Electrostatic Assist of Liquid Transfer between Flat Surfaces · Electrostatic Assist • 10-100 kV...

Electrostatic Assist of Liquid Transfer between

Flat Surfaces

Chung-Hsuan Huang and Satish Kumar

Department of Chemical Engineering and Materials ScienceUniversity of Minnesota

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

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

Incomplete liquid transfer can generate defects that are detrimental to device operation

Schematic of printing defects

Incomplete Liquid Transfer and Defects

Electric fields are sometimes used to enhance liquid transfer,a technique is known as electrostatic assist (ESA)

without ESA with ESAhttp://www.eltex.com


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)

Printing Methods: Overview

Flexographic (grocery bags)

Gravure (magazines)

Lithographic (newspapers)

Screen/Stencil (clothing)

Inkjet (printers)

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

The Liquid Transfer Problem

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

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

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

Objective: Compare model predictions and experimental data

Previous Work: ExperimentsH. Chen et al., Soft Matter 10 (2014) 2503

• 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

h(z,t)

Slender-jetapproximation

Governing Equations

• 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

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

• 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

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)


Contact-Line Motion at Ca = 0.1

• 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


OTS PEMA

2.0 μl Glycerol U

θr = 83.9° θr = 61.7°

Effect of Ca

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


Contact-Line Motion at Ca = 1.32

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

• 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

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

Electric fields are sometimes used to enhance liquid transfer,a technique is known as electrostatic assist (ESA)

without ESA with ESAhttp://www.eltex.com



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 |


• Develop a mathematical model of electrostatic effects on liquid

transfer

• Perform flow visualization experiments and compare results to

model predictions

Objectives

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

- -

- -

- -

- -

+ +

- -

-

h(z,t)

Slender-jetapproximation

Mathematical Model

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

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 |

| Δθr |


θtop = 60°

θbottom = 40° to 80°


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

Pressure in Slender-Jet Limit

𝑝𝑝 =𝜅𝜅𝐶𝐶𝐶𝐶

− 𝑣𝑣𝑧𝑧 − χ𝛽𝛽2𝐸𝐸2

R1

R2

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

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

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


Perfect dielectric (𝜒𝜒 = 50)

Leaky dielectric (𝜒𝜒 = 50)

Leaky Dielectrics

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

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

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

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

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

• 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

• 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


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

Electrostatic Assist of Liquid Transfer between Flat Surfaces · Electrostatic Assist • 10-100 kV...

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