A heterogeneous multiscale model for discrete cell gravure roll coating is presented along with experimental results for the purpose of model validation. The cell volume, generalized cell shape, and the gravure patterning are considered in the model which is based on a multiscale description of the flow in the coating bead. The inclusion of a web-to-roll contact term accounts for the special gravure case when the web-roll separation tends to zero. The results show how the coating bead responds to changes in operating conditions. These are presented as profile plots of the fluid properties and coating bead shape.
REFERENCES
1.
Becerra
, M.
and Carvalho
, M. S.
, “Stability of viscoelastic liquid curtain
,” Chem. Eng. Process.
50
, 445
–449
(2011
).2.
Benkreira
, H.
, Edwards
, M. F.
, and Wilkinson
, W. L.
, “Mathematical modelling of the reverse and metering roll coating flow of Newtonian fluids
,” Chem. Eng. Sci.
37
, 277
–282
(1982
).3.
Benkreira
, H.
and Patel
, R.
, “Direct gravure roll coating
,” Chem. Eng. Sci.
48
, 2329
–2335
(1993
).4.
Booth
, G. L.
, Coating Equipment and Processes
(Lockwood Publishing Company
, New York
, 1970
).5.
Bretherton
, F.
, “The motion of long bubbles in tubes
,” J. Fluid Mech.
10
, 166
–188
(1961
).6.
7.
Carvalho
, M.
and Scriven
, L.
, “Flows in forward deformable roll coating gaps: Comparison between spring and plane-strain models of roll cover
,” J. Comput. Phys.
138
, 449
–479
(1997
).8.
Carvalho
, M. D. S.
, “Elastohydrodynamics of tensioned web roll coating process
,” Int. J. Numer. Methods Fluids
41
, 561
–576
(2003
).9.
Coyle
, D.
, Macosko
, C.
, and Scriven
, L.
, “The fluid dynamics of reverse roll coating
,” AIChE J.
36
, 161
–174
(1990
).10.
de Boer
, G.
, Gao
, L.
, Hewson
, R.
, and Thompson
, H.
, “Heterogeneous multiscale methods for modelling surface topography in EHL line contacts
,” Tribol. Int.
113
, 262
–278
(2017
).11.
de Boer
, G. N.
, Hewson
, R. W.
, Thompson
, H. M.
, Gao
, L.
, and Toropov
, V. V.
, “Two-scale EHL: Three-dimensional topography in tilted-pad bearings
,” Tibol. Int.
79
, 111
–125
(2014
).12.
de Kraker
, A.
, Van Ostayen
, R. A. J.
, and Rixen
, D. J.
, “Development of a texture averaged Reynolds equation
,” Tribol. Int.
43
, 2100
–2109
(2010
).13.
de Kraker
, A.
, van Ostayen
, R. A.
, van Beek
, A.
, and Rixen
, D. J.
, “A multiscale method modeling surface texture effects
,” J. Tribol.
129
, 221
–230
(2007
).14.
Dodds
, S.
, Carvalho
, M.
, and Kumar
, S.
, “Stretching liquid bridges with moving contact lines: The role of inertia
,” Phys. Fluids
23
, 092101
(2011
).15.
Dodds
, S.
, Carvalho
, M. D.
, and Kumar
, S.
, “Stretching and slipping of liquid bridges near plates and cavities
,” Phys. Fluids
21
, 092103
(2009
).16.
Gao
, L.
, de Boer
, G.
, and Hewson
, R. W.
, “The role of micro-cavitation on EHL: A study using a multiscale mass conserving approach
,” Tribol. Int.
90
, 324
–331
(2015
).17.
Gao
, L.
and Hewson
, R.
, “A multiscale framework for EHL and micro-EHL
,” Tribol. Trans.
55
, 713
–722
(2012
).18.
Gao
, L.
, Hewson
, R.
, Thompson
, H.
, Raske
, N.
, and Toropov
, V.
, “A multiscale method for optimising surface topography in elastohydrodynamic lubrication (EHL) using metamodels
,” Struct. Multidiscip.
54
, 483
(2016
).19.
Gaskell
, P. H.
, Rees
, S. R.
, Savage
, M. D.
, and Storey
, S. P.
, “A mathematical model of roll-to-web kiss coating
,” Chem. Eng. Res. Des
76
, 29
–37
(1998
).20.
Greener
, J.
and Middleman
, S.
, “Theoretical and experimental studies of the fluid dynamics of a two-roll coater
,” Ind. Eng. Chem. Fundam.
18
, 35
–41
(1979
).21.
Hanumanthu
, R.
, “Variation of gravure coating thickness during early stages of doctor blade wear
,” AIChE J.
45
, 2487
–2494
(1999
).22.
Hewson
, R.
, et al. “Modelling the discrete-cell gravure roll coating process
,” Europ. Phys. J. Special Topics
166
(1
), 99
–102
(2009
).23.
Hewson
, R.
, Kapur
, N.
, and Gaskell
, P.
, “A two-scale model for discrete cell gravure roll coating
,” Chem. Eng. Sci.
66
, 3666
–3674
(2011
).24.
Hewson
, R. W.
, Kapur
, N.
, and Gaskell
, P. H.
, “A theoretical and experimental investigation of tri-helical gravure roll coating
,” Chem. Eng. Sci.
61
, 5487
–5499
(2006
).25.
Hoda
, N.
and Kumar
, S.
, “Boundary integral simulations of liquid emptying from a model gravure cell
,” Phys. Fluids
20
, 092106
(2008
).26.
Huang
, W.-X.
, Lee
, S.-H.
, Sung
, H. J.
, Lee
, T.-M.
, and Kim
, D.-S.
, “Simulation of liquid transfer between separating walls for modeling micro-gravure-offset printing
,” Int. J. Heat Fluid Flow
29
, 1436
–1446
(2008
).27.
Jalkanen
, T.
, Mäkilä
, E.
, Määttänen
, A.
, Tuura
, J.
, Kaasalainen
, M.
, Lehto
, V.-P.
, Ihalainen
, P.
, Peltonen
, J.
, and Salonen
, J.
, “Porous silicon micro- and nanoparticles for printed humidity sensors
,” Appl. Phys. Lett.
101
, 263110 (2012
).28.
Jin
, J.
, Ko
, J.-H.
, Yang
, S.
, and Bae
, B.-S.
, “Rollable transparent glass-fabric reinforced composite substrate for flexible devices
,” Adv. Mater.
22
, 4510
–4515
(2010
).29.
Kapur
, N.
, “Flow phenomena in fixed-gap and gravure roll coating sytems
,” Ph.D. thesis, University of Leeds
, 1999
.30.
Kapur
, N.
, “A parametric study of direct gravure coating
,” Chem. Eng. Sci.
58
, 2875
–2882
(2003
).31.
Kapur
, N.
, Gaskell
, P. H.
, and Bates
, A.
, “A parametric study of offset gravure coating
,” Chem. Eng. Res. Des.
79
, 41
–50
(2001
).32.
Krebs
, F. C.
, “Fabrication and processing of polymer solar cells: A review of printing and coating techniques
,” Sol. Energy Mater. Sol. Cells
93
, 394
–412
(2009
).33.
Kumar
, S.
, “Liquid transfer in printing processes: Liquid bridges with moving contact lines
,” Annu. Rev. Fluid Mech.
47
, 67
–94
(2015
).34.
Landau
, L.
and Levich
, B.
, “Dragging of a liquid by a moving plate
,” Acta Physicochim. URSS
17
, 42
(1942
).35.
Mäkelä
, T.
, Haatainen
, T.
, Majander
, P.
, and Ahopelto
, J.
, “Continuous roll to roll nanoimprinting of inherently conducting polyaniline
,” Microelectron. Eng.
84
, 877
–879
(2007
).36.
Michels
, J. J.
, Peter
, M.
, Salem
, A.
, van Remoortere
, B.
, and van den Brand
, J.
, “A combined experimental and theoretical study on the side ingress of water into barrier adhesives for organic electronics applications
,” J. Mater. Chem. C
2
, 5759
–5768
(2014
).37.
Patir
, N.
and Cheng
, H. S.
, “An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication
,” J. Lubr. Technol.
100
, 12
–17
(1978
).38.
Pérez-ràfols
, F.
, Larsson
, R.
, Lundström
, S.
, Wall
, P.
, and Almqvist
, A.
, “A stochastic two-scale model for pressure-driven flow between rough surfaces
,” Proc. R. Soc. A
472
, 20160069
(2016
).39.
Poole
, J. L.
, “Fluid metering roller
,” U.S. patent application No. 4,301,583. 24 Nov. 1981.40.
Powell
, C. A.
, Savage
, M. D.
, and Gaskell
, P. H.
, “Modelling the meniscus evacuation problem in direct gravure coating
,” Chem. Eng. Res. Des.
78
, 61
–67
(2000
).41.
Pudas
, M.
, Niina
, H.
, Granat
, P.
, and Vähäkangas
, J.
, “Gravure printing of conductive particulate polymer inks on flexible subtrates
,” Prog. Org. Coat.
54
, 310
–316
(2005
).42.
Pudas
, M.
, Hagberg
, J.
, and Leppävuori
, S.
, “Gravure offset printing of polymer inks for conductors
,” Prog. Org. Coat.
49
, 324
–335
(2004
).43.
Rees
, S. R.
, “An experimental and theoretical investigation of gravure roll coating
,” Ph.D. thesis, University of Leeds
, 1995
.44.
Romero
, O. J.
, Scriven
, L. E.
, and Carvalho
, M. S.
, “Slot coating of mildly viscoelastic liquids
,” J. Non-Newtonian Fluid Mech.
138
, 63
–75
(2006
).45.
Sahlin
, F.
, Almqvist
, A.
, Larsson
, R.
, and Glavatskih
, S.
, “A cavitation algorithm for arbitrary lubricant compressibility
,” Tribol. Int.
40
, 1294
–1300
(2007
).46.
Schwartz
, L.
, Moussalli
, P.
, Campbell
, P.
, and Eley
, R.
, “Numerical modelling of liquid withdrawal from gravure cavities in coating operations
,” Chem. Eng. Res. Des.
76
, 22
(1998
).47.
Storey
, S. P.
, “A theoretical investigation of the flow between a web and roll, with application to gravure coating
,” Ph.D. thesis, University of Leeds
, 1996
.48.
Tobjörk
, D.
, Kaihovirta
, N. J.
, Mäkelä
, T.
, Pettersson
, F. S.
, and Österbacka
, R.
, “All-printed low-voltage organic transistors
,” Org. Electron.
9
, 931
–935
(2008
).49.
Weinan
, E.
and Engquist
, B.
, “The heterogenous multiscale methods
,” Commun. Math. Sci.
1
(1
), 87
–132
(2003
).50.
Yin
, X.
and Kumar
, S.
, “Lubrication flow between a cavity and a flexible wall
,” Phys. Fluids
17
, 063101
(2005
).51.
Yin
, X.
and Kumar
, S.
, “Two-dimensional simulations of flow near a cavity and a flexible solid boundary
,” Phys. Fluids
18
, 063103
(2006
).© 2017 Author(s).
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Author(s)
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