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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”
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