Electrostatic Assist of Liquid Transfer between Flat Surfaces · Electrostatic Assist • 10-100 kV...
Transcript of Electrostatic Assist of Liquid Transfer between Flat Surfaces · Electrostatic Assist • 10-100 kV...
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Electrostatic Assist of Liquid Transfer between
Flat Surfaces
Chung-Hsuan Huang and Satish Kumar
Department of Chemical Engineering and Materials ScienceUniversity of Minnesota
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Motivation: Printed Electronics
• OLED displays and lighting• Photovoltaics• Electronic paper• Transistors• Sensors• Batteries• Biomedical products
Market size2017: $29.3 Billion2027: $73.4 Billion
Source: IDTechEx
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Gravure Printing
Liquid bridge
• Best for long print runs requiring high resolution
• Defects detrimental for printed electronics
• Emptying of cavities essential for avoiding defects!
Cell dimensions: ~ 50 µm deep, 50-100 µm wideWeb speeds: ~ 1-10 m/s
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Incomplete liquid transfer can generate defects that are detrimental to device operation
Schematic of printing defects
Incomplete Liquid Transfer and Defects
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Electric fields are sometimes used to enhance liquid transfer,a technique is known as electrostatic assist (ESA)
without ESA with ESAhttp://www.eltex.com
Schematic of printing defects
Electrostatic Assist
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Electrostatic Assist
• 10-100 kV potential difference
• Used for ~50 years to improve ink transfer
• How does it work?
Electrostatic assist (ESA) no ESA ESA
K. Morris, Printing Technol. 12 (1968)
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Printing Methods: Overview
Flexographic (grocery bags)
Gravure (magazines)
Lithographic (newspapers)
Screen/Stencil (clothing)
Inkjet (printers)
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Printing: A Brief History~200 BC: Seals/Stamps, Woodblock printing---China
~1000: Movable type (clay) printing---China
~1200: Movable type (metal) printing---Korea
~1440-1450: Gutenberg’s press with movable (metal) type---Germany
~1400-1500: Etching (Printing plates with recessed areas)---Europe
~1860: Earliest gravure press---France
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The Liquid Transfer Problem
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Gravure Printing
forces viscousforces inertial
Reµ
ρUL=
forces tension surfaceforces viscous
CaσµU
=
forces viscousforces nalgravitatio
G2
UgLµρ
=
What forces are important at the scale of a cell?
~10-4 to 102 ~10-4 to 10 ~10-1 or less
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This Talk
I. Liquid transfer in the absence of electric fields
C.-H. Huang, M. S. Carvalho, and S. Kumar, Soft Matter 12 (2016) 7457
II. Liquid transfer in the presence of electric fields
C.-H. Huang and S. Kumar, Langmuir, submitted
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This Talk
I. Liquid transfer in the absence of electric fields
C.-H. Huang, M. S. Carvalho, and S. Kumar, Soft Matter 12 (2016) 7457
II. Liquid transfer in the presence of electric fields
C.-H. Huang and S. Kumar, Langmuir, submitted
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S. Dodds, M. S. Carvalho, and S. KumarPhys. Fluids 21 (2009) 092103Phys. Fluids 23 (2011) 092101 J. Fluid Mech. 707 (2012) 521
Bridge length
1D
2D
Brid
ge ra
dius
Previous Work: Modeling
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Objective: Compare model predictions and experimental data
Previous Work: ExperimentsH. Chen et al., Soft Matter 10 (2014) 2503
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• 1D slender-jet model
• 2D model solved by Galerkin finite-element method
• Zero shear stress condition at moving contact lines allows them to slip freely
U
U
Models
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h(z,t)
Slender-jetapproximation
Governing Equations
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• Both models show good agreement with these experiments
• Liquid transfer ratio mainly controlled by difference of
receding contact angle between the two surfaces
Both models overestimate transfer
ratio when
Both models underestimate transfer
ratio when
case 8Δθr = 15°
Ca = O(10-7)
H. Chen et al., Soft Matter 10 (2014) 2503C.-H. Huang et al., Soft Matter 12 (2016) 7457
Comparison to Experiments
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H. Chen et al., Soft Matter 10 (2014) 2503C.-H. Huang et al., Soft Matter 12 (2016) 7457
Simple slip boundary condition is able to capture essential features of liquid bridge stretching
Rt (2D FEM) Rt (Exp.)
Rb (Exp.)Rb (2D FEM)
break point
Top
Bottom
Contact-Line Motion
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• Liquid transfer ratio approaches 50% as Ca increases
• 2D model predictions agree better with experimental data for Ca > 0.2 and Ca < 0.01
• 1D model predictions slowly converge to 50% due to different contact-line motion
H. Chen et al., Phys. Fluids 27 (2015) 112102C.-H. Huang et al., Soft Matter 12 (2016) 7457
OTS PEMA
2.0 μl Glycerol U
θr = 83.9° θr = 61.7°
Effect of Ca
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Deviation between model predictions and
experiments makes the predicted transfer ratio
much larger than the experimental value
OTS coated surface (bottom)PEMA coated surface (top)
H. Chen et al., Phys. Fluids 27 (2015) 112102C.-H. Huang et al., Soft Matter 12 (2016) 7457
Contact-Line Motion at Ca = 0.1
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• Liquid transfer ratio approaches 50% as Ca increases
• 2D model predictions agree better with experimental data for Ca > 0.2 and Ca < 0.01
• 1D model predictions slowly converge to 50% due to different contact-line motion
H. Chen et al., Phys. Fluids 27 (2015) 112102C.-H. Huang et al., Soft Matter 12 (2016) 7457
OTS PEMA
2.0 μl Glycerol U
θr = 83.9° θr = 61.7°
Effect of Ca
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PEMA coated surface (top) OTS coated surface (bottom)
Contact radius difference between two plates predicted by 2D model is similar to experimental results [Δr = 0.17 mm (Exp.) to 0.27 mm (2D model)]
2D model is better able to predict transfer ratio than 1D model
1.16 mm
0.89 mm1.16 mm
1.33 mm
H. Chen et al., Phys. Fluids 27 (2015) 112102C.-H. Huang et al., Soft Matter 12 (2016) 7457
Contact-Line Motion at Ca = 1.32
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t = 1.17t = 3.86
t = 5.85 Largest pressure gradients at early
times are near both plates
Axial pressure gradient dominates at
times close to bridge breakup
1D model neglects any radial
pressure gradientsC.-H. Huang et al., Soft Matter 12 (2016) 7457
Ca = 1.32
Pressure Field
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• Transfer ratio from 2D model approaches 50% for larger Ca
• Model predictions deviate significantly from experimental data at intermediate Ca due to surface heterogeneities
• Model predictions are in good agreement with transfer ratio and contact-line motion when Ca is very small [O(10-2)]
• 1D model predicts more contact-line movement than 2D model because it neglects axial pressure gradients
Exp
2D model
Summary
C.-H. Huang et al., Soft Matter 12 (2016) 7457
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This Talk
I. Liquid transfer in the absence of electric fields
C.-H. Huang, M. S. Carvalho, and S. Kumar, Soft Matter 12 (2016) 7457
II. Liquid transfer in the presence of electric fields
C.-H. Huang and S. Kumar, Langmuir, submitted
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Electric fields are sometimes used to enhance liquid transfer,a technique is known as electrostatic assist (ESA)
without ESA with ESAhttp://www.eltex.com
Schematic of printing defects
Electrostatic Assist
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Challenge: Improving Liquid Transfer at High Speeds
Only 50% of liquid transfers to the substrate at high speeds
Can electrostatic forces improve liquid transfer
at higher capillary numbers?
= μU/𝛾𝛾
WithoutESA
WithESA?
Stretching at high speeds
Δθr = θbottom - θtop
| Δθr |
| Δθr |
C.-H. Huang et al., Soft Matter 12 (2016) 7457
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• Develop a mathematical model of electrostatic effects on liquid
transfer
• Perform flow visualization experiments and compare results to
model predictions
Objectives
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Perfect dielectrics
• Liquid bridge has no conductivity
• No charge accumulates at air-liquid interface
Leaky dielectrics
• Polarizable, weakly conducting liquid
• Charge accumulates only at air-liquid interface
Electrohydrodynamics
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+ +
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h(z,t)
Slender-jetapproximation
Mathematical Model
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DimensionlessParameter Symbol Physical Meaning Values
Electro-viscous number
Electro-capillary number
Permittivityconstant
Conductivity
O(10-3 – 105)
O(10-3 – 105)
O(100 – 102)
O(10-3 – 106)
Voltage: Vo ~ 102 – 104 volts
Conductivity: K ~ 10-12 – 10-2 S/m
Vacuum permittivity: εo ≈ 8.85×10-12 F/m
Relative permittivity: εr ~ 100 – 102
Typical Parameter Values
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Challenge: Improving Liquid Transfer at High Speeds
Only 50% of liquid transfers to the substrate at high speeds
Can electrostatic forces improve liquid transfer
at higher capillary numbers?
= μU/𝛾𝛾
WithoutESA
WithESA?
Stretching at high speeds
Δθr = θbottom - θtop
| Δθr |
| Δθr |
C.-H. Huang et al., Soft Matter 12 (2016) 7457
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θtop = 60°
θbottom = 40° to 80°
Δθr = θbottom - θtop
Ca = 𝜇𝜇U/ 𝛾𝛾 = 1Λ = L/2R = 1𝛽𝛽 = 1.74
• Electric field enhances liquid transfer to the more wettable surface
• Greater pressure difference in electrified bridge due to charge polarization helps push liquid to the more wettable surface
No electric field (𝜒𝜒 = 0)
Electric field (𝜒𝜒 = 50)
Perfect Dielectrics
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Pressure in Slender-Jet Limit
𝑝𝑝 =𝜅𝜅𝐶𝐶𝐶𝐶
− 𝑣𝑣𝑧𝑧 − χ𝛽𝛽2𝐸𝐸2
R1
R2
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𝜒𝜒 = 0 (No electric field) 𝜒𝜒 = 50 (Electric field)
θtop = 60°
θbottom = 70°
Ca = 1
• Electric field enhances liquid transfer to the more wettable surface
• Greater pressure difference in electrified bridge due to charge polarization helps push liquid to the more wettable surface
Perfect Dielectrics
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EE
t
Dimensionless tangential stress
• Tangential stress due to surface charge may have a significant effect on
liquid bridge shape
• Direction of tangential stress can be controlled by direction of electric
field and sign of surface charge
tt
Leaky Dielectrics
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Ca = 𝜇𝜇U/𝛾𝛾 = 1Λ = L/2R = 1
𝜒𝜒 = 50
θtop = 60°
θbottom = 40° to 80°
• Transfer ratio is nearly 100% with non-zero initial surface charge
• Tangential stress pushes liquid to top surface, and thus liquid
transfer increases
No electric field (𝜒𝜒 = 0)
Perfect dielectric (𝜒𝜒 = 50)
Leaky dielectric (𝜒𝜒 = 50)
Leaky Dielectrics
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Top surface: Aluminum
(Receding contact angle: 13∘±2∘)
Bottom surface: PS-coated aluminum
(Receding contact angle: 58∘±1∘)
Stretching speed: 6.25 mm/s
Electric potential: 0 – 1.5 kV
Liquid properties 88wt% Glycerol
Viscosity (cP) 119.6
Surface tension (mN/m) 66.5
Dielectric constant 45.9
Conductivity (𝜇𝜇S/cm) 0.4Electric current < 10 mA
Flow Visualization
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ɸ = 0 kV ɸ ~ 1 kV
Narrowest diameter: 1.04 mm Narrowest diameter: 1.15 mm
• Narrowest bridge radius increases when electric field is applied
• Average transfer ratio for both cases is ~ 50%
• Influence of surface charge is probably negligible in these experiments
Aluminum
Aluminum
Aluminum
Aluminum
No Wettability Difference
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Ca = 0.01 ɸ = 0 V, 𝜒𝜒 = 0 ɸ = 1.5 kV, 𝜒𝜒 = 27
Transfer ratio (%)34.3 ± 2% 42.2 ± 1.5%
PS-coated surface
Aluminum Aluminum
PS-coated surface
• Transfer ratio increases when electric field is present
• Electrified bridge breaks up at a longer length
• How well does predicted transfer ratio compare to experimental results?
θr = 13°
θr = 58°
Stretching with Wettability Difference
Aluminum
PS-coated surface
Aluminum
PS-coated surface
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Ca = 0.01
Bottom contact line Top contact line Breakup length
No electric field Pinned Pinned 2.06 mm
Electric field Unpinned Pinned 3.03 mm
Aluminum
PS-coated surface
Aluminum
PS-coated surface
ɸ = 0 V (𝜒𝜒 = 0) ɸ = 1.5 kV (𝜒𝜒 = 27)
Contact-Line Motion and Breakup Length
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Transfer ratio(1D model)
Transfer ratio(Experiment) Breakup length
No electric field 34% 34 ± 2% 2.03 mm (2.06 mm)
Electric field 45% 42 ± 1.5% 2.25 mm (3.03 mm)
ɸ = 0 V ɸ = 1.5 kV
Comparison of Experiment & 1D Model
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• Electric field stabilizes bridge and decreases contact angles
• Bottom contact angle reaches receding value and thus contact line slips
• Transfer ratio predicted by the 1D model agrees well with experiments
No electric fieldElectric field
Mechanism for Enhanced Liquid Transfer
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• Electrostatic forces can improve liquid transfer
• 1D model predictions agree well with experimental results
• Application of electric field Smaller contact angles Depinning of contact line
Aluminum
Conclusions
No electric field (𝜒𝜒 = 0)
Perfect dielectric (𝜒𝜒 = 50)
Leaky dielectric (𝜒𝜒 = 50)
ɸ = 0 V ɸ = 1.5 kV
Slide Number 1Slide Number 2Gravure PrintingSlide Number 4Slide Number 5Electrostatic AssistPrinting Methods: OverviewPrinting: A Brief HistorySlide Number 9Gravure PrintingSlide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Challenge: Improving Liquid Transfer at High SpeedsSlide Number 28Slide Number 29Slide Number 30Slide Number 31Challenge: Improving Liquid Transfer at High SpeedsSlide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47