasound in medicine & biology.

[5]  J. F. Dijksman,et al.  Hydrodynamics of small tubular pumps , 1984, Journal of Fluid Mechanics.

[6]  Hsien-Hsueh Lee,et al.  Inkjet printing of nanosized silver colloids , 2005, Nanotechnology.

[7]  Wallace W. Carr,et al.  An experimental study of drop-on-demand drop formation , 2006 .

[8]  Lydéric Bocquet,et al.  Large Slip Effect at a Nonwetting Fluid-Solid Interface , 1999 .

[9]  Jens Eggers,et al.  Theory of drop formation , 1995 .

[10]  Michael Selwyn Longuet-Higgins,et al.  The deformation of steep surface waves on water - I. A numerical method of computation , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[11]  T. Lundgren,et al.  Satellite formation in capillary jet breakup , 1990 .

[12]  J. D. Hosson,et al.  Influence of surface roughness on the wetting angle , 1995 .

[13]  Edmé ca. Mariotte,et al.  Traité du mouvement des eaux et des autres corps fluides ... , 1970 .

[14]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[15]  W. Beltman,et al.  Viscothermal wave propagation including acousto-elastic interaction, part I: theory , 1999 .

[16]  R. J. Pinnington,et al.  Practical industrial method of increasing structural damping in machinery, II: Squeeze-film damping with liquids , 1987 .

[17]  Grigory Panasenko,et al.  A model of a homogenized cavity corresponding to a multinozzle droplet generator for continuous ink‐jet printers , 1998 .

[18]  James Clerk Maxwell,et al.  On physical lines of force , 2010 .

[19]  O. Basaran,et al.  Analysis of the drop weight method , 2005 .

[20]  Herman Wijshoff Manipulating Drop Formation in Piezo Acoustic Inkjet , 2006 .

[21]  College de France,et al.  Molecular Weight Dependence of Spreading Rates of Ultrathin Polymeric Films , 1998 .

[22]  T. Önsay Effects of Layer Thickness on the Vibration Response of a Plate-Fluid Layer System , 1993 .

[23]  M. Gottlieb,et al.  Surface-tension-driven breakup of viscoelastic liquid threads , 1982, Journal of Fluid Mechanics.

[24]  C. Brennen Cavitation and Bubble Dynamics , 1995 .

[25]  C. B. Sawyer,et al.  The Use of Rochelle Salt Crystals for Electrical Reproducers and Microphones , 1931, Proceedings of the Institute of Radio Engineers.

[26]  S. Tomotika Breaking up of a Drop of Viscous Liquid Immersed in Another Viscous Fluid Which is Extending at a Uniform Rate , 1936 .

[27]  Andrea Prosperetti,et al.  Dynamics of bubble growth and detachment from a needle , 1993, Journal of Fluid Mechanics.

[28]  W. J. Merz Piezoelectric Ceramics , 1972, Nature.

[29]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[30]  Andrea Prosperetti,et al.  The Dynamics of Vapor Bubbles in Acoustic Pressure Fields , 1999 .

[31]  Detlef Lohse,et al.  Single bubble sonoluminescence , 2002 .

[32]  R. Chang,et al.  Lasing Droplets: Highlighting the Liquid-Air Interface by Laser Emission , 1986, Science.

[33]  C. Clanet,et al.  Making a splash with water repellency , 2007, cond-mat/0701093.

[34]  Michel Bruneau,et al.  On the propagation constant of higher order modes in a cylindrical waveguide , 1988 .

[35]  E. Stemme,et al.  The piezoelectric capillary injector—A new hydrodynamic method for dot pattern generation , 1973 .

[36]  H. Stone,et al.  Satellite and subsatellite formation in capillary breakup , 1992, Journal of Fluid Mechanics.

[37]  J. Eggers Drop formation – an overview , 2005 .

[38]  George Gabriel Stokes,et al.  Mathematical and Physical Papers vol.1: On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids , 2009 .

[39]  Osman A. Basaran,et al.  Small‐scale free surface flows with breakup: Drop formation and emerging applications , 2002 .

[40]  D. Schwartz,et al.  Microfluidics without microfabrication , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Fredericus Joseph Marie van der Eerden Noise reduction with coupled prismatic tubes , 2000 .

[42]  W. Ranz,et al.  Some experiments on orifice sprays , 1958 .

[43]  Minoru Usui,et al.  Development of the New MACH (MACH with MLChips) , 1999 .

[44]  L. Walker,et al.  Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance , 2002 .

[45]  Detlef Lohse,et al.  Analysis of Rayleigh–Plesset dynamics for sonoluminescing bubbles , 1998, Journal of Fluid Mechanics.

[46]  Jooho Moon,et al.  Influence of fluid physical properties on ink-jet printability. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[47]  M. B. Groot Wassink Inkjet printhead performance enhancement by feedforward input design based on two-port modeling , 2007 .

[48]  L. M. Hocking A moving fluid interface on a rough surface , 1976, Journal of Fluid Mechanics.

[49]  J. .. Habbottle Anisotropic irradiation creep of zircaloy-2 , 1978 .

[50]  Detlef Lohse,et al.  Phase diagrams for sonoluminescing bubbles , 1996 .

[51]  L. Redekopp,et al.  The nonlinear capillary instability of a liquid jet. Part 1. Theory , 1980, Journal of Fluid Mechanics.

[52]  E. P. Furlani Thermal modulation and instability of newtonian liquid microjets , 2005 .

[53]  R. A. Wentzell,et al.  Hydrodynamic and Hydromagnetic Stability. By S. CHANDRASEKHAR. Clarendon Press: Oxford University Press, 1961. 652 pp. £5. 5s. , 1962, Journal of Fluid Mechanics.

[54]  D. Lohse,et al.  Spiraling bubbles: how acoustic and hydrodynamic forces compete. , 2001, Physical review letters.

[55]  R. Bird Dynamics of Polymeric Liquids , 1977 .

[56]  Chris Williams,et al.  Ink-jet printers go beyond paper , 2006 .

[57]  Gérard A. Maugin,et al.  Continuum Mechanics of Electromagnetic Solids , 1989 .

[58]  Breakup and Coalescence of Free Surface Flows , 2005 .

[59]  W. T. Pimbley Drop formation from a liquid jet: a linear one-dimensional analysis considered as a boundary value problem , 1976 .

[60]  Detlef Lohse,et al.  Marangoni flow on an inkjet nozzle plate , 2007 .

[61]  Evert Klaseboer,et al.  A collapsing bubble-induced micro-pump using the jetting effect , 2005 .

[62]  Hermann Seitz,et al.  Modelling of a microfluidic device with piezoelectric actuators , 2004 .

[63]  Osman A. Basaran,et al.  Dynamics and breakup of a contracting liquid filament , 2004, Journal of Fluid Mechanics.

[64]  Charles Vernon Boys,et al.  Soap-bubbles, their colours and the forces which mould them , 1912 .

[65]  D. Lohse,et al.  Giant bubble pinch-off. , 2006, Physical review letters.

[66]  E. Michaelides Hydrodynamic Force and Heat/Mass Transfer From Particles, Bubbles, and Drops—The Freeman Scholar Lecture , 2003 .

[67]  P. Atten,et al.  Experimental investigation of capillary instability: results on jet stimulated by pressure modulations , 1996 .

[68]  James A. Sethian,et al.  A coupled quadrilateral grid level set projection method applied to ink jet simulation , 2005 .

[69]  Johan Frederik Dijksman,et al.  Precision ink jet printing of polymer light emitting displays , 2007 .

[70]  H. Tijdeman On the propagation of sound waves in cylindrical tubes , 1974 .

[71]  J. R. Richards,et al.  Steady laminar flow of liquid–liquid jets at high Reynolds numbers* , 1993 .

[72]  N. de Jong,et al.  Acoustical and optical characterization of air entrapment in piezo-driven inkjet printheads , 2005, IEEE Ultrasonics Symposium, 2005..

[73]  Andrea Prosperetti,et al.  Entrapped air bubbles in piezo-driven inkjet printing: Their effect on the droplet velocity , 2006 .

[74]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

[75]  U. Gösele,et al.  Theory of bimolecular reaction rates limited by anisotropic diffusion , 1976 .

[76]  Andrea Prosperetti,et al.  PHYSALIS: a new method for particle simulation part II: two-dimensional Navier--Stokes flow around cylinders , 2003 .

[77]  F. Lugli,et al.  Atomistic Simulation of Drop-on-Demand Inkjet Dynamics , 2008 .

[78]  Shinri Sakai,et al.  Micro-Piezoelectric Head Technology of Color Inkjet Printer , 2001 .

[79]  Lohse,et al.  Bubble shape oscillations and the onset of sonoluminescence. , 1995, Physical review letters.

[80]  D. Bonn,et al.  Inhibition of the finite-time singularity during droplet fission of a polymeric fluid. , 2001, Physical review letters.

[81]  T. D. Blake,et al.  DYNAMIC WETTING STUDIED BY MOLECULAR MODELING SIMULATIONS OF DROPLET SPREADING , 1999 .

[82]  R Seemann,et al.  Dewetting patterns and molecular forces: a reconciliation. , 2001, Physical review letters.

[83]  M. Brenner,et al.  A Cascade of Structure in a Drop Falling from a Faucet , 1994, Science.

[84]  K. F. Teng,et al.  Mathematical models of ink jet printing in thick-film hybrid microelectronics , 1988 .

[85]  N. Ashgriz,et al.  Nonlinear instability of liquid jets with thermocapillarity , 1995, Journal of Fluid Mechanics.

[86]  Andrei G. Fedorov,et al.  Droplet formation and ejection from a micromachined ultrasonic droplet generator: Visualization and scaling , 2005 .

[87]  B. Auld Wave propagation and resonance in piezoelectric materials , 1981 .

[88]  Martin Hegner,et al.  Rapid functionalization of cantilever array sensors by inkjet printing , 2004 .

[89]  T. Blake,et al.  Dynamic wetting by liquids of different viscosity. , 2002, Journal of colloid and interface science.

[90]  Marios M. Fyrillas,et al.  Dissolution or growth of soluble spherical oscillating bubbles , 1994, Journal of Fluid Mechanics.

[91]  S. Luther,et al.  Viscosity destabilizes sonoluminescing bubbles. , 2006, Physical review letters.

[92]  Herman Wijshoff Free surface flow and acousto-elastic interaction in piezo inkjet , 2004 .

[93]  Ken Kiyono,et al.  Simulation of a Dripping Faucet , 1998, chao-dyn/9811020.

[94]  P.M. Sarro,et al.  Characterization of a Nozzle-Integrated Capacitive Sensor for Microfluidic Jet Systems , 2007, 2007 IEEE Sensors.

[95]  H. Stone,et al.  CAPILLARY BREAKUP OF A VISCOUS THREAD SURROUNDED BY ANOTHER VISCOUS FLUID , 1998 .

[96]  E. Trinh,et al.  Large-amplitude free and driven drop-shape oscillations: experimental observations , 1982, Journal of Fluid Mechanics.

[97]  C. W. Hirt,et al.  A lagrangian method for calculating the dynamics of an incompressible fluid with free surface , 1970 .

[98]  H. Weiser,et al.  The Mechanism of the Dehydration of Zeolites , 1937 .

[99]  S. C. Pope,et al.  The chaotic behavior of the leaky faucet , 1985 .

[100]  A. Prosperetti,et al.  The Effect of Viscosity on the Spherical Stability of Oscillating Gas Bubbles , 1999 .

[101]  C. Poulard,et al.  Spontaneous spreading of nematic liquid crystals. , 2005, Langmuir : the ACS journal of surfaces and colloids.

[102]  C. W. Hirt,et al.  Numerical Simulation of Boiling Water Reactor Vent-Clearing Hydrodynamics , 1980 .

[103]  Yong Zhou Measurement of the Displacement of a Shear Mode Piezoelectric Transducer Using Laser Doppler Vibrometer , 1999 .

[104]  Harvey Thomas Banks,et al.  The modeling of piezoceramic patch interactions with shells, plates, and beams , 1995 .

[105]  Hariprasad J. Subramani,et al.  Dripping-jetting transitions in a dripping faucet. , 2004, Physical review letters.

[106]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[107]  A. Rothert,et al.  Formation of a drop: viscosity dependence of three flow regimes , 2003 .

[108]  Michael R. Moldover,et al.  Gas‐filled spherical resonators: Theory and experiment , 1986 .

[109]  A. Haenlein Über den Zerfall eines Flüssigkeitsstrahles , 1931 .

[110]  R. Plunkett,et al.  Formulas for Stress and Strain , 1965 .

[111]  Abraham M. Lenhoff,et al.  Drop formation in liquid-liquid systems before and after jetting , 1995 .

[112]  J. E. Fromm,et al.  Numerical calculation of the fluid dynamics of drop-on-demand jets , 1984 .

[113]  Kenichi Kugai,et al.  A New Compact High Resolution Solid Ink Print Head and its Application to a Plate Making Printer , 1999 .

[114]  R. Sedev,et al.  The critical condition for transition from steady wetting to film entrainment , 1991 .

[115]  Gerald Recktenwald,et al.  Development of an Improved Model for Piezo-Electric Driven Ink Jets , 2003, NIP & Digital Fabrication Conference.

[116]  Kai-Dietrich Wolf Electromechanical Energy Conversion in asymmetric Piezoelectric Bending Actuators , 2001 .

[117]  R. Furbank,et al.  Drop formation from particulate suspensions , 2004 .

[118]  H. F. Tiersten,et al.  Linear Piezoelectric Plate Vibrations , 1969 .

[119]  Sidney Yip,et al.  Handbook of Materials Modeling , 2005 .

[120]  Arthur C. Wilbur,et al.  Ink Jet Printing , 1987, Photonics West - Lasers and Applications in Science and Engineering.

[121]  Johannes Lyklema,et al.  Fundamentals of Interface and Colloid Science , 1991 .

[122]  John Zeleny,et al.  The Electrical Discharge from Liquid Points, and a Hydrostatic Method of Measuring the Electric Intensity at Their Surfaces , 1914 .

[123]  D. Juric,et al.  A front-tracking method for the computations of multiphase flow , 2001 .

[124]  H. Kato,et al.  A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section , 1992, Journal of Fluid Mechanics.

[125]  T.G.H. Basten,et al.  On the acousto-elastic behaviour of double-wall panels with a viscothermal air layer , 2001 .

[126]  Hiroyuki Kawamoto,et al.  Fundamental investigation on electrostatic ink jet phenomena in pin-to-plate discharge system , 2005 .

[127]  O. Voinov Hydrodynamics of wetting , 1976 .

[128]  J. Womersley Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known , 1955, The Journal of physiology.

[129]  D. Papageorgiou ON THE BREAKUP OF VISCOUS LIQUID THREADS , 1995 .

[130]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[131]  Peter Koltay,et al.  Simulation of a Micro Dispenser Using Lumped Models , 2002 .

[132]  C. H. Hertz,et al.  Intensity modulation of ink-jet oscillographs , 1969, Medical and biological engineering.

[133]  Shi,et al.  Iterated instabilities during droplet fission. , 1994, Physical review letters.

[134]  William P. Robbins,et al.  A Theoretical Examination of Mems Microactuator Responses with an Emphasis on Materials and Fabrication , 1994 .

[135]  Weng-Sing Hwang,et al.  A numerical study of the effect of operating parameters on drop formation in a squeeze mode inkjet device , 2004 .

[136]  Leslie Y. Yeo,et al.  The Dynamics of Marangoni-Driven Local Film Drainage between Two Drops. , 2001, Journal of colloid and interface science.

[137]  Jeffrey F. Morris,et al.  An experimental study of particle effects on drop formation , 2004 .

[138]  M. Gad-el-Hak The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture , 1999 .

[139]  Dominique Legendre,et al.  The lift force on a spherical bubble in a viscous linear shear flow , 1998, Journal of Fluid Mechanics.

[140]  D. Bidwell,et al.  Formation , 2006, Revue Francophone d'Orthoptie.

[141]  E. P. Eernisse,et al.  Design of Resonant Piezoelectric Devices , 1969 .

[142]  Christophe Clanet,et al.  Transition from dripping to jetting , 1999, Journal of Fluid Mechanics.

[143]  Katherine W. Ferrara,et al.  The natural frequency of nonlinear oscillation of ultrasound contrast agents in microvessels. , 2007, Ultrasound in medicine & biology.

[144]  D. A. Dunnett Classical Electrodynamics , 2020, Nature.

[145]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[146]  Farzad Mashayek,et al.  Temporal analysis of capillary jet breakup , 1995, Journal of Fluid Mechanics.

[147]  Osman A. Basaran,et al.  Nonlinear oscillations of viscous liquid drops , 1992, Journal of Fluid Mechanics.

[148]  E. Furlani Temporal instability of viscous liquid microjets with spatially varying surface tension , 2005 .

[149]  Sidney R. Nagel,et al.  Breakdown of scaling in droplet fission at high Reynolds number , 1997 .

[150]  C. P. Germano Flexure Mode Piezoelectric Transducers , 1971 .

[151]  Lawrence A. Crum,et al.  Bjerknes forces on bubbles in a stationary sound field , 1975 .

[152]  Willem Martinus Beltman Viscothermal wave propagation, including acousto‐elastic interaction , 2004 .

[153]  P. Coussot,et al.  Gravity flow instability of viscoplastic materials: the ketchup drip. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[154]  I. P. Ivanov,et al.  Oscillations of an air bubble in an ink jet , 1984 .

[155]  Osman A. Basaran,et al.  Computational analysis of drop-on-demand drop formation , 2007 .

[156]  Brian Derby,et al.  Oscillatory Incompressible Fluid Flow in a Tapered Tube With a Free Surface in an Inkjet Print Head , 2005 .

[157]  P N Scharbach,et al.  A Dynamical Theory of the Electromagnetic Field , 1983 .

[158]  A. Prosperetti,et al.  Bubble Dynamics and Cavitation , 1977 .

[159]  J. F. Dijksman Hydro-Acoustics of Piezoelectrically Driven Ink-Jet Print Heads , 1998 .

[160]  S. N. Prasad,et al.  TWO-PORT ELECTROACOUSTIC MODEL OF A PIEZOELECTRIC COMPOSITE CIRCULAR PLATE , 2002 .

[161]  Andrea Prosperetti,et al.  The thermal behaviour of oscillating gas bubbles , 1991, Journal of Fluid Mechanics.

[162]  B. Noheda,et al.  Bridging phases at the morphotropic boundaries of lead oxide solid solutions , 2005, cond-mat/0511256.

[164]  O. Basaran,et al.  Computational and experimental analysis of pinch-off and scaling. , 2002, Physical review letters.

[165]  John R. Lister,et al.  Coalescence of liquid drops , 1999, Journal of Fluid Mechanics.

[166]  David B. Wallace,et al.  Applicatons of Ink-Jet Printing Technology to BioMEMS and Microfluidic Systems , 2001, MOEMS-MEMS.

[167]  Constantin,et al.  Droplet breakup in a model of the Hele-Shaw cell. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[168]  S. Zaleski,et al.  Modelling Merging and Fragmentation in Multiphase Flows with SURFER , 1994 .

[169]  A. Mccarthy Development , 1996, Current Opinion in Neurobiology.

[170]  Duncan L. MacFarlane,et al.  Microjetted lenslet triplet fibers , 1996 .

[171]  Alvin U. Chen,et al.  A new method for significantly reducing drop radius without reducing nozzle radius in drop-on-demand drop production , 2002 .

[172]  李幼升,et al.  Ph , 1989 .

[173]  J. Toennies,et al.  Cryogenic microjet source for orthotropic beams of ultralarge superfluid helium droplets. , 2003, Physical review letters.

[174]  P.J.M. van der Hoogt,et al.  Air loads on a rigid plate oscillating normal to a fixed surface , 1997 .

[175]  K. Uchino,et al.  “Monomorph Actuators” Using Semiconductive Ferroelectrics , 1987 .

[176]  Delia Radulescu,et al.  3 D Printing of Biological Materials for Drug Delivery and Tissue Engineering Applications , 2005 .

[177]  Herman Wijshoff,et al.  Structure- and fluid-dynamics in piezo inkjet printheads , 2008 .

[178]  S. Quake,et al.  Microfluidics: Fluid physics at the nanoliter scale , 2005 .

[179]  Herman Wijshoff Better printheads via simulation : flow-3D helped double the print speed of a new wide-format printer without sacrificing quality , 2007 .

[180]  J. Eggers,et al.  Universal pinching of 3D axisymmetric free-surface flow. , 1993, Physical review letters.

[181]  T. Dupont,et al.  Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation , 1992, physics/0110081.

[182]  Wallace W. Carr,et al.  Visualization of drop-on-demand inkjet: Drop formation and deposition , 2006 .

[183]  M. Sussman,et al.  A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows , 2000 .

[184]  J. Keller,et al.  Surface Tension Driven Flows , 1983 .

[185]  Aa Anton Darhuber,et al.  Thermocapillary actuation of liquid flow on chemically patterned surfaces , 2003 .

[186]  P. N. Whitton,et al.  The damping of structural vibration by thin gas films , 1980 .

[187]  James Lighthill,et al.  Waves In Fluids , 1966 .

[188]  S. Bankoff,et al.  Long-scale evolution of thin liquid films , 1997 .

[189]  George Keith Batchelor,et al.  An Introduction to Fluid Dynamics. , 1969 .

[190]  E. Charlaix,et al.  Boundary slip on smooth hydrophobic surfaces: intrinsic effects and possible artifacts. , 2005, Physical review letters.

[191]  Donald J. Hayes,et al.  Microjet printing of high-precision microlens array for packaging of fiber optic components , 2002, SPIE OPTO.

[192]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[193]  J. Sethian Evolution, implementation, and application of level set and fast marching methods for advancing fronts , 2001 .

[194]  Howard A. Stone,et al.  Drop formation in viscous flows at a vertical capillary tube , 1997 .

[195]  H. Bauer Free Liquid Surface Response Induced by Fluctuations of Thermal Marangoni Convection , 1984 .

[196]  H. C. Lee Drop formation in a liquid jet , 1974 .

[197]  T. Veijola,et al.  Compact damping models for laterally moving microstructures with gas-rarefaction effects , 2001 .

[198]  Geoffrey Ingram Taylor,et al.  Disintegration of water drops in an electric field , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[199]  R. S. Dhariwal,et al.  Electric field breakdown at micrometre separations in air and vacuum , 1999 .

[200]  H. C. Lee Boundary layer around a liquid jet , 1977 .

[201]  Oliver E. Jensen,et al.  Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture , 1992, Journal of Fluid Mechanics.

[202]  Zhang Dynamics of Growth and Breakup of Viscous Pendant Drops into Air. , 1999, Journal of colloid and interface science.

[203]  Michael P Brenner,et al.  The optimal faucet. , 2004, Physical review letters.

[204]  L. Rayleigh,et al.  Some Applications of Photography , 1891, Nature.

[205]  S. Zaleski,et al.  DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW , 1999 .

[206]  T. Leighton The Acoustic Bubble , 1994 .

[207]  Thomas Podgorski,et al.  Corners, cusps, and pearls in running drops. , 2001, Physical review letters.

[208]  Michael D. Barnes,et al.  SINGLE-MOLECULE ANALYSIS OF ULTRADILUTE SOLUTIONS WITH GUIDED STREAMS OF 1-MU M WATER DROPLETS , 1999 .

[209]  Qi Xu,et al.  Simplicity and complexity in a dripping faucet , 2005 .

[210]  T. A. KowalewskiCenter On the separation of droplets from a liquid jet , 1996 .

[211]  Jianying Cui,et al.  Bubble pulsations between parallel plates. , 2006, The Journal of the Acoustical Society of America.

[212]  J. W. Woods,et al.  Application of ink jet technology to a word processing output printer , 1977 .

[213]  Robert D. Carnahan,et al.  Ink Jet Technology , 1977, IEEE Transactions on Industry Applications.

[214]  Nagano Shiojiri,et al.  Ink Jet Head with Multi-Layer Piezoelectric Actuator , 1998 .

[215]  Frank E. Talke,et al.  Experimental and theoretical study of wave propagation phenomena in drop-on-demand ink jet devices , 1984 .

[216]  James L. Winkler,et al.  Accessing Genetic Information with High-Density DNA Arrays , 1996, Science.

[217]  Ilhan A. Aksay,et al.  Electromechanical Behavior of PZT-Brass Unimorphs , 1999 .

[218]  C. Weber Zum Zerfall eines Flüssigkeitsstrahles , 1931 .

[219]  William L. Grosshandler,et al.  A simple piezoelectric droplet generator , 1997 .

[220]  C. W. Hirt,et al.  An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , 1997 .

[221]  R. Shinnar,et al.  Breakup of a laminar capillary jet of a viscoelastic fluid , 1969, Journal of Fluid Mechanics.

[222]  Joachim Kretschmer,et al.  Design Parameters of a Shear Mode Piezo Printhead for a Given Resolution , 1999 .

[223]  P. Hofstaetter [Similarity]. , 2020, Psyche.

[224]  Joseph B. Keller,et al.  Slender jets and thin sheets with surface tension , 1990 .

[225]  Takaaki Tsurumi,et al.  Analysis of Bending Displacement of Lead Zirconate Titanate Thin Film Synthesized by Hydrothermal Method , 1993 .

[226]  David P. Trauernicht,et al.  Surface tension induced instability of viscous liquid jets , 2001 .

[227]  S. Heister,et al.  Droplet size control in liquid jet breakup , 1996 .

[228]  Kenji Uchino,et al.  Recent topics of ceramic actuators how to develop new ceramic devices , 1989 .

[229]  Brian Derby,et al.  Oscillatory limited compressible fluid flow induced by the radial motion of a thick-walled piezoelectric tube. , 2003, The Journal of the Acoustical Society of America.

[230]  Aa Anton Darhuber,et al.  PRINCIPLES OF MICROFLUIDIC ACTUATION BY MODULATION OF SURFACE STRESSES , 2005 .

[231]  Göran Stemme,et al.  A valve-less planar fluid pump with two pump chambers , 1995 .

[232]  T. Howes,et al.  Capillary jet instability under the influence of gravity , 2004 .

[233]  Patrick K. Notz,et al.  Satellite drops: Unexpected dynamics and change of scaling during pinch-off , 2001 .

[234]  I. Hutchings,et al.  Inkjet printing - the physics of manipulating liquid jets and drops , 2008 .

[235]  W. M. Beltman Viscothermal wave propagation including acousto-elastic interaction, part II: applications , 1999 .

[236]  Frank E. Talke,et al.  Axisymmetric Motion of Radially Polarized Piezoelectric Cylinder Used in Ink Jet Printing , 1983, IBM J. Res. Dev..

[237]  J. Eggers,et al.  Comment on "Dynamic wetting by liquids of different viscosity," by T.D. Blake and Y.D. Shikhmurzaev. , 2003, Journal of colloid and interface science.

[238]  Jens Eggers Singularities in Droplet Pinching with Vanishing Viscosity , 2000, SIAM J. Appl. Math..

[239]  W. B. Tucker,et al.  Studies in Drop Formation as Revealed by the High-speed Motion Camera , 1937 .

[240]  O. Reynolds I. On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil , 1886, Proceedings of the Royal Society of London.

[241]  Herman Wijshoff,et al.  Modeling the drop formation process in inkjet printheads , 2007 .

[242]  David B. Wallace,et al.  Acoustic phenomena in a demand mode piezoelectric ink jet printer , 2002 .

[243]  P. Gennes,et al.  Capillarity and Wetting Phenomena , 2004 .

[244]  L. Scriven,et al.  Hydrodynamic Model of Steady Movement of a Solid / Liquid / Fluid Contact Line , 1971 .

[245]  S. Kawano Molecular dynamics of rupture phenomena in a liquid thread , 1998 .

[246]  D. Peregrine,et al.  The bifurcation of liquid bridges , 1990, Journal of Fluid Mechanics.

[247]  Marieke Henriette Cathrien Hannink,et al.  Acoustic resonators for the reduction of sound radiation and transmission , 2007 .

[248]  J. Li,et al.  Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method , 2000 .

[249]  H. C. Lee,et al.  Satellite droplet formation in a liquid jet , 1977 .

[250]  P D Mininni,et al.  Small-scale structures in three-dimensional magnetohydrodynamic turbulence. , 2006, Physical review letters.

[251]  Stephen H. Davis,et al.  Nonlinear theory of film rupture , 1982 .

[252]  P. Marmottant,et al.  Controlled vesicle deformation and lysis by single oscillating bubbles , 2003, Nature.

[253]  C. Menzel,et al.  MEMS Solutions for Precision MicroFluidic Dispensing Application , 2004 .

[254]  K. Hynynen,et al.  Forced linear oscillations of microbubbles in blood capillaries. , 2004, The Journal of the Acoustical Society of America.

[255]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[256]  P. Lenard Ueber die Schwingungen fallender Tropfen , 1887 .

[257]  Reiter,et al.  Dewetting of thin polymer films. , 1992, Physical review letters.

[258]  Joachim Kretschmer,et al.  Function and Performance of a Shear Mode Piezo Printhead , 1999 .

[259]  Scott D. Phillips,et al.  Computational and experimental analysis of dynamics of drop formation , 1999 .

[260]  Paul A Dayton,et al.  Direct observations of ultrasound microbubble contrast agent interaction with the microvessel wall. , 2007, The Journal of the Acoustical Society of America.

[261]  J. Rosell-Llompart,et al.  Generation of submicron monodisperse aerosols in electrosprays , 1990 .

[262]  R. Lipowsky,et al.  Contact Angles on Heterogeneous Surfaces: A New Look at Cassie's and Wenzel's Laws , 1998, cond-mat/9809089.

[263]  L. E. Cross,et al.  Tetragonal-to-monoclinic phase transition in a ferroelectric perovskite : The structure of PbZr0.52Ti0.48O3 , 2000 .

[264]  Herman Wijshoff,et al.  Flows on the nozzle plate of an inkjet printhead , 2007 .

[265]  D. Legendre,et al.  Some Aspects of the Lift Force on a Spherical Bubble , 1998 .

[266]  Pomeau,et al.  Disjoining potential and spreading of thin liquid layers in the diffuse-interface model coupled to hydrodynamics , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[267]  S. Herminghaus,et al.  Thin liquid polymer films rupture via defects , 1998 .

[268]  Diane M. Henderson,et al.  On the pinch-off of a pendant drop of viscous fluid , 1997 .

[269]  W. Hardy,et al.  III. The spreading of fluids on glass , 1919 .

[270]  Ashutosh Sharma,et al.  Instability of thin polymer films on coated substrates : Rupture, dewetting, and drop formation , 1996 .

[271]  D. Weaire,et al.  The optimal tap: three-dimensional nozzle design , 2005 .

[272]  I. Eames,et al.  The Motion of High-Reynolds-Number Bubbles in Inhomogeneous Flows , 2000 .

[273]  Jens Eggers Dynamics of liquid nanojets. , 2002, Physical review letters.

[274]  G. Stemme,et al.  A valveless diffuser/nozzle-based fluid pump , 1993 .

[275]  Drop formation instabilities induced by entrapped gas bubbles , 1990 .

[276]  A. Prosperetti,et al.  Physalis: a new o(N) method for the numerical simulation of disperse systems: potential flow of spheres , 2001 .

[277]  Howard Brenner,et al.  Droplets Speeding on Surfaces , 2001, Science.

[278]  Daniel Bonn,et al.  Controlling droplet deposition with polymer additives , 2000, Nature.

[279]  S. Sakai,et al.  Dynamics of Piezoelectric Inkjet Printing Systems. , 2000 .

[280]  John R. Blake,et al.  Collapsing cavities, toroidal bubbles and jet impact , 1997, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[281]  Sharma,et al.  Instability and morphology of thin liquid films on chemically heterogeneous substrates , 2000, Physical review letters.

[282]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[283]  Norman Chigier,et al.  Breakup of liquid sheets and jets , 1999 .

[284]  P. G. de Gennes,et al.  A model for contact angle hysteresis , 1984 .

[285]  Evert Klaseboer,et al.  A collapsing bubble-induced micropump: An experimental study , 2007 .

[286]  Eiji Ando,et al.  Direct matrix-assisted laser desorption/ionization time-of-flight mass spectrometric identification of proteins on membrane detected by Western blotting and lectin blotting. , 2005, Journal of proteome research.

[287]  A Combined Experimental and Computational Fluid Dynamics Analysis of the Dynamics of Drop Formation , 2005 .

[288]  J. Perelaer Microstructures Prepared via Inkjet Printing and Embossing Techniques , 2005 .

[289]  Omar Matar,et al.  Nonlinear evolution of thin free viscous films in the presence of soluble surfactant , 2002 .

[290]  Katherine W Ferrara,et al.  Acoustic response of compliable microvessels containing ultrasound contrast agents , 2006, Physics in medicine and biology.

[291]  J. Guzmán,et al.  HYDRODYNAMICS OF LAMINAR LIQUID JETS. EXPERIMENTAL STUDY AND COMPARISON WITH TWO MODELS , 1987 .

[292]  E. Villermaux,et al.  Physics of liquid jets , 2008 .

[293]  David A. Tence,et al.  Ink Manifold Design of Phase Change Piezoelectric Ink Jets , 1999 .

[294]  Goldstein,et al.  Topology transitions and singularities in viscous flows. , 1993, Physical review letters.

[295]  Howard A. Stone,et al.  Dynamics of Drop Deformation and Breakup in Viscous Fluids , 1994 .

[296]  Detlef Lohse,et al.  Predictions for upscaling sonoluminescence , 1998 .

[297]  P. Zhong,et al.  Dynamics of bubble oscillation in constrained media and mechanisms of vessel rupture in SWL. , 2001, Ultrasound in medicine & biology.

[298]  P. Steen,et al.  Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge , 1997, Journal of Fluid Mechanics.

[299]  J. Pelesko,et al.  Modeling MEMS and NEMS , 2002 .

[300]  Balasubramaniam Ramaswamy,et al.  Numerical simulation of unsteady viscous free surface flow , 1990 .

[301]  Andrea Prosperetti,et al.  The ‘acoustic scallop’: a bubble-powered actuator , 2006 .

[302]  Kevin L. Moore,et al.  Iterative Learning Control: An Expository Overview , 1999 .

[303]  N. Yoshioka,et al.  Steady laminar round jets of a viscous liquid falling vertically in the atmosphere , 1990 .

[304]  Nikolaus Rott,et al.  Damped and thermally driven acoustic oscillations in wide and narrow tubes , 1969 .

[305]  Steve B. Brown,et al.  Fabricating optical fiber imaging sensors using ink jet printing technology: a pH sensor proof-of-concept. , 2006, Biosensors & bioelectronics.

[306]  O. Basaran,et al.  Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops , 2002 .

[307]  Eli Ruckenstein,et al.  Spontaneous rupture of thin liquid films , 1974 .

[308]  J. Eggers Nonlinear dynamics and breakup of free-surface flows , 1997 .

[309]  Richard W. Longman,et al.  Iterative learning control and repetitive control for engineering practice , 2000 .

[310]  H. Tillema,et al.  Noise reduction of rotating machinery by viscoelastic bearing supports. , 2003 .

[311]  Michel Bruneau,et al.  Heat Conduction Effects on the Acoustic Response of a Membrane Separated by a Very Thin Air Film from a Backing Electode , 1990 .

[312]  Peter Koltay,et al.  Modelling Free Jet Ejection on a System Level – An approach for microfluidics , 2002 .

[313]  A. Alteraifi,et al.  Spreading of liquid drops over solid substrates: 'like wets like' , 2006 .

[314]  J. Strutt Scientific Papers: On the Instability of a Cylinder of Viscous Liquid under Capillary Force , 2009 .

[315]  Alberto Piqué,et al.  Direct-write technologies for rapid prototyping applications : sensors, electronics and integrated power sources , 2002 .

[316]  J. Brünahl,et al.  Physics of piezoelectric shear mode inkjet actuators , 2003 .

[317]  T. D. Blake,et al.  A maximum speed of wetting , 1979, Nature.

[318]  John William Strutt,et al.  Scientific Papers: On the Instability of Cylindrical Fluid Surfaces , 2009 .

[319]  Detlef Lohse,et al.  Air entrapment in piezo-driven inkjet printheads , 2006 .

[320]  G. I. Barenblatt,et al.  Similarity, Self-Similarity and Intermediate Asymptotics , 1979 .

[321]  Neelesh A. Patankar,et al.  On the Modeling of Hydrophobic Contact Angles on Rough Surfaces , 2003 .

[322]  John R. Lister,et al.  SELF-SIMILAR CAPILLARY PINCHOFF OF AN INVISCID FLUID , 1997 .

[323]  D. Lohse,et al.  Phase diagrams for sonoluminescing bubbles: A comparison between experiment and theory , 2003 .

[324]  U. Schubert,et al.  Inkjet Printing of Polymers: State of the Art and Future Developments , 2004 .

[325]  Harold E. Edgerton,et al.  The Application of the High-speed Motion Picture Camera to Research on the Surface Tension of Liquids. , 1935 .

[326]  Horng-Show Koo,et al.  LCD-based color filter films fabricated by a pigment-based colorant photo resist inks and printing technology , 2006 .

[327]  M. Renardy,et al.  PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method , 2002 .

[328]  Oliver E. Jensen,et al.  The spreading of heat or soluble surfactant along a thin liquid film , 1993 .

[329]  R. G. Sweet High Frequency Recording with Electrostatically Deflected Ink Jets , 1965 .

[330]  Christian Rembe,et al.  Nonreproducible phenomena in thermal ink jets with real high-speed cine photomicrography , 1998, Other Conferences.

[331]  Diane M. Henderson,et al.  The motion of a falling liquid filament , 2000 .

[332]  J. Yeomans,et al.  Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[333]  David A. Tence,et al.  Multiple Dot Size Fluidics for Phase Change Piezoelectric Ink Jets , 1999 .

[334]  Free Vibration Analysis Of Rectangular Plates With Structural Inhomogeneity , 1993 .

[335]  Timothy G. Leighton,et al.  Primary Bjerknes forces , 1990 .

[336]  Andrea Prosperetti,et al.  Growth and collapse of a vapor bubble in a narrow tube , 2000 .

[337]  N. P. Hine Deaeration systel for a high-performance drop-on-demand ink jet , 1991 .

[338]  J. Eggers,et al.  Inviscid coalescence of drops , 2002, Journal of Fluid Mechanics.

[339]  O. Basaran,et al.  Deformation and breakup of stretching bridges of Newtonian and shear-thinning liquids: comparison of one- and two-dimensional models , 2001 .

[340]  M. Möbius Clustering instability in a freely falling granular jet. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[341]  R. Schulkes,et al.  The evolution and bifurcation of a pendant drop , 1994, Journal of Fluid Mechanics.

[342]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[343]  M. Fermigier,et al.  Avoided critical behavior in dynamically forced wetting. , 2006, Physical review letters.

[344]  U. Landman,et al.  Formation, stability, and breakup of nanojets , 2000, Science.

[345]  Kenji Uchino,et al.  Piezoelectric Actuators and Ultrasonic Motors , 1996 .

[346]  H. Reiss Methods of thermodynamics , 1965 .

[347]  Andrea Prosperetti,et al.  The oscillation of gas bubbles in tubes: Experimental results , 1999 .

[348]  A two-port model for wave propagation along a long circular microchannel , 2007 .

[349]  Thomas Young,et al.  An Essay on the Cohesion of Fluids , 1800 .

[350]  Timothy G. Leighton,et al.  Acoustic detection of gas bubbles in a pipe , 1998 .

[351]  R. Ritter Analysis of drop intervals in jets modelling obstruction of the urinary tract. , 1974, Physics in medicine and biology.

[352]  L. Rayleigh On The Instability Of Jets , 1878 .

[353]  S. Middleman,et al.  Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops , 1995 .

[354]  Roeland Papen,et al.  Nanolitre dispensing — a new innovation in robotic liquid handling , 1998 .

[355]  Victor Starov,et al.  Spreading of liquid drops over dry surfaces , 1994 .

[356]  M. Yuen,et al.  Experiments on liquid jet instability , 1970, Journal of Fluid Mechanics.

[357]  Detlef Lohse,et al.  Effect of an entrained air bubble on the acoustics of an ink channel. , 2008, The Journal of the Acoustical Society of America.

[358]  Mohamed Haddar,et al.  Simulation of Viscothermal Losses on the Acoustic Behaviour of a Thin Fluid Layer Enclosed between Two Oscillating Plates , 2006 .

[359]  Andrea Prosperetti,et al.  Nonlinear bubble dynamics , 1988 .

[360]  A. Cazabat,et al.  Dynamics of wetting: Effects of surface roughness. , 1986 .

[361]  Donald J. Hayes,et al.  Direct Write Using Ink-Jet Techniques , 2002 .

[362]  M. T. Plateau XXXVII. On the recent theories of the constitution of jets of liquid issuing from circular orifices , 1856 .

[363]  G. Jameson,et al.  Theoretical prediction of the sizes of drops formed in the breakup of capillary jets , 1970 .

[364]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[365]  Rev. T. Drummond LXIII. On planetary influences on the atmosphere , 1816 .

[366]  Eliav I. Haskal,et al.  21.1: Ink Jet Printing of Passive‐Matrix Polymer Light Emitting Displays , 2002 .

[367]  B Ambravaneswaran,et al.  Theoretical analysis of a dripping faucet. , 2000, Physical review letters.

[368]  Xiaoguang Zhang,et al.  An experimental study of dynamics of drop formation , 1995 .

[369]  Hydrodynamical models for the chaotic dripping faucet , 2004, Journal of Fluid Mechanics.

[370]  Scaling of Piezoelectric Drop-on-Demand Jets for High Resolution Applications , 1999 .

[371]  P. Simpkins,et al.  On air entrainment in coatings. , 2003, Journal of colloid and interface science.

[372]  A. Kalaaji,et al.  Breakup length of forced liquid jets , 2003 .

[373]  Detlef Lohse,et al.  Acoustic measurement of bubble size in an inkjet printhead. , 2009, The Journal of the Acoustical Society of America.

[374]  A. Bailey,et al.  ELECTROSTATIC SPRAYING OF LIQUIDS , 1988 .

[375]  S. Dietrich,et al.  Motion of nanodroplets near chemical heterogeneities. , 2007, Langmuir : the ACS journal of surfaces and colloids.

[376]  Lloyd M Smith,et al.  Single-pulse nanoelectrospray ionization. , 2002, Analytical chemistry.

[377]  M. Yuen Non-linear capillary instability of a liquid jet , 1968, Journal of Fluid Mechanics.

[378]  James Q. Feng A General Fluid Dynamic Analysis of Drop Ejection in Drop-on-Demand Ink Jet Devices , 2002 .

[379]  J. de Jong Air entrapment in piezo inkjet printing , 2007 .

[380]  C. Meinhart,et al.  The flow structure inside a microfabricated inkjet printhead , 2000, Journal of Microelectromechanical Systems.

[381]  Plateau instability of a liquid crystalline cylinder in a magnetic field. , 2004, Journal of colloid and interface science.

[382]  A. Rothert,et al.  Transition from symmetric to asymmetric scaling function before drop pinch-off. , 2001, Physical review letters.

[383]  Andrea Prosperetti,et al.  The natural frequency of oscillation of gas bubbles in tubes , 1998 .

[384]  H. Le,et al.  Progress and Trends in Ink-jet Printing Technology , 1998, Journal of Imaging Science and Technology.

[385]  S. Troian,et al.  Dynamics of capillary spreading along hydrophilic microstripes. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[386]  Philip H. Gaskell,et al.  Flow Structure and Transfer Jets in a Contra-Rotating Rigid-Roll Coating System , 2004 .

[387]  Anca Badea,et al.  Optimization of a multinozzle ink-jet printer , 2001 .

[388]  Thomas Geertruida Henricus Basten,et al.  Noise reduction by viscothermal acousto-elastic interaction in double wall panels , 2001 .

[389]  Howard A. Stone,et al.  An experimental study of transient effects in the breakup of viscous drops , 1986, Journal of Fluid Mechanics.

[390]  Dominique Legendre,et al.  The viscous drag force on a spherical bubble with a time-dependent radius , 1998 .

[391]  T. Blake,et al.  Response to the comment on [J. Colloid Interface Sci. 253 (2002) 196] by J. Eggers and R. Evans , 2004 .

[392]  M. Cloupeau,et al.  Electrostatic spraying of liquids in cone-jet mode , 1989 .

[393]  Mary C. Pugh,et al.  SINGULARITY FORMATION IN THIN JETS WITH SURFACE TENSION , 1998 .

[394]  Joseph B. Keller,et al.  Spatial instability of a jet , 1973 .

[395]  Andrea Prosperetti,et al.  Thermal processes in the oscillations of gas bubbles in tubes , 1998 .

[396]  Wolfgang V. Ohnesorge,et al.  Die Bildung von Tropfen an Düsen und die Auflösung flüssiger Strahlen , 1936 .

[397]  Geoffrey Ingram Taylor,et al.  The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[398]  M. Brenner,et al.  Pinching threads, singularities and the number 0.0304... , 1996 .

[399]  D. Michael,et al.  The equilibrium and stability of axisymmetric pendent drops , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[400]  L. E. Cross,et al.  The monoclinic phase in PZT: new light on morphotropic phase boundaries , 2000 .

[401]  Michel Bruneau,et al.  General formulation of the dispersion equation in bounded visco-thermal fluid, and application to some simple geometries , 1989 .

[402]  J. Plateau,et al.  Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires , 1873 .

[403]  A. Ballato,et al.  Piezoelectricity: old effect, new thrusts , 1995, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[404]  J. Lowengrub,et al.  Quasi–incompressible Cahn–Hilliard fluids and topological transitions , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[405]  F. J. García,et al.  Comment on “Breakup length of forced liquid jets” [Phys. Fluids 15, 2469 (2003)] , 2006 .

[406]  P. Gennes Wetting: statics and dynamics , 1985 .

[407]  T. Tate Esq.,et al.  XXX. On the magnitude of a drop of liquid formed under different circumstances , 1864 .

[408]  Xiaoguang Zhang,et al.  Dynamics of drop formation in viscous flows , 1999 .

[409]  Guo,et al.  Origin of the high piezoelectric response in PbZr1-xTixO3 , 1999, Physical review letters.

[410]  Timo Veijola,et al.  Compact models for squeezed-film dampers with inertial and rarefied gas effects , 2004 .

[411]  Robbins,et al.  Simulations of contact-line motion: Slip and the dynamic contact angle. , 1989, Physical review letters.

[412]  E. Kimmel,et al.  Gas bubble pulsation in a semiconfined space subjected to ultrasound. , 2001, The Journal of the Acoustical Society of America.

[413]  K. F. Teng A mathematical model of impulse jet mechanism , 1988 .

[414]  I. Milosevic,et al.  Pinch-off modes and satellite formation in liquid/liquid jet systems , 2002 .

[415]  A. F. Ulitko Theory of electromechanical energy conversion in nonuniformly deformable piezoceramics , 1977 .

[416]  C. Hendricks,et al.  Source of Uniform-Sized Liquid Droplets , 1964 .

[417]  Andrea Prosperetti,et al.  Modelling of spherical gas bubble oscillations and sonoluminescence , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[418]  F. T. Trouton,et al.  On the coefficient of viscous traction and its relation to that of viscosity , 1906 .

[419]  T. Maxworthy,et al.  The nonlinear capillary instability of a liquid jet. Part 3. Experiments on satellite drop formation and control , 1980, Journal of Fluid Mechanics.

[420]  D. C. Emmony,et al.  The role of ‘splashing’ in the collapse of a laser-generated cavity near a rigid boundary , 1999, Journal of Fluid Mechanics.

[421]  Werner Zapka,et al.  Application of inkjet technology for the deposition of magnetic nanoparticles to form micron-scale structures , 2003 .

[422]  Uwe Thiele,et al.  Wetting of textured surfaces , 2002 .

[423]  Ingo Reinhold,et al.  Inkjet printing of phase-change materials with Xaar1001 printheads , 2010 .

[424]  L. E. Cross,et al.  Performance analysis of piezoelectric cantilever bending actuators , 1998 .

[425]  R. Schulkes,et al.  The contraction of liquid filaments , 1996, Journal of Fluid Mechanics.

[426]  D. Bogy Drop Formation in a Circular Liquid Jet , 1979 .

[427]  Franklin T. Dodge,et al.  The spreading of liquid droplets on solid surfaces , 1988 .

[428]  Ole Sigmund,et al.  Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads , 2009 .

[429]  James B. Mehl,et al.  Acoustic resonance frequencies of deformed spherical resonators. II , 1982 .

[430]  Brian Derby,et al.  Numerical and experimental comparisons of mass transport rate in a piezoelectric drop-on-demand inkjet print head , 2004 .

[431]  Eiji Ando,et al.  Direct MS/MS analysis of proteins blotted on membranes by a matrix-assisted laser desorption/ionization-quadrupole ion trap-time-of-flight tandem mass spectrometer. , 2005, Journal of proteome research.

[432]  N. Ashgriz,et al.  Coalescence and separation in binary collisions of liquid drops , 1990, Journal of Fluid Mechanics.

[433]  F. Heslot,et al.  Molecular layering in the spreading of wetting liquid drops , 1989, Nature.

[434]  Wijshoff H.M.A.,et al.  Drop formation mechanisms in piezo-acoustic inkjet , 2007 .

[435]  F. Wagner,et al.  New technique for high-speed microjet breakup analysis , 2003 .

[436]  F. J. Kamphoefner Ink jet printing , 1972 .

[437]  Asimina Sierou,et al.  Self-similar recoil of inviscid drops , 2004 .