Hostname: page-component-76d6cb85b7-hqrjx Total loading time: 0 Render date: 2026-07-12T00:06:28.381Z Has data issue: false hasContentIssue false
  • English
  • Français

Confinement effects in dip coating

Published online by Cambridge University Press:  18 August 2017

Onyu Kim Open the ORCID record for Onyu Kim [Opens in a new window]  and
Jaewook Nam Open the ORCID record for Jaewook Nam [Opens in a new window]
Onyu Kim
Affiliation:
Department of Chemical Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do 16419, Korea
Jaewook Nam*
Affiliation:
Department of Chemical Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do 16419, Korea
*
†Email address for correspondence: jaewooknam@skku.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

When a flat plate is withdrawn from a liquid pool, a liquid film is deposited on the plate. This simple process is called dip coating. In the case of vertically upward withdrawal, gravity competes with the surface tension and viscous drag, and the balance between those determine the meniscus shape and hence the film thickness. Most of the previous studies on dip coating assumed that the pool is sufficiently large so that the stationary container wall does not affect the film thickness. However, the cases where the stationary wall affects the entrained film have not been examined thoroughly so far. In this confined dip coating, the film thickness deviates from that of unconfined dip coating under the same conditions such as the withdrawal speed and the physical properties of the liquid. The meniscus in a confined pool is more curved than that in an unconfined pool owing to wetting on the stationary wall, which is parallel to the plate. Besides, a channel between the moving plate and the stationary wall appears; therefore, the flow inside the channel should be included in an analysis of confined dip coating. In the present study, we analyse the mechanism that determines the film thickness, both theoretically and numerically.

JFM classification

Interfacial Flows (free surface): Capillary flows Materials Processing Flows: Coating Interfacial Flows (free surface): Thin films

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , pp. 1 - 30
Check for updates
Copyright
© 2017 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.)

Article purchase

Temporarily unavailable

References

Abedijaberi, A., Bhatara, G., Shaqfeh, E. S. G. & Khomami, B. 2011 A computational study of the influence of viscoelasticity on the interfacial dynamics of dip coating flow. J. Non-Newton. Fluid Mech. 166, 614–627.Google Scholar
Afanasiev, K., Münch, A. & Wagner, B. 2007 Landau–Levich problem for non-Newtonian liquids. Phys. Rev. E 76, 036307.Google Scholar
Ahn, K., Kim, D., Kim, O. & Nam, J. 2015 Analysis of transparent conductive silver nanowire films from dip coating flow. J. Coat. Technol. Res. 12, 855–862.Google Scholar
Benilov, E. S., Chapman, S. J., Mcleod, J. B., Ockendon, J. R. & Zubkov, V. S. 2010 On liquid films on an inclined plate. J. Fluid Mech. 663, 53–69.CrossRefGoogle Scholar
Benilov, E. S. & Zubkov, V. S. 2008 On the drag-out problem in liquid film theory. J. Fluid Mech. 617, 283–299.Google Scholar
Blake, T. D. & Ruschak, K. J. 1979 A maximum speed of wetting. Nature 282, 489–491.Google Scholar
Bolstad, J. H. & Keller, H. B. 1986 A multigrid continuation method for elliptic problems with folds. SIAM J. Sci. Stat. Comput. 7, 1081–1104.CrossRefGoogle Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.Google Scholar
Campana, D. M., Ubal, S., Giavedoni, M. D. & Saita, F. A. 2010 Numerical prediction of the film thickening due to surfactants in the Landau–Levich problem. Phys. Fluids 22, 032103.CrossRefGoogle Scholar
Campana, D. M., Ubal, S., Giavedoni, M. D. & Saita, F. A. 2013 Dip coating of fibers in the visco-inertial regime: numerical analysis. Ind. Engng Chem. Res. 52, 12646–12653.Google Scholar
Carvalho, M. S. & Kheshgi, H. S. 2006 Low-flow limit in slot coating: theory and experiments. AIChE J. 46, 1907–1917.Google Scholar
Coyle, D. J. 1997 Knife and roll coating. In Liquid Film Coating, pp. 539–571. Springer.Google Scholar
Dixit, H. N. & Homsy, G. M. 2013a The elastic Landau–Levich problem. J. Fluid Mech. 732, 5–28.CrossRefGoogle Scholar
Dixit, H. N. & Homsy, G. M. 2013b The elastocapillary Landau–Levich problem. J. Fluid Mech. 735, 1–28.Google Scholar
Duff, I. S., Erisman, A. M. & Reid, J. K. 1989 Direct Methods for Sparse Matrices. Oxford University Press.Google Scholar
Esmail, M. N. & Hummel, R. L. 1975a A note on linear solutions to free coating onto a vertical surface. Chem. Engng Sci. 30, 1195–1196.Google Scholar
Esmail, M. N. & Hummel, R. L. 1975b Nonlinear theory of free coating onto a vertical surface. AIChE J. 21, 958–965.Google Scholar
Filali, A., Khezzar, L. & Mitsoulis, E. 2013 Some experiences with the numerical simulation of Newtonian and Bingham fluids in dip coating. Comput. Fluids 82, 110–121.CrossRefGoogle Scholar
Gao, P., Li, L., Feng, J. J., Ding, H. & Lu, X.-Y. 2016 Film deposition and transition on a partially wetting plate in dip coating. J. Fluid Mech. 791, 358–383.Google Scholar
Hocking, L. M. 2001 Meniscus draw-up and draining. Eur. J. Appl. Maths 12, 195–208.Google Scholar
Javidi, M., Pope, M. A. & Hrymak, A. N. 2016 Investigation on dip coating process by mathematical modeling of non-Newtonian fluid coating on cylindrical substrate. Phys. Fluids 28, 063105.Google Scholar
Jenny, M. & Souhar, M. 2009 Numerical simulation of a film coating flow at low capillary numbers. Comput. Fluids 38, 1823–1832.Google Scholar
Jin, B., Acrivos, A. & Münch, A. 2005 The drag-out problem in film coating. Phys. Fluids 17, 103603.Google Scholar
Kamotani, Y., Ostrach, S. & Kizito, J. P. 1999 Experimental free coating flows at high Capillary and Reynolds number. Exp. Fluids 27, 235–243.Google Scholar
Kheshgi, H. S., Kistler, S. F. & Scriven, L. E. 1992 Rising and falling film flows: viewed from a first-order approximation. Chem. Engng Sci. 47, 683–694.Google Scholar
Krechetnikov, R. & Homsy, G. M. 2005 Experimental study of substrate roughness and surfactant effects on the Landau–Levich law. Phys. Fluids 17, 102108.Google Scholar
Krechetnikov, R. & Homsy, G. M. 2006 Surfactant effects in the Landau–Levich problem. J. Fluid Mech. 559, 429–450.Google Scholar
Landau, L. & Levich, V. G. 1942 Dragging of a liquid by a moving plate. Acta Physiochim. USSR 17, 42–54.Google Scholar
Lee, C. Y. & Tallmadge, J. A. 1974 Meniscus shapes in withdrawal of flat sheets from liquid baths. Dynamic profile data at low Capillary numbers. Ind. Engng Chem. Fundam. 13, 356–360.Google Scholar
Maillard, M., Bleyer, J., Andrieux, A. L., Boujlel, J. & Coussot, P. 2016 Dip-coating of yield stress fluids. Phys. Fluids 28, 053102.CrossRefGoogle Scholar
Münch, A. 2002 The thickness of a Marangoni-driven thin liquid film emerging from a meniscus. SIAM J. Appl. Maths 62, 2045–2063.Google Scholar
Münch, A. & Evans, P. L. 2005 Marangoni-driven liquid films rising out of a meniscus onto a nearly-horizontal substrate. Physica D 209, 164–177.Google Scholar
Münch, A. & Evans, P. L. 2006 Interaction of advancing fronts and meniscus profiles formed by surface-tension-gradient-driven liquid films. SIAM J. Appl. Maths 66, 1610–1631.Google Scholar
Oliver, J. F., Huh, C. & Mason, S. G. 1977 Resistance to spreading of liquids by sharp edges. J. Colloid Interface Sci. 59, 568–581.Google Scholar
Papanastasiou, T. C., Malamataris, N. & Ellwood, K. 1992 A new outflow boundary condition. Intl J. Numer. Meth. Fluids 14, 587–608.Google Scholar
Park, C.-W. & Homsy, G. M. 1984 Two-phase displacement in Hele-Shaw cells: theory. J. Fluid Mech. 139, 291–308.CrossRefGoogle Scholar
Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31, 347–384.Google Scholar
Réglat, O., Labrie, R. & Tanguy, P. A. 1993 A new free surface model for the dip coating process. J. Comput. Phys. 109, 238–246.Google Scholar
Renardy, M. 1997 Imposing ‘no’ boundary condition at outflow: why does it work? Intl J. Numer. Meth. Fluids 24, 413–417.Google Scholar
Ruschak, K. J. 1985 Coating flows. Annu. Rev. Fluid Mech. 17, 65–89.Google Scholar
de Ryck, A. & Quéré, D. 1996 Inertial coating of a fibre. J. Fluid Mech. 311, 219–237.CrossRefGoogle Scholar
de Ryck, A. & Quéré, D. 1998 Gravity and inertia effects in plate coating. J. Colloid Interface Sci. 203, 278–285.Google Scholar
de Santos, J. M.1991 Two-phase cocurrent downflow through constricted passages. PhD thesis, University of Minnesota.Google Scholar
Schunk, P. R., Hurd, A. J. & Brinker, C. J. 1997 Free-meniscus coating processes. In Liquid Film Coating, pp. 673–708. Springer.Google Scholar
Scriven, L. E. 1988 Physics and applications of dip coating and spin coating. MRS Symp. Proc. 121, 717–729.Google Scholar
Snoeijer, J. H., Delon, G., Fermigier, M. & Andreotti, B. 2006 Avoided critical behavior in dynamically forced wetting. Phys. Rev. Lett. 96, 174504.Google Scholar
Snoeijer, J. H., Ziegler, J., Andreotti, B., Fermigier, M. & Eggers, J. 2008 Thick films of viscous fluid coating a plate withdrawn from a liquid reservoir. Phys. Rev. Lett. 100, 244502.Google Scholar
Spiers, R. P., Subbaraman, C. V. & Wilkinson, W. L. 1974 Free coating of a Newtonian liquid onto a vertical surface. Chem. Engng Sci. 29, 389–396.Google Scholar
Tallmadge, J. A. & Soroka, A. J. 1969 The additional parameter in withdrawal. Chem. Eng. Sci. 24, 377–383.Google Scholar
Tallmadge, J. A. & Stella, R. 1968 Some properties of the apparent water paradox in entrainment. AIChE J. 14, 838–840.Google Scholar
Van Rossum, J. J. 1958 Viscous lifting and drainage of liquids. Appl. Sci. Res. 7, 121–144.Google Scholar
Vinokur, M. 1983 On one-dimensional stretching functions for finite-difference calculations. J. Comput. Phys. 50, 215–234.Google Scholar
Weinstein, S. J. & Ruschak, K. J. 2001 Dip coating on a planar non-vertical substrate in the limit of negligible surface tension. Chem. Eng. Sci. 56, 4957–4969.Google Scholar
White, D. A. & Tallmadge, J. A. 1965 Theory of drag out of liquids on flat plates. Chem. Engng Sci. 20, 33–37.Google Scholar
Wilson, S. D. R. 1982 The drag-out problem in film coating theory. J. Engng Maths 16, 209–221.Google Scholar