Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T21:08:59.435Z Has data issue: false hasContentIssue false
  • English
  • Français

Liquid transfer from single cavities to rotating rolls

Published online by Cambridge University Press:  23 April 2014

Diego M. Campana  and
Marcio S. Carvalho
Diego M. Campana
Affiliation:
Instituto de Desarrollo Tecnológico para la Industria Química (INTEC-CONICET), Güemes 3450, Santa Fe (3000), República Argentina Department of Mechanical Engineering, Pontifícia Universidade Católica do Rio de Janeiro (PUC-RIO), Rio de Janeiro, RJ 22453-900, Brazil
Marcio S. Carvalho*
Affiliation:
Department of Mechanical Engineering, Pontifícia Universidade Católica do Rio de Janeiro (PUC-RIO), Rio de Janeiro, RJ 22453-900, Brazil
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Liquid bridges
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 545 - 571
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benkreira, H. & Patel, R. 1993 Direct gravure roll coating. Chem. Engng Sci. 48 (12), 2329–2335.CrossRefGoogle Scholar
Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid Interface Sci. 299 (1), 1–13.Google Scholar
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, 375–403.3.0.CO;2-O>CrossRefGoogle Scholar
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, 1803–1809.Google Scholar
Christodoulou, K. N., Kistler, S. F. & Schunk, P. R. 1997 Advances in Computational Methods for Free-Surface Flows. Chapman Hall.Google Scholar
Christodoulou, K. N. & Scriven, L. E. 1992 Discretization of free surface flows and other moving boundary problems. J. Comput. Phys. 99 (1), 39–55.CrossRefGoogle Scholar
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, 216–222.Google Scholar
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, 1088–1095.CrossRefGoogle Scholar
COMSOL Multiphysics 1998–2013 Comsol. http://www.comsol.com/.Google Scholar
Darhuber, A. A., Troian, S. M. & Wagner, S. 2001 Physical mechanisms governing pattern fidelity in microscale offset printing. J. Appl. Phys. 90 (7), 3602–3609.CrossRefGoogle Scholar
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, 459–464.Google Scholar
Dodds, S.2011 Stretching and slipping liquid bridges: liquid transfer in industrial printing. PhD thesis, University of Minnesotta.Google Scholar
Dodds, S., Carvalho, M. S. & Kumar, S. 2009 Stretching and slipping of liquid bridges near plates and cavities. Phys. Fluids 21, 092103.Google Scholar
Dodds, S., Carvalho, M. S. & Kumar, S. 2011 Stretching liquid bridges with moving contact lines: the role of inertia. Phys. Fluids 23, 092101.Google Scholar
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, 521–540.Google Scholar
Gupta, C., Mensing, G. A., Shannon, M. A. & Kenis, P. J. A. 2007 Double transfer printing of small volumes of liquids. Langmuir 23, 2906–2914.Google Scholar
Hoda, N. & Kumar, S. 2008 Boundary integral simulations of liquid emptying from a model gravure cell. Phys. Fluids 20, 092106.Google Scholar
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, 1436–1446.Google Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85–101.Google Scholar
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.Google Scholar
Kapur, N. 2003 A parametric study of direct gravure coating. Chem. Engng Sci. 58, 2875–2882.Google Scholar
Krebs, F. 2009 Fabrication and processing of polymer solar cells: a review of printing and coating techniques. Solar Energy Mater. Solar Cells 93, 394–412.Google Scholar
Lai, W. M., Rubin, D. & Krempl, E. 1999 Introduction to Continuum Mechanics. 3rd edn Butterworth-Heinemann.Google Scholar
Lamb, S. H. 1975 Hydrodynamics. 6th edn Cambridge University Press, London, UK.Google Scholar
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), 1–8.Google Scholar
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, 3355–3359.Google Scholar
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), 338–355.Google Scholar
Pudas, M., Hagberg, J. & Leppävuori, S. 2004a Gravure offset printing of polymer inks for conductors. Prog. Org. Coat. 49, 324–335.Google Scholar
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, 2943–2950.Google Scholar
Pulkrabek, W. W. & Munter, J. D. 1983 Knurl roll design for stable rotogravure coating. Chem. Engng Sci. 38 (8), 1309–1314.Google Scholar
Santa-Nokki, H., Kallioinen, J., Kololuoma, T., Tuboltsev, V. & Korppi-Tommola, J. 2006 Dynamic preparation of ${\rm TiO}_2$ films for fabrication of dye-sensitized solar cells. J. Photoch. Photobio. A 182, 187–191.Google Scholar
Schenk, O. & Gärtner, K. 2004 Solving unsymmetric sparse systems of linear equations with PARDISO. J. Future Gener. Comput. Syst. 20 (3), 475–487.Google Scholar
Shikhmurzaev, Y. D. 2006 Singularities at the moving contact line. Mathematical, physical and computational aspects. Physica D 217 (2), 121–133.Google Scholar
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269–292.Google Scholar
Sprittles, J. E. & Shikhmurzaev, Y. D. 2012 Finite element framework for describing dynamic wetting phenomena. Intl J. Numer. Meth. Fluids 68, 1257–1298.Google Scholar
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.Google Scholar
Weinstein, S. J. & Ruschak, K. J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36, 29–53.Google Scholar
Yin, X. & Kumar, S. 2006 Flow visualization of the liquid-emptying process in scaled-up gravure grooves and cells. Chem. Engng Sci. 61, 1146–1156.Google Scholar