Design of Piezo Inkjet Print Heads

From Acoustics to Applications
 
 
Wiley-VCH (Verlag)
  • 1. Auflage
  • |
  • erschienen am 15. Oktober 2018
  • |
  • XXII, 430 Seiten
 
E-Book | ePUB mit Adobe-DRM | Systemvoraussetzungen
978-3-527-80696-6 (ISBN)
 
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.
1. Auflage
  • Englisch
  • Newark
  • |
  • Großbritannien
  • Reflowable
  • 20
  • |
  • 150 s/w Abbildungen, 20 farbige Abbildungen
  • 30,40 MB
978-3-527-80696-6 (9783527806966)
weitere Ausgaben werden ermittelt
J. Frits Dijksman 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.
INTRODUCTION

SINGLE, TWO, THREE AND FIVE DEGREES OF FREEDOM
Effect of Nozzle Shape
Schematic of Fluidic and Acoustic System
Surface Tension, Viscosity and Compressibility, Frequency Dependent Damping
Piezo Theory
Rayleigh's Method
Pulse Shape Definition
Non-Linear Effects
Fluidic Cross-Talk
Examples

LONG WAVE GUIDE THEORY SINGLE & MULTI NOZZLE PRINT HEAD
Wave Speed
Governing Equations
Solution Strategies
Damping
Complex Pulse Shapes, Multi Pulsing
Examples

DROPLET FORMATION
Energy Consideration
Influence of Meniscus Position on Droplet Speed and Size
Influence of Droplet Formation on Dynamics of Fluid Motion
Cooling of Free Flying Droplet
Jetting of Viscoelastic Inks
Examples

REFILLING
Surface Tension Driven Refilling
Inertia Effects
Start-up Effects
Multi Pulsing & Gray Scaling
Examples

IMPACTING DROPLETS
Viscosity and Surface Tension Dominated Spreading
Inertia Dominated Spreading
Splashing
Examples

PERMEATION AND DRYING
Washburn Theory
Drying of Liquid Droplets
Examples

CONCLUSIONS AND OUTLOOK

List of Symbols


Geometric Data


V, R
volume and radius droplet
Rthd, Rt, L
radius tail head droplet, radius tail, and length tail
Rj
radius jet
Rm
radius of curvature of meniscus
R1, L1, A1, P1
radius, length, cross section, and perimeter nozzle
R2, L2, A2
radius, length, and cross section throttle
R3, L3
radius and length of hose pillar
Lsupply, Bsupply,
length, width, cross section, and volume main supply channel
Asupply, Vsupply
Lpitch
pitch at which pumps are integrated in multi-nozzle print head
n
number of pumps integrated in multi-nozzle print head
k
number of activated pumps
Vc
volume pump chamber
L, A
length and cross section pump chamber
H, W
cross-sectional dimensions rectangular channel
Rcd1, Lcd1, Acd1
radius, length, and cross section of connecting duct between throttle and pump section of pump chamber
Rcd2, Lcd2, Acd2
radius, length, and cross section of connecting duct between pump section of pump chamber and nozzle
Rpc, Lpc, Apc
radius, length, and cross section of pump section of pump chamber
z
co-ordinate measuring distance from throttle in pump chamber
Rmean
mean radius thin walled cylinder
h
wall thickness cylinder, height of dome of fluid
b
outer radius thick walled cylinder
?0
half opening angle conical entrance region, half opening angle conical nozzle
Linertia, Lviscous
equivalent lengths defined to compare the inertia and viscous effects in non-cylindrical nozzles to cylindrical nozzles (used for conical and bell-mouth nozzles)

Material Data


µ, ?, ?0, ?
viscosity, density, density at ambient conditions, and surface tension of ink
K
bulk viscosity
KB
bulk modulus
c
general reference to the speed of sound (wave speed, also referred to as isentropic speed of sound)
E, ?
Young's (elastic) modulus and Poisson's ratio
d33
piezo property relating applied voltage to displacement
er
relative permittivity
e0
permittivity of free space

Symbols Related to Kinematics


v
velocity droplet
vj
jet velocity (function of z, the co-ordinate measuring distance along the jet starting at the nozzle)
vmax, ?0
maximum velocity in nozzle and radian frequency of motion of fluid in nozzle
Q
volume rate of flow
?V0
volume displacement actuator
?Vc, ?Vs 
volume displacements actuator following cos ?t and sin ?t, respectively
?Vsupply, ?Vci,
volume displacement in main supply channel, activated and
?Vcj
non-activated pumps
w
radial displacement wall thin walled cylinder
x1, x2
mean fluid displacement in nozzle and throttle
xM
static mean meniscus position with respect to rim nozzle due to suction pressure setting
?
dimensionless fluid displacement in nozzle
mean velocity of fluid in nozzle and throttle
mean acceleration of fluid in nozzle and throttle
x1i, x2i
fluid displacements in nozzles and throttles of activated nozzles (counted by index i)
y1j, y2j
fluid displacements in nozzles and throttles of non-activated pumps (counted by the index j, always it holds that i?+?j?=?n, n being the number of pumps integrated in the print head)
x3
mean fluid displacement through hose pillar
scd1, spc, scd2
mean fluid displacement in connecting ducts and pump section (functions of z)
vcd1, vpc, vcd2
mean fluid velocity in connecting ducts and pump section (functions of z)
ss, s1s, s2s
local displacements in supply channel
vs, v1s, v2s
local velocities in supply channel

Symbols Related to Dynamics


M, K, C, F0
mass, damping, stiffness and load of single degree of freedom mass-spring-damper system
M1, K1, C11, C12,
mass, damping and stiffness coefficients of a two degrees of
M2, K2, C21, C22
freedom mass-spring-damper system
M3, K3, C33,
additional mass, damping and stiffness coefficients for a five
C23, C32
degrees of freedom mass-spring-damper arrangement
c*
speed of sound (wave speed) corrected for compliance structure
cbubble
local wave speed corrected for the presence of a bubble
ccd1, cpc, ccd2
local values of the speed of sound (connecting ducts and pump section)
pc, psupply
gauge pressure in pump chamber and gauge pressure in main supply channel
pcd1, ppc, pccd2
local gauge pressures in connecting channels and pump section
psupply, pci, pcj
gauge pressure in main supply channel, activated pumps and non-activated pumps
pcap, i, pcap, j
capillary pressures in activated and non-activated pumps
pnozzle
pressure at nozzle rim cross-section needed to push forward fluid of droplet
dimensionless capillary pressure
ßnozzle, ßthrottle
dimensionless pressure gradient factor
F
force
I
rotational moment of inertia
r1, r2
outer radius and inner radius of oscillating half cylinder
?
constant needed to define meniscus motion with conservation of volume
meniscus position after release of droplet
e
added mass factor

Evaporation, Droplet Temperature, Air Drag and Spreading Calculations


xA, xA0, xA8
mole fraction, mole fraction at surface droplet, mole fraction at infinity of species A
c, cA
molar density, molar density of species A
MA
molar mass
P
partial pressure
R
gas constant
T
absolute temperature
WA0
number of moles transported through surface area droplet
kxm
mass transfer coefficient
DAB
diffusion coefficient
TcA, pcA, TcB,
constants of Slattery-Bird formula to calculate diffusion
pcB, a, b
coefficient
molar heat of evaporation
...

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