Fluid Mechanics of Coating Flows
-
Upload
desipoet726 -
Category
Documents
-
view
44 -
download
0
description
Transcript of Fluid Mechanics of Coating Flows
1
byAnupam Sengupta
Title of Presentation
Doctoral Researcher
Centre of Advanced Fluid MechanicsAm Weichselgarten 34, D-91058 Erlangen, FRG
Fluid Mechanics of
Coating Flows
2 Contents of Presentation
The presentation:
• Conventional and Modern Coating Techniques
• Navier-Stokes equations in relevance to coating flows
• Slot Coating and Coating Windows
• Recent Works on Dip Coating
• Final remarks
3 Current State and Scopes
• Coating Technology is important from an industrial point of viewCoating Technology is important from an industrial point of view
•• Extensively used in: Extensively used in:
a) Papera) Paper
b) Pharmaceuticalsb) Pharmaceuticals
c) Packagingc) Packaging
d) Textiles d) Textiles
e) Electronics etc.e) Electronics etc.
•• Industries still rely upon trial and error methods and techniquIndustries still rely upon trial and error methods and techniques es
•• Considerable scope of innovations exists: applications of fluidConsiderable scope of innovations exists: applications of fluid mechanicsmechanics
•• Understanding the roles of surface and rheological properties fUnderstanding the roles of surface and rheological properties for improving or improving
coating productscoating products
•• Detailed fluid mechanics studies are possible these days using Detailed fluid mechanics studies are possible these days using
numerical/analytical methodsnumerical/analytical methods
4 Classifications
Wet Film(micro)
Vacuum(nano-micro)
Coating
Pre Metered
•Slot Coating
•Slide Coating
Self Metered
•Dip Coating
•Roll Coating
•Knife Coating
Chemical
• CVD
•Etching
•Lithography
Physical
•PVD:Sputtering
•Evaporation
5 Premetered Coating Techniques
• Premetered Coating : Mass flow of the coating liquid pre-decided by the
desired wet film thickness
Slot Coating : Curtain Mode Slide Coating
M=ρ.UW.h
6 Self-metering Coating Techniques
• Self-metered Coating : Mass of coating liquid is not pre-decided by the
desired wet film thickness
• Generally substrate emerges from an infinite bath. Film thickness is
controlled by varying substrate velocity or post treatments
Substrate Web speedwU
1x
2xg
Coating liquid
h
Dip Coating
Knife Coating
Air-Knife Coating
7 Navier-Stokes Equations
0
i
i
xU
t Mass Conservation
ji
ij
ji
ji
j gxx
PxU
Ut
U
23
j i kij ij
i j k
U U Uµ µx x x
Momentum Conservation
i
jij
j
j
i
i
ii x
UxU
Pxq
xeU
te
with
Energy Conservation
ii x
Tq
8 Application of NS equations
• Mass Conservation• Momentum Consrv.• Surface Properties• Rheology
• Mass Conservation• Momentum Consrv.• Energy Consrv.
Substrate Wet Film Dry Film
Coating Liquid
Coating is done in a sequence of processes
Wet film coating takes place at high speeds : 2000m/min
9 Application of NS equations:Slot Coating in Bead Mode
• All coating flows can be analysed by NS equations
• What is that differentiates various coating flows ?
• Boundary Conditions !
• Let us try to look into some basic flows related to coating :
10 Slot Coating in Bead Mode
• Pre metered coating technique• Various modes of operation : Bead, Curtain, Extrusion, Slide
11 Slot Coating and NS Equations
1 2
1 2
0U Ux x
2 21 1 1 1 1
1 2 12 21 2 1 1 2
] [ ]U U U P U UU U µ gt x x x x x
21 2 1 2 2
1
12
dU x C x Cµ dx
2 22 2 2 2 2
1 2 22 21 2 2 1 2
] [ ]U U U P U UU U µ gt x x x x x
1xIn direction :
2xIn direction :
2 2 1P g x x
12 Boundary Conditions in Slot Coating
Boundary Conditions :
13 Resultant Flow Equation
Downstream Flow
where
Upstream Flow
14 Interpretation of Flow
15 Interpretation of Flow
Hagen Poiseuille Term
Couette Flow Term
1 2d dFor the flow equation reduces to :
21 2 2 2
1 2w
LinearTermQuadraticTerm
x UU x x d x dx µ d
16 Pressure Variation within the Die
23
1 1.34oP P Ca h
3 UU
P Pr
2 3 26 wµU lP P
d
1 2 261 2 wh µU lP P
d d
(Ruschak)
17 Concept of Coating Window
• Pressure term arising across the upstream meniscus can have 2 extremes : depending upon curvature
• When liquid-air interface is convex :
• When liquid-air interface is concave :
• Combining :
3 3U UP P P P ve
3 3U UP P P P ve
3 3 3,min ,max
,min ,max
( ) ( ) ( )
( ) ( ) ( )
U U Uconcave convex
concave convexU U U
P P P P P P
r r r
18 Concept of Coating Window
• From geometrical considerations of the meniscus :
,max
,min
1 , for convex surface
1 , for concave surface
UU
UU
Cosrd
Cosrd
0.22 0.33 0.04=541 aU C where (E.B.Guthoff, C.E.Kendrick (1982),AIChE Journal)
Front-pinned convex Front-pinned concave
Back-pinned convex Back-pinned concave
The meniscus has the flexibility to adjust itself in any of the above depending upon the sub pressure applied
19 Concept of Coating WindowPressure vs Web Speed
20 Industrial Relevance
• Typically thickness and coating speeds are adjusted through practical knowledge
• The flows can be analysed using fluid mechanics
• Innovative techniques can be introduced by applying fundamentals of fluid mechanics
• Knowledge of subpressure values applicable and introduction of appropriate pressure chambers at the back meniscus
• Extend the current knowledge for more challenging cases
21 Dip Coating
• One of the earliest methods of coating
• Self metering coating technique : Process defines thickness
• Continuous or discontinuous : Physics is identical
g
Substrate
,,
wU
H
h
hH
Coating liquid
Roller
,,
Substrate
Discontinuous
Continuous
,,
22 Analytical Treatment
2 2
2 2] [ ]x x x x xx y
U U U P U UU U µ gt x y x x y
reduces to 2
2xU Pµ
y x
23 Analytical Treatment
.p nR Young-Laplace Relation :
3
2 2
2 2
2 2
( )11
( ) ( )
xx
Rx x
x x
where
32
2 3 0x xUµy x
Finally :
Boundary Conditions :
1) No slip B.C :
2) Free Surface :
@ 0xU U y
0@xxy
Uµ yy
24 Flow Profile
Integrating the D.E for a constant x wrt y, we get :3 2
3( )2xyU y U y
µ x
For determining ,we conserve the mass over the film thickness x
0 0
w
x fU y dydz U w
where is the width if the plate in the cross direction.
Finally the thickness is obtained as :
w
25 Solution by Landau and Levich
• One of the earliest solutions
• Valid for only low capillary number cases
• Formulation does not hold good for very low and for high capillary numbers
• Solution based on matched asymptotic expansion and lubrication approx.
23
WµUH cg
Valid for (???)210WµUCa
h 0=
( g/U
)1/2
Ca10-4 10-3 10-2 10-1 100 101 102
1.0
0.8
0.6
0.4
0.2
0.0
Landau-Levich (1942)
Data of Gutfinger and Tallmadge (1965)
White and Tallmadge (1965)
Spiers et al.(1974)
Results of Shunk et al.
26 Observed anomalies
• Discrepencies in the measured and computed film thickness
• Discrepancy was prominent not only at higher capillary numbers (as expected) but also at capillary numbers where the relation should have held good
• Need for a fundamental treatment : Non dimensional analysis
• According to Landau-Levich :
• Far from being complete
• Overprediction and underprediction of experimental results
23 2
3.WµUH c H c Cag
27 Dimensional Analysis
thH
1 2, ...H f • Non dimensional thickness should be
• Aim : To identify 1 2, ,...
gUfH Wth ,,,,
H WU g
L
0 1 1 1 0 0
1 -1 -3 0 1 1
0 -1 0 -2 -1 -2
•Buckingham theorem : Dependence of coating thickness expressed by all the parameters that have an influence on
• Number of dimensionless parameters : N = number of influencing parameters – rank of the dimensional matrix
(5) – (3)
28 Dimensional Analysis
Hence, 1 2 3,H f
1 : 0 0 0H g M L T
0
3 1
2 2 0
12
Thus, 2/11 /
Bog
HH
Similarly, and CaUW
/2
Dig
4/1
3
,thH f Ca Di
29 Numerical Simulations
• The dip coating processs was then numerically simulated using a FEM tool
• The capillary number was varied for different set of Dip Numbers
30 Comparison with Landau-Levich
Underprediction
Overprediction
31 Physical Interpretation :Dip Number
•Interplay of three different characteristic velocities :
Coating Velocity
Adjustment velocity of a free surface on a viscous fluid
Adjustment velocity of liquid with free surface after verticaldisplacement
WU
/
4/1
g
32 Interpretation
• : upward moving free surface adjusts with static meniscus
• This is the zone of typical variation of with : for low dip numbers
this takes place at low capillary numbers and vice versa
• : Distortion of free surface faster than readjustment ( which is
controlled by )
• : Substrate-Liquid interactions take place through London-vander Waals forces which diffuse double layers
1WU Caµ
H Ca
1Ca
µ
1Ca
33 Concept of Drainage Number
• Additional physical process present in dip coating process : Drainage
• Drainage : of the liquid film that takes place when substrate comes out
of the liquid bath
• Takes place with a characteristic velocity
• Can be defined as
• For final thickness does not depend on the generating velocity
4/1
g
4/1// gUDr W
1Dr
34 Discussion and Conclusion
• It is most likely that available expression, is a theoretical limit
• Thus dependence on or does not show up in the expression
• Scope for setting a physical limit of coatability from very low to very high capillrary numbers : Coating window for dip coating
• Defining as a closed mathematical form based on thenumerical data obtained
• Compare the numerical results with experimental data
• Incorporation of surface and rheological aspects and their influence
3/2.. CaconstH
H Di Dr
,thH f Ca Di
Thank You !!!