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Delaying the onset of dynamic wetting failure through meniscus confinement

  • Eric Vandre (a1), Marcio S. Carvalho (a2) and Satish Kumar (a1)
Abstract

Dynamic wetting is crucial to processes where liquid displaces another fluid along a solid surface, such as the deposition of a coating liquid onto a moving substrate. Numerous studies report the failure of dynamic wetting past some critical process speed. However, the hydrodynamic factors that influence the transition to wetting failure remain poorly understood from an empirical and theoretical perspective. The objective of this investigation is to determine the effect of meniscus confinement on the onset of dynamic wetting failure. A novel experimental system is designed to simultaneously view confined and unconfined wetting systems as they approach wetting failure. The experimental apparatus consists of a scraped steel roll that rotates into a bath of glycerol. Confinement is imposed via a gap formed between a coating die and the roll surface. Flow visualization is used to record the critical roll speed at which wetting failure occurs. Comparison of the confined and unconfined data shows a clear increase in the relative critical speed as the meniscus becomes more confined. A hydrodynamic model for wetting failure is developed and analysed with (i) lubrication theory and (ii) a two-dimensional finite-element method (FEM). Both approaches do a remarkable job of matching the observed confinement trend, but only the two-dimensional model yields accurate estimates of the absolute values of the critical speeds due to the highly two-dimensional nature of the stress field in the displacing liquid. The overall success of the hydrodynamic model suggests a wetting failure mechanism primarily related to viscous bending of the meniscus.

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Corresponding author
Email addresses for correspondence: msc@puc-rio.br, kumar030@umn.edu
References
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1. Abràmoff, M. D., Magalhães, P. J. & Ram, S. J. 2004 Image processing with imagej. Biophoton. Intl 11, 3642.
2. Benkreira, H. & Ikin, J. B. 2010 Dissolution and growth of entrained bubbles when dip coating in a gas under reduced pressure. Chem. Engng Sci. 65, 58215829.
3. Benkreira, H. & Khan, M. I. 2008 Air entrainment in dip coating under reduced air pressures. Chem. Engng Sci. 63, 448459.
4. Blake, T. D. 1993 Dynamic contact angles and wetting kinetics. In Wettability (ed. Berg, J. C. ). pp. 249309. Marcel Dekker.
5. Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid Interface Sci. 299, 113.
6. Blake, T. D., Bracke, M. & Shikhmurzaev, Y. D. 1999 Experimental evidence of non-local hydrodynamic influence on the dynamic contact angle. Phys. Fluids 11, 19952007.
7. Blake, T. D., Dobson, R., Batts, G. N. & Harrison, W. J. 1995 Coating processes. US Patent no. 5391401.
8. Blake, T. D. & Ruschak, K. J. 1979 A maximum speed of wetting. Nature 282, 489491.
9. Blake, T. D. & Ruschak, K. J. 1997 Wetting: static and dynamic contact lines. In Liquid Flim Coating (ed. Kistler, S. F. & Schweizer, P. M. ). pp. 6397. Chapman & Hall.
10. Bolstad, J. H. & Keller, H. B. 1986 A multigrid continuation method for elliptic problems with folds. SIAM J. Sci. Comput. 7, 10811104.
11. Bolton, B. & Middleman, S. 1980 Air entrainment in a roll coating system. Chem. Engng Sci. 35, 597601.
12. Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739805.
13. Burley, R. & Jolly, R. P. S. 1984 Entrainment of air into liquids by a high speed continuous solid surface. Chem. Engng Sci. 39, 13571372.
14. Carlson, A., Do-Quang, M. & Amberg, G. 2011 Dissipation in rapid dynamic wetting. J. Fluid Mech. 682, 213240.
15. Carvalho, M. S. & Kheshgi, H. S. 2000 Low-flow limit in slot coating: theory and experiments. AIChE J. 46, 19071917.
16. Christodoulou, K. N., Kistler, S. F. & Schunk, P. R. 1997 Advances in computational methods for free-surface flows. In Liquid Film Coating (ed. Kistler, S. F. & Schweizer), P. M. ). pp. 297367. Chapman & Hall.
17. Christodoulou, K. N. & Scriven, L. E. 1992 Discretization of free surface flows and other moving boundary problems. J. Comput. Phys. 99, 3955.
18. Clarke, A., Bower, C. L. & Goppert, K. E. 2003 Apparatus and method of coating a web. US Patent no. 6638576 B2.
19. Clarke, A. & Stattersfield, E. 2006 Direct evidence supporting non-local hydrodynamic influence on the dynamic contact angle. Phys. Fluids 18, 048106.
20. Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169194.
21. Delon, G., Fermigier, M., Snoeijer, J. H. & Andreotti, B. 2008 Relaxation of a dewetting contact line. Part 2. Experiments. J. Fluid Mech. 604, 5575.
22. Dussan V, E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371400.
23. Dussan V, E. B. & Davis, S. H. 1974 On the motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 65, 7195.
24. Eggers, J. 2001 Air entrainment through free-surface cusps. Phys. Rev. Lett. 86, 42904293.
25. Eggers, J. 2004 Toward a description of contact line motion at higher capillary numbers. Phys. Fluids 16, 34913494.
26. Eggers, J. 2005 Existence of receding and advancing contact lines. Phys. Fluids 17, 082106.
27. Eggers, J. & Courrech du Pont, S. 2009 Numerical analysis of tips in viscous flow. Phys. Rev. E 79, 066311.
28. Ernst, R. C., Watkins, C. H. & Ruwe, H. H. 1936 The physical properties of the ternary system ethyl alcohol–glycerin–water. J. Phys. Chem. 40, 627635.
29. de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827863.
30. Gutoff, E. B. & Kendrick, C. E. 1982 Dynamic contact angles. AIChE J. 28, 459466.
31. Gutoff, E. B. & Kendrick, C. E. 1987 Low flow limits of coatability on a slide coater. AIChE J. 33, 141145.
32. Hens, J. & Abbenyen, W. V. 1997 Slide coating. In Liquid Film Coating (ed. Kistler, S. F. & Schweizer, P. M. ), pp. 427462. Chapman & Hall.
33. Hoffman, R. L. 1975 A study of the advancing interface. i. Interface shape in liquid–gas systems. J. Colloid Interface Sci. 50, 228241.
34. Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85101.
35. Jacqmin, D. 2004 Onset of wetting failure in liquid–liquid systems. J. Fluid Mech. 517, 209228.
36. Jennings, S. G. 1988 The mean free path in air. J. Aerosol Sci. 19, 159166.
37. Kistler, S. F. 1993 Hydrodynamics of wetting. In Wettability (ed. Berg, C. ), pp. 311429. Marcel Dekker.
38. Krechetnikov, R. 2010 On application of lubrication approximations to non-unidirectional coating flows with clean and surfactant interfaces. Phys. Fluids 22, 092102.
39. Kuck, V. J. & Simpkins, P. G. 2000 Bubble prevention in coating of filaments. US Patent no. 6131416.
40. Lauga, E., Brenner, M. P. & Stone, H. A. 2005 Microfluidics: the no-slip boundary condition. In Handbook of Experimental Fluid Dynamics (ed. Tropea, C., Foss, J. F. & Yarin, A. ). Springer.
41. Legait, B. & Sourieau, P. 1985 Effect of geometry on advancing contact angles in fine capillaries. J. Colloid Interface Sci. 107, 1420.
42. Lowndes, J. 1980 The numerical simulation of the steady movement of a fluid meniscus in a capillary tube. J. Fluid Mech. 101, 631646.
43. Min, Q., Duan, Y.-Y., Wang, X.-D., Liang, Z.-P. & Si, C. 2011 Does macroscopic flow geometry influence wetting dynamic? J. Colloid Interface Sci. 362, 221227.
44. Miyamoto, K. & Katagiri, Y. 1997 Curtain coating. In Liquid Film Coating (ed. Kistler, S. F. & Schweizer, P. M. ), pp. 461494. Chapman & Hall.
45. Mues, W., Hens, J. & Boiy, L. 1989 Observation of a dynamic wetting process using laser-doppler velocimetry. AIChE J. 35, 15211526.
46. Nam, J. & Carvalho, M. S. 2009 Mid-gap invasion in two-layer slot coating. J. Fluid Mech. 631, 397417.
47. Neto, C., Evans, D. R., Bonaccurso, E., Butt, H.-J. & Craig, V. S. J. 2005 Boundary slip in Newtonian liquids: a review of experimental studies. Rep. Prog. Phys. 68, 28592897.
48. Ngan, C. G. & Dussan V, E. B. 1982 On the nature of the dynamic contact angle: an experimental study. J. Fluid Mech. 118, 2740.
49. Perry, R. T. 1967 Fluid mechanics of entrainment through liquid–liquid and liquid–solid junction. PhD thesis, University of Minnesota.
50. Peters, I., Snoeijer, J. H., Daerr, A. & Limat, L. 2009 Coexistence of two singularities in dewetting flows: regularizing the corner tip. Phys. Rev. Lett. 103, 114501.
51. Quiel, R. R., Gros, A. E., Finnicum, D. S. & Joos, F. M. 2003 Slide bead coating method. US Patent no. 6511711 B2.
52. Ralston, J., Popescu, M. & Sedev, R. 2008 Dynamics of wetting from an experimental point of view. Annu. Rev. Mater. Res. 38, 2343.
53. Ravinutala, S. & Polymeropoulos, C. 2002 Entrance meniscus in a pressurized optical fibre coating applicator. Exp. Therm. Fluid Sci. 26, 573580.
54. Savelski, M. J., Shetty, S. A., Kolb, W. B. & Cerro, R. L. 1995 Flow patterns associated with the steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 176, 117127.
55. Sbragaglia, M., Sugiyama, K. & Biferale, L. 2008 Wetting failure and contact line dynamics in a Couette flow. J. Fluid Mech. 614, 471493.
56. Severtson, Y. C. & Aidun, C. K. 1996 Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems. J. Fluid Mech. 312, 173200.
57. Shikhmurzaev, Y. D. 1993 The moving contact line on a solid surface. Intl J. Multiphase Flow 19, 589610.
58. Shikhmurzaev, Y. D. 2008 Capillary Flows with Forming Interfaces. Chapman & Hall/CRC.
59. Silliman, W. J. & Scriven, L. E. 1980 Separating flow near a static contact line: slip at a wall and shape of a free surface. J. Comput. Phys. 34, 287313.
60. Simpkins, P. G. & Kuck, V. J. 2000 Air entrapment in coatings by way of tip-streaming meniscus. Nature 403, 641643.
61. Simpkins, P. G. & Kuck, V. J. 2003 On air entrainment in coatings. J. Colloid Interface Sci. 263, 562571.
62. Snoeijer, J. H. & Andreotti, B. 2008 A microscopic view on contact angle selection. Phys. Fluids 20, 057101.
63. Snoeijer, J. H., Andreotti, B., Delon, G. & Fermigier, M. 2007a Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation. J. Fluid Mech. 579, 6383.
64. Snoeijer, J. H., Delon, G., Fermigier, M. & Andreotti, B. 2006 Avoided critical behaviour in dynamically forced wetting. Phys. Rev. Lett. 96, 174504.
65. Snoeijer, J. H., Le Grand-Piteira, N., Limat, L., Stone, H. A. & Eggers, J. 2007b Cornered drops and rivulets. Phys. Fluids 19, 042104.
66. Snoeijer, J. H., Rio, E., Le Grand, N. & Limat, L. 2005 Self-similar flow and contact line geometry at the rear of cornered drops. Phys. Fluids 17, 072101.
67. Sprittles, J. E. & Shikhmurzaev, Y. D. 2012 Finite element framework for describing dynamic wetting phenomena. Intl J. Numer. Meth. Fluids 68, 12571298.
68. Tilton, J. N. 1988 The steady motion of an interface between two viscous liquids in a capillary tube. Chem. Engng Sci. 43, 13711384.
69. Voinov, O. V. 1976 Hydrodynamics of wetting. Fluid Dyn. 11, 714721.
70. Weinstein, S. J. & Ruschak, K. J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36, 2953.
71. Wilkinson, W. L. 1975 Entrainment of air by a solid surface entering a liquid/air interface. Chem. Engng Sci. 30, 12271230.
72. Wilson, M. C. T., Summers, J. L., Shikhmurzaev, Y. D., Clarke, A. & Blake, T. D. 2006 Non-local hydrodynamic influence on the dynamic contact angle: slip models versus experiment. Phys. Rev. E 73, 041606.
73. Yamamura, M. 2007 Assisted dynamic wetting in liquid coatings. Colloids Surf. A: Physicochemical and Engineering Aspects 311, 5560, Engineering Particle Technology.
74. Yue, P. & Feng, J. J. 2011 Can diffuse-interface models quantitatively describe moving contact lines? Eur. Phys. J. – Special Topics 197, 3746.
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