Misting in Forward Roll Coating:Misting in Forward Roll Coating:Structure Structure –– Property Property –– Processing RelationshipsProcessing Relationships

Michael S. OwensMichael S. OwensPhD. Advisors: PhD. Advisors:

L. E. Scriven & C. W. MacoskoL. E. Scriven & C. W. MacoskoCoating Process Fundamentals and Microstructured ProgramsCoating Process Fundamentals and Microstructured Programs

Department of Chemical Engineering & Materials Science Department of Chemical Engineering & Materials Science University of Minnesota, Minneapolis, 55455, USAUniversity of Minnesota, Minneapolis, 55455, USA

0 1 2 3 4 5 6 7 81

10

100

GR

AV

ITY

EFF

ECT

App

. Ext

ensi

onal

Vis

cosi

ty, P

a-s

Hencky Strain

vs.

Doctoral DefenseUniversity of Minnesota

October 27, 2004

FORWARD-ROLL COATING

+

+

Several methods to pre-meter

the applied or “wet” thickness

2-roll direct-rigid

The goal is to

apply a UNIFORM film

+

+

+

3-roll offset-rigid

++++

+

5-roll offset-deformable

COATING DEFECTS

+

+Uniform thickness – no defects

Periodic variation in thickness “Ribbing”

+

+

. ......

.. .......

.......... ...

..

.

...

...... .. ..

Formation of droplets“Misting’’

What is misting and why do industrial coaters care ?

WHAT IS MISTING ?

• Generation of liquid droplets

upon splitting liquid through a gap

or nip.

• Occurs at high roll velocities

• Mist consists of particle

Diameters < 50 μm

• Health, quality, cleanup, and cost

issue.

What is the state of the misting literature?

MISTING LITERATURE –A STATE OF DISARRAY

STRUCTURELinear polymer solutions Mist RISESBranched polymer solutions Mist FALLS

BUTDilute, entangled, MW, extent of branching, ….. ?

PROPERTYElasticity said to raise misting

BUTRelative to what ?

PROCESSINGMisting rises and falls with process conditions

BUTWhat are the physics, mechanism(s),

Relative significance of process conditions controlling mist concentration ?

Empirical treatments BUT no solutions or understanding

THESIS GOALSMist Mechanisms

& mist concentrationat the

film-split

Relevant Flow

Physics

Visualize high-speed eventsEstablish technique for measuring mist

Solution Rheology

Surface Tension

Newtonian

Non-Newtonian

Characterize low viscosity – weakly elastic liquidschallenge modern rheometers

PolymerStructure

Linear Polymers

Branched Polymers

High MW branched polymersmodel structures

ProcessingConditions

Control physics by process

Optimal Conditions

HOW WAS MIST CREATED

VISAULIZED

AND MEASURED ?

MIST MEASUREMENT• PAN FED TWO-ROLL COATER

Roll diameter, 10.2 & 15.2 cmRoll velocity, 96-306 m/minVelocity ratio, 1.0-3.0 Rubber diameter, 60 SHORE-ARoll clearance, Negative by wt.

• FLOW VISUALIZATIONHigh-speed cameras, 1,000-6,000 frames/sec.Positive roll clearance, Easily-viewed length scales45-90o views, Cross-web direction

What is known about misting of “simple” coating liquids ?

• MIST MEASUREMENTAerosizer DSPTM, Drop count, size, and mass concentration.Sampling location, 8 cm from film-splitSampling flow rate, 2.5 L/minSampling time 3 minutesTube length 20 cm

NEWTONIAN LIQUIDS

• Misting of Newtonian silicones occurs at high roll velocities

• But only misting of non-Newtonian materials has been studied

• Instabilities prior to misting have been studied (Vinjamur 2002, ISCST)

butEvolution of misting instabilities has not been defined

Mist has not been characterized (number, size, mass)

Physics is not understood

What is the Newtonian misting mechanism ?

EDGE THICKENS

EVOLUTION OF MISTINGNEWTONIAN LIQUIDS

As velocity is raisedseptum is dragged downstream

thins cross-webedge detaches and breaks-up

Smooth coating transitions to one with ribsas capillary number is raised

As roll velocity is raisedribs are dragged downstream and septa form

A septum slides atop a riboscillates in the cross-web

and downstream directions EDGE EXTENDS

EDGETHINS

BREAKUP

Tension SurfaceDrag Viscous

=⎟⎟⎠

⎞⎜⎜⎝

⎛≡

σηVCa

MODELING 3-D UNSTEADY FLOW IS TOUGH: GO TO EXPERIMENTS

SEPTA

MISTING PHYSICS MATERIALS

0 20 40 60 80 100 1200.0

1.6

2.0

2.4

2.8

3.2

Dro

p si

ze, μ

m

Capillary number

MATERIAL VARIABLES (η, σ)

WHAT ABOUT PROCESS VARIABLES ?

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0

1x106

2x106

3x106

, m/s

GLYCEROL / WATER

PPG

PDMS

Dro

p co

unt

Surface tension Shear viscosity

192 m/min

Septum becomes unstable as it thins; Viscous drag causes thinning BUT surface tension resists drop count

EDGE THICKENS

EDGE EXTENDS

EDGETHINS

BREAKUP

drop size

Critical thickness reached leading to edge detaching

Surface tension pinches it BUT viscosity slows breakup

εησω

η uRhR

o +≥⎟⎟⎠

⎞⎜⎜⎝

⎛ unstable

0 20 40 60 80 100 1200.0

1.6

2.0

2.4

2.8

3.2

Dro

p si

ze, μ

m

Capillary number0 80 100 120 140 160 180 200

0.0

5.0x105

1.0x106

1.5x106

2.0x106

280 mPa-s 230 mPa-s

75 mPa-s

Dro

p co

unt

Roll velocity, m/min

MISTING PHYSICS – ROLL VELOCITYAs roll velocity is raised

Viscous drag from a ribpulls a septum downstream

Extensional rate rises

Septum Breaks More Often 100 200 300 400 5000

5x106

1x107

2x107

Mass ~ number x (diameter)3 !!

.ε ~ V1.9

Exte

nsio

nal R

ate,

s-1

Roll Velocity, m/min

MISTING PHYSICS SPEED RATIO

As velocity ratio riseslocal thickness rises

andExtension rates fall

Less likely to rupture

FEWER DROPS

7.0

2

1

2

1

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

VV

hh

,

IN FORWARD ROLL COATING

Roll velocity ratio (V1/V2)

What about the average roll diameter ?

1.0 1.5 2.0 2.5 3.00.0

8.0x105

1.2x106

1.6x106

2.0x106

Dro

p co

unt

Roll velocity ratio

AVERAGE VELOCITYCONSTANT

droplet # ~7.0

21

−

⎟⎟⎠

⎞⎜⎜⎝

⎛

VV

h = thicknessV = roll velocity

MISTING PHYSICS – ROLL DIAMETER

80 100 120 140 160 180 200

0

10

20

30

40

50

Mis

t con

cent

ratio

n, m

g/m

3

Roll speed, m/m in

D= 0.10 m

D= 0.15 m

Large roll rotates slowlydrag viscous≈ωηo

Extensional rate falls as septum retreats

Rate to critical thickness falls

At equal roll velocity

RATE FALLS WITH 1/( εD )2.

Septum not as easily extended

0.4 0.8 1.20

1x107

2x107

3x107

Exte

nsio

nal r

ate,

s-1

Roll diameter, m

191 m/min

ε ~ 1D2

.

Need to consolidate misting data

SIMPLIFY MISTING TRENDS MATERIALSSiliconePolypropylene glycolGlycerol / waterSurface tension, σ

22 – 65 mN/m

Shear viscosity, η75 – 1200 mPa-s

7.021

2

2

)/()( VVDVV

εση

⎟⎟⎠

⎞⎜⎜⎝

⎛

Correlates misting of Newtonian liquids

PROCESS

Average roll velocity ,96 – 306 m/min

Roll velocity ratio,1-3

Separation velocity,D = 0.1 – 0.15 m

ε = 45,000 s-1

V

2/1 VV

Dε.

10-7 10-6 10-5 10-4

0

10

20

30

40

50

What about polymer solutions ?

Mis

t con

cent

ratio

n, m

g/m

3Misting Number

0

0

LINEAR SCALE

POLYMER SOLUTIONS• Addition of linear polymer known to increase mist

(Glass & Fernando 84, Roper 97, MacPhee 97)

• Addition of branched polymer known to lower mist (Chung97, Gelarden98, Clark01, ……)

• Mechanism for paint spatter in polymer solutions filament breakup

• Flow field downstream of film-split is both shear and extensional

Isolate extensional rheology with Newtonian shear rheology

How does molecular architecture control:

Mechanism(s), Rheology, Mist concentration ?

Relative to what?

EVOLUTION OF MISTINGDILUTE POLYMER SOLUTIONS

Ribs become extended

Form septa

Slide atop ribs

Filaments formslide atop ribs

develop beads,then break leaving mist

ORBreak at roll ends and retract

Form LARGE droplets

ORBreak at midplane

retract leave no mist

Low Ca

Smooth coating

Develops ribs

Hole formsgrows radially

detach a filament

As Ca is raised further

AS CAPILLARY NUMBER, , IS RAISEDσ

ηVCa ≡

Rheology Misting ?

106 105 104 103 102 101 100 10-1 10-2 10-3Viscosity, Pa-s

OPPOSED NOZZLES

CAPILLARY THINNING

FIBER SPINNINGROTATING CLAMPS

ROTATING CYLINDERSFILAMENT STRETCHING

ROD PULLING

EXTENSIONAL RHEOLOGYCOATING SOLUTIONS

For low-viscosity coating liquids

CAPILLARY THINNING

Capillary pressure squeezes bridgeViscous and elastic stresses slow thinning

Diameter measured vs. time

Fit to a “working equation” viscosity and relaxation time

No transducer needed low viscosity solutions

HIGH SPEED VIDEO

MO

TOR

MO

TOR

MO

TOR

MO

TOR

NEWTONIAN LIQUIDS POLYMER SOLUTIONS

-55 0 50 100 150 200 250 300

0.0

0.4

0.8

1.2

1.6D

IAM

ETE

R, m

m

TIME ms

-55 0 20 40 60 80 100

0.0

0.5

1.0

1.5

2.0

DIA

MET

ER

, mm

TIME, ms

ts

XDtD

ησ

6)12(

1)(−

−=)3/exp(1)( λtDtD −=

CAPILLARY THINNING

CAPILLARY THINNING EXPERIMENTAL DATA

• Diameter falls exponentially w/ time• Extensional rate approaches a constant

BUTIs determined by force balance ofSurface tension and elastic stress

0 1 2 3 4 5 6 7 81

10

100

GR

AV

ITY

EFF

EC

T

App

. Ext

ensi

onal

Vis

cosi

ty, P

a-s

Hencky Strain

Viscosity rises 100 x Newtonian value

-55 0 50 100 150 200 250 300

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

All data obtainable with surface tension

and measured diameter !

Dia

met

er, m

m

Time, ms

-55 0 50 100 150 200 250 30010

20

30

40

50

60

70

80

Ext

ensi

onal

Rat

e, s

-1

Time, ms

λ = 50 ms

IS IT ACCURATE ?

CAPILLARY THINNING INDEXER OR RHEOMETER ?

Polystyrene oligomer: Picolastic A-5, η0= 33 Pa-s at 25oC

Polystyrene polymers: 1.8 M (PDI = 1.02)6.0 M (PDI = 1.20)

Capillary Thinning is an Indexer

Model elastic liquidsc* = overlap concentration

Dilute solutions definedbelow c*

c** more conservative estimate ofdilute solution (Graessley 1980)

c** ~ 0.1c*

10-2 10-1 1000.1

1

10

100

1.8 M

6.0 M

Rel

axat

ion

time,

sec

onds

c/c**

Shear relaxation times

λ(c) non-dilute behaviorExperimental error at low conc.

Compare apparent elasticity of coating solutions vs. misting

EXTENSIONAL RHEOLOGY OF LINEAR PEO SOLUTIONS

1 10 100 1000 100000

50

100

150

200

250

300

350

5000

1000

Molecular Wt.kg/mol

Rel

axat

ion

time,

ms

Concentration, ppm

mN/m5552~

ms3500~

s-mPa200150~0

−

−

−

σ

λ

η

PEG:Water:PEO

Characterize drop size, drop count, and concentrationvs.

Relaxation time

MIST CHARACTERIZATION50%GLYCEROL : WATER : PEO

η0 = 15 mPa-s, σ = 60 mN/m, Misting Number ~ 10-7 - 10-6

0 30 60 90 120 1500.0

1.2

1.6

2.0

2.4

2.8

3.2

V = 192 m/min

NEW

TON

IAN

Dro

p di

amet

er, μ

m

Relaxation time, ms0 30 60 90 120 150

0

2x105

4x105

6x105

8x105

1x106

V = 192 m/min

NEW

TON

IAN

Dro

p co

unt

Relaxation time, ms

0 30 60 90 120 150

0.0

0.5

1.0

1.5

2.0

2.5

V = 192 m/min

COATINGWINDOW

Mis

t con

cent

ratio

n, m

g/m

3

Relaxation time, ms

As relaxation time is raised

DROP SIZE RISES&

DROP COUNT FALLS

Competition determines misting window

COATING WINDOW

0 30 60 90 120 1500.1

1.0

10.0Roll speed m/min

306268230192

Mis

t con

cent

ratio

n, m

g/m

3

Relaxation time, ms

Coating window SHRINKS at roll speed is raisedLiterature

Branched solutions reduce mist

Linear polymers increase mist NO !

IS BRANCHED BETTER THAN LINEAR AND IF SO WHY?

Solution Rheology

Newtonian

Strain Hardening

Capillary Thinning Relaxation time

Mist Mechanisms& mist concentration

at the film-split

Extensional flow

Newtonian Polymer solutionSmooth ribs Septa mist OR Smooth ribs Septa filaments-> mist

Misting Number Misting Window

THESIS GOALS

PolymerStructure

Linear Polymers

Branched Polymers

High MW branched polymersmodel structures

ProcessingConditions

Formulation specific

Experiments And

Molecular models

Mist Mechanisms& mist concentration

at the film-split

Extensional flow

Newtonian Polymer solutionSmooth ribs Septa mist OR Smooth ribs Septa filaments-> mist

Misting Number Misting Window

Solution Rheology

Newtonian

Strain Hardening

Capillary Thinning Relaxation time

ProcessingConditions

Formulation specific

POLYDIMETHYLSILOXANE (PDMS)POLYMER SOLUTIONS

Clark et al. 2002 – Polymer additive for reducing mist

Chain Extension

Chain Branching

BranchesOn

Branches

RANDOM BRANCHING

BRANCHING ANALYSISMULTI-ANGLE LIGHT SCATTERING

10 15 20 25 30

0.0

0.5

1.0

1.5

2.0

2.5

Branched silicone

Linear silicone

Nor

mal

ized

Sig

nal,

volts

Retention Volume, mls

Branched PDMS very polydisperse0 5.0x105 1.0x106 1.5x106 2.0x106 2.5x106

0

15

30

45

60

75

90

Branched PDMS

Linear PDMS

Rad

ius

of G

yrat

ion,

nm

Mw, g/mol

Compare Rg vs. MW

BRANCHING RISES AS RATIO FALLS

0 5.0x105 1.0x106 1.5x106 2.0x106 2.5x

0.44

0.48

0.52

0.56

Bra

nchi

ng R

atio

Mw, g/mol

Rg BRANCHEDRg LINEAR

• High Mw fraction dominates rheology

• Define concentration where Rg OVERLAP

25% of overall Mw “ACTIVE”0.2 wt% branched polymerIs 500ppm active.

“LOW” MW1800 kg/mol

“HIGH” MW6600 kg/mol

INTERMEDIATEMW

4400 kg/mol

2 4 6 8 10 120

5

10

15

20

25

30

35

Branched No Elasticity Detected

Branched λ = 7 ms

Linearλ = 14 ms

App

. Ext

ensi

onal

Vis

cosi

ty, P

a-s

Hencky Strain

BRANCHED VS. LINEARDILUTE PDMS RHEOLOGY

Lower molecular weight LINEAR SOLUTION has

LONGER relaxation time and MORE strain hardening

Do branched solutions have fewer but more drops than linear ?

BRANCHED VS. LINEAR PDMS

Linear polymer solution hasfewer droplets of larger size than

branched polymer at equal Mw

0 500 1000 15000.02.0

2.5

3.0

3.5

NEWTONIAN

Branched polymers500 ppmη0=280mPa-s

Linear polymers500 ppmη0=280mPa-s

Dro

p di

amet

er, μ

m

Mw ,kg/mol

0 500 1000 1500 20000

1x106

2x106Newtonian Branched polymers

500 ppmη0=280mPa-s

Linear polymers500 ppmη0=280mPa-sD

rop

coun

t

Mw, kg/mol

WHY ?Model systems by computation

MOLECULAR MODEL

SPRINGS REPRESENT POLYMER ELASTICITY

Dilute solutions – no polymer/polymer interactions

FORCE BLOWS UPMAXWELL SPRING

OLDROYD-BGEISEKUS STEADY-STATE

FENE MODELS

CHAIN EXTENSION

FOR

CE

INFINITE CHAIN EXTENSIONHOOKEAN SPRING

R2

end-to-enddistance

Rg2

Doesn’t allow for Branched polymer

structures

Non-linear spring lawto describe

Finitely extendible reality

BEAD IS POINT OF

VISCOUS DRAGSIMPLIFY AS

2 BEADS CONNECTEDBY SPRING

GENERAL CONNECTIVITYGoal: To design a framework that describes all possible

molecular architecture and gives a coarse description of chain contour.

Solution: Connectivity matrix or Incidence arrayBead, i N

Spr

ing,

iN

-1

110000000011000000001100000000110000000011000000001100000000110000000011

−−

−−

−−

−−

Bead, i N

Spr

ing,

iN

-1

110000000010000100001100000000010100000011000000001100000000110000000011

−−

−−

−−

−− Can easily design:

stars, combs,loops, dendrimers, branches-on-branches,ect……….

BEAD-SPRING CHAINS

Contour represented by series of beads and springs

? Brownian Force

Viscous Force

Non-linear elastic force

Coarse-grained chain contour

* OTHER FORCES MAY INCLUDESolvent / Polymer interactions

Hydrodynamic interactionsConformation dependant drag

Chain interactions if not dilute

BROWNIAN DYNAMICS EQUATION OF STATE

Ensemble Average of the

Polymer Stress(spring separation)

And Polymer Relaxation Time

Brownian force is a time and spatially randomForce exerted by the solvent on the chain

solvent the bybeads on exerted

forces random to owing

velocity Bead

Spring of Extension from ForceLinear -Non to owing velocity Bead velocitysolvent

by owing velocity Bead

position bead ofChange-of-Rate

int

Tk

i

iib

Tkir

Tvdtidr B

i

ii

k

B ~)2/1(6

21

23

21

23

1

11 ⋅⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

Δ+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−

−−

−

−+⋅∇=

−

−− ζλ

λλ

λ

λλ

ζ

Solve for bead positions (ri) by Euler integration

λi is a ratio of bead to separation to theirmaximum allowed separation

0 5 10 15 20 250

20000

40000

60000

80000

Stre

ss, τ

11-τ

22

Time

MODEL DILUTE POLYMER SOLUTIONS

Relaxation time rises with molecular weight

Brownian DynamicsSimulations

10 1001

10

100

λ Linear > λ branched

Corresponds to stress

STAR POLYMER

LinearPolymers

Rel

axat

ion

tim

e

Number of beads ~ MW

Polystyrene Boger liquidsCapillary thinning

106 107 1081

10

100

1000

How does stress correspond to mist mechanism ?

Rel

axat

ion

time,

sec

onds

Molecular weight, g/mol

T-star PS

Linear PSMw =2, 6, 20 M

Anna et al. JOR 2001

MOLECULAR STRUCTURE CONTROLS MISTING

PolymerSolventRττ

σ+=

Capillary ForceActing to SqueezeFilament

Newtonian ViscosityResists Pinching

Polymer Elastic Stress

Resists Pinching

High polymer stressstabilizes filaments

AND

Linear polymer givesgreater stress than branched

at equal Mw

Linear gives less mistthan branched

Breakup mechanisms

Increasing polymer stress or relax’n time

0 1100

1x10 6

Dro

p co

unt

R e laxation tim e, m s

Increasing Mw

Decreasing branching

STRUCTURE PROPERTYOPERATIONAL DIAGRAM

NEWTONIANNEWTONIAN

SEPTUMEDGE FAILURE

BREAK-UPMECHANISM

STRAINSTRAIN--HARDENHARDEN

SEPTUM EDGE RUPTUREFILAMENT EXTENDED

BREAKUP MECHANISMS

NEWTONIAN CONCLUSIONS

10-7 10-6 10-5 10-4

0

10

20

30

40

50

Mis

t con

cent

ratio

n, m

g/m

3Misting Number

0

0

LINEAR SCALE

MechanismRibs septum edge failure mist

Mass concentration of mist summarized by Non-dimensional misting number

Short-term solution: Polymer solutions

Change the mechanism by which mist is formedLong-term solution: Different Coating Technique

Change the technique so instabilities leading to mist do not form

Optimal Material/Process design

High surface tensionLow viscosityLarge rollsSpeed ratio

DILUTE POLYMER SOLUTION CONCLUSIONSMechanism

Ribs septum hole growth filamentbeads-on-string dropssingle bead big but few dropsbreaks and retracts no drops

Mass concentration of mist defined byMisting Window

0 30 60 90 120 150

0.0

0.5

1.0

1.5

2.0

2.5

V = 192 m/min

COATINGWINDOW

Mis

t con

cent

ratio

n, m

g/m

3

Relaxation time, msShort-term solution: Semi-dilute and entangled solutions

Low surface tension w/ more elasticity to get new window no drops Long-term solution: Different Coating Technique

Slot/tensioned web or reverse roll coating

no septum (no mist)

Optimal Material/Process designLow surface tensionLow viscosityWeak elasticityLarge rollsSpeed ratio

FUTURE WORK

0 30 60 90 120 150

0.0

0.5

1.0

1.5

2.0

2.5

V = 192 m/min

COATINGWINDOW

Mis

t con

cent

ratio

n, m

g/m

3

Relaxation time, ms

Entangled solutions

“Slinging”COATINGWINDOW

Does another coating window exist ?

• New coating window (Practical and Fundamental interest) • 3-D CFD of septa mist & septa filaments mist (Physics of misting)• Misting of viscoelastic-plastic inks ? (Practical and Fundamental interest)

What is the origin of error(s) during elastocapillary thinning ?• Fluid mechanics and equilibrium shape analysis (Fundamental and commercial interest)• Brownian dynamics of multiple chains in extensional flow (Fundamental and practical)

entanglements of dilute solutionsinterchain hydrodynamics

• Fluorescently tagged chains in experiment and PIV to follow capillary thinning dynamics

ACKNOWLEDGMENTS• Advisors,

Chris Macosko and Skip Scriven

• Committee members, Marcio Carvalho, Satish Kumar, Tim Lodge

• Conspirators inCoating Process Fundamentals and

Microstructured Polymers Programs

• 2000-2004 Summer Undergraduate Research Participants

• Friends and family, “The non-academics”