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Liquid transfer from single cavities to rotating rolls

  • Diego M. Campana (a1) (a2) and Marcio S. Carvalho (a2)
Abstract

In this work we study computationally the dynamics of a liquid bridge formed between a two-dimensional trapezoidal cavity, which represents an axisymmetric cell or a plane groove engraved in a roll, and a moving plate. The flow is a model of the liquid transfer process in gravure printing systems. The considered plate kinematics represents the actual motion of a roll-to-roll system, which includes extension, shear and rotation relative to the cavity. The fluid flow is modelled by solving the Stokes equations, discretized with the finite element method; the evolving free surfaces are accommodated by employing a pseudosolid mesh deforming algorithm. The results show that as the roll radius is reduced, thus increasing the lateral and rotational motions of the top plate relative to the cavity, a larger volume of liquid is transferred to the plate. However, due to lateral displacement of the contact lines, special care must be taken concerning the wettability properties of the substrate to avoid errors in the pattern fidelity. The predictions also show a strong nonlinear behaviour of the liquid fraction extracted from a cavity as a function of the capillary number. At high capillary numbers the fluid dynamics is mainly controlled by the extensional motion due to the strong contact line pinning. However, at low values of the capillary number, the contact lines have higher mobility and the liquid fraction primarily depends on the lateral and rotational plate velocity. These mechanisms tend to drag the fluid outside the cavity and increase the liquid fraction transferred to the plate, as has been observed in experiments.

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Corresponding author
Email address for correspondence: msc@puc-rio.br
References
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Benkreira, H. & Patel, R. 1993 Direct gravure roll coating. Chem. Engng Sci. 48 (12), 23292335.
Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid Interface Sci. 299 (1), 113.
Cairncross, R. A., Schunk, P. R., Baer, T. A., Rao, R. R. & Sackinger, P. A. 2000 A finite element method for free surface flows of incompressible fluids in three dimensions. Part 1. Boundary fitted mesh motion. Intl J. Numer. Meth. Fluids 33, 375403.
Campana, D. M., Ubal, S., Giavedoni, M. D. & Saita, F. A. 2007 Stability of the steady motion of a liquid plug in a capillary tube. Ind. Engng Chem. Res. 46, 18031809.
Christodoulou, K. N., Kistler, S. F. & Schunk, P. R. 1997 Advances in Computational Methods for Free-Surface Flows. Chapman Hall.
Christodoulou, K. N. & Scriven, L. E. 1992 Discretization of free surface flows and other moving boundary problems. J. Comput. Phys. 99 (1), 3955.
Chuang, H.-K., Lee, C.-C. & Liu, T.-J. 2008 An experimental study of the pick-up of scaled-up gravure cells. Intl Polym. Process. 23, 216222.
Chung, D.-Y., Huang, J., Bradley, D. C. & Campbel, A. J. 2010 High performance, flexible polymer light-emitting diodes (pleds) with gravure contact printed hole injection and light emitting layers. Org. Electron. 11, 10881095.
COMSOL Multiphysics 1998–2013 Comsol. http://www.comsol.com/.
Darhuber, A. A., Troian, S. M. & Wagner, S. 2001 Physical mechanisms governing pattern fidelity in microscale offset printing. J. Appl. Phys. 90 (7), 36023609.
Ding, J. M., Vornbrock, A. F., Ting, C. & Subramanian, V. 2009 Patternable polymer bulk heterojunction photovoltaic cells on plastic by rotogravure printing. Solar Energy Mater. Solar Cells 93, 459464.
Dodds, S.2011 Stretching and slipping liquid bridges: liquid transfer in industrial printing. PhD thesis, University of Minnesotta.
Dodds, S., Carvalho, M. S. & Kumar, S. 2009 Stretching and slipping of liquid bridges near plates and cavities. Phys. Fluids 21, 092103.
Dodds, S., Carvalho, M. S. & Kumar, S. 2011 Stretching liquid bridges with moving contact lines: the role of inertia. Phys. Fluids 23, 092101.
Dodds, S., Carvalho, M. S. & Kumar, S. 2012 The dynamic of three-dimensional liquid bridges with pinned and moving contact lines. J. Fluid Mech. 707, 521540.
Gupta, C., Mensing, G. A., Shannon, M. A. & Kenis, P. J. A. 2007 Double transfer printing of small volumes of liquids. Langmuir 23, 29062914.
Hoda, N. & Kumar, S. 2008 Boundary integral simulations of liquid emptying from a model gravure cell. Phys. Fluids 20, 092106.
Huang, W.-X., Lee, S.-H., Sung, H. J., Lee, T.-M. & Kim, D.-S. 2008 Simulation of liquid transfer between separating walls for modelling micro-gravure-offset printing. Intl J. Heat Fluid Flow 29, 14361446.
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85101.
Kang, H. W., Sung, H. J., Lee, T.-M., Kim, D.-S. & Kim, C.-J. 2009 Liquid transfer between two separating plates for micro-gravure-offset printing. J. Micromech. Microengng 19, 015025.
Kapur, N. 2003 A parametric study of direct gravure coating. Chem. Engng Sci. 58, 28752882.
Krebs, F. 2009 Fabrication and processing of polymer solar cells: a review of printing and coating techniques. Solar Energy Mater. Solar Cells 93, 394412.
Lai, W. M., Rubin, D. & Krempl, E. 1999 Introduction to Continuum Mechanics. 3rd edn Butterworth-Heinemann.
Lamb, S. H. 1975 Hydrodynamics. 6th edn Cambridge University Press, London, UK.
Lee, T.-M., Lee, S.-H., Noh, J.-H., Kim, D.-S. & Chun, S. 2010a The effect of shear force on ink transfer in gravure offset printing. J. Micromech. Microengng 20 (125026), 18.
Lee, T.-M., Noh, J.-H., Kim, C. H., Jo, J. & Kim, D.-S. 2010b Development of a gravure offset printing system for the printing electrodes of flat panel display. Thin Solid Films 518, 33553359.
Powell, C. A., Savage, M. D. & Guthrie, J. T. 2002 Computational simulation of the printing of Newtonian liquid from a trapezoidal cavity. Intl J. Numer. Meth. Heat Fluid Flow 12 (4), 338355.
Pudas, M., Hagberg, J. & Leppävuori, S. 2004a Gravure offset printing of polymer inks for conductors. Prog. Org. Coat. 49, 324335.
Pudas, M., Hagberg, J. & Leppävuori, S. 2004b Printing parameters and ink components affecting ultra-fine-line gravure-offset printing for electronics applications. J. Eur. Ceram. Soc. 24, 29432950.
Pulkrabek, W. W. & Munter, J. D. 1983 Knurl roll design for stable rotogravure coating. Chem. Engng Sci. 38 (8), 13091314.
Santa-Nokki, H., Kallioinen, J., Kololuoma, T., Tuboltsev, V. & Korppi-Tommola, J. 2006 Dynamic preparation of films for fabrication of dye-sensitized solar cells. J. Photoch. Photobio. A 182, 187191.
Schenk, O. & Gärtner, K. 2004 Solving unsymmetric sparse systems of linear equations with PARDISO. J. Future Gener. Comput. Syst. 20 (3), 475487.
Shikhmurzaev, Y. D. 2006 Singularities at the moving contact line. Mathematical, physical and computational aspects. Physica D 217 (2), 121133.
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269292.
Sprittles, J. E. & Shikhmurzaev, Y. D. 2012 Finite element framework for describing dynamic wetting phenomena. Intl J. Numer. Meth. Fluids 68, 12571298.
Ubal, S., Xu, B., Derby, B. & Grassia, P. 2012 Continuous deposition of a liquid thread onto a moving substrate. Numerical analysis and comparison with experiments. J. Fluids Engng 134 (2), 021301.
Weinstein, S. J. & Ruschak, K. J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36, 2953.
Yin, X. & Kumar, S. 2006 Flow visualization of the liquid-emptying process in scaled-up gravure grooves and cells. Chem. Engng Sci. 61, 11461156.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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