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Simultaneous liquid flow and drying on rotating cylinders

Chance Parrish and Satish Kumar*

  • Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA

  • *Corresponding author: kumar030@umn.edu
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Phys. Rev. Fluids 5, 034001 – Published 4 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.034001

Abstract

The coating and drying of nonflat discrete objects is a key manufacturing step for a wide variety of products. Flow of a thin nonvolatile liquid film on the outside of a rotating cylinder is commonly used as a model problem to study the coating of discrete objects. However, the behavior of a volatile particle-laden coating remains an important open problem. In this work we use lubrication theory to study the evolution of a liquid film laden with colloidal particles in the presence of solvent evaporation. Two coupled evolution equations describing variations in coating thickness and composition as a function of time and the angular coordinate are solved numerically. In the limit of a rapidly rotating cylinder, gravitational effects are negligible and linear stability analysis and nonlinear simulations demonstrate that nonuniform drying at higher drying rates may cause thickness and composition disturbances to regrow after initially decaying. When gravitational effects are significant, poor liquid redistribution at lower rotation rates and higher drying rates leads to less uniform coatings. Colloidal particles hinder liquid redistribution at high concentrations by increasing the viscosity, but help prevent rupture of the coating at more moderate concentrations. A parametric study reveals that both thickness and composition variations are minimized at high rotation rate, low drying rate, and moderate initial particle concentration.

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References (55)

  1. D. Castro, S. Wu, K. L. Woolbright, K. W. Scheinpflug, S. F. A. Hossainy, and L. Chen, Apparatus and method for depositing a coating onto a surface of a prosthesis, U.S. Patent No. 6,395,326 (28 May 2002).
  2. P. Heller, A. Heldman, J. Foehlich, and D. Kim, Method and apparatus for coating an endoprosthesis, U.S. Patent Application No. 20030215564 (pending).
  3. Y. Chen and H. Ho, System and method for coating an implantable medical device, U.S. Patent No. 7,563,324 (21 July 2009).
  4. R. A. Chappa, A. G. Bach, and M. Macgregor, Apparatus and methods for coating medical devices, U.S. Patent No. 9,623,215 (18 April 2017).
  5. S. M. Benjamin, S. M. Bennett, J. C. Bew, and J. L. Swank, Process for preparing a sugar coating on an irregular shaped confection, U.S. Patent Application No. 20080026131 (pending).
  6. D. N. Cade and D. H. Xiongwei, Hydroxypropyl methyl cellulose hard capsules and process of manufacture, U.S. Patent No. 9,655,860 (23 May 2017).
  7. A. Lee, P. T. Brun, J. Marthelot, G. Balestra, F. Gallaire, and P. M. Reis, Fabrication of slender elastic shells by the coating of curved surfaces, Nat. Commun. 7, 11155 (2016).
  8. N. Keefer and B. Bosch, Molded fuel tank and method of manufacturing the same, U.S. Patent No. 10,023,322 (17 July 2018).
  9. N. Fujitaka and A. Kobayashi, Rotational-molded resin fuel tank, U.S. Patent Application No. 20060068139 (pending).
  10. C. M. Cardinal, Y. D. Jung, K. H. Ahn, and L. F. Francis, Drying regime maps for particulate coatings, AIChE J. 56, 2769 (2010).
  11. P. L. Evans, L. W. Schwartz, and R. V. Roy, Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Two-dimensional theoretical and numerical modeling, Phys. Fluids 16, 2742 (2004).
  12. P. L. Evans, L. W. Schwartz, and R. V. Roy, Three-dimensional solutions for coating flow on a rotating horizontal cylinder: Theory and experiment, Phys. Fluids 17, 072102 (2005).
  13. H. K. Moffatt, Behaviour of a viscous film on the outer surface of a rotating cylinder, J. de Mécanique 16, 651 (1977).
  14. M. A. Kelmanson, Theoretical and experimental analyses of the maximum-supportable fluid load on a rotating cylinder, J. Eng. Math. 29, 271 (1995).
  15. L. Preziosi and D. D. Joseph, The run-off condition for coating and rimming flows, J. Fluid Mech. 187, 99 (1988).
  16. E. J. Hinch and M. A. Kelmanson, On the decay and drift of free-surface perturbations in viscous thin-film flow exterior to a rotating cylinder, Proc. R. Soc. London A 459, 1193 (2003).
  17. V. V. Pukhnachev, Motion of a liquid film on the surface of a rotating cylinder in a gravitational field, J. Appl. Mech. Tech. Phys. 18, 344 (1977).
  18. T. P. Hynes, Stability of thin films, Ph.D. thesis, University of Cambridge, 1978.
  19. E. A. Karabut, Two regimes of liquid film flow on a rotating cylinder, J. Appl. Mech. Tech. Phys. 48, 55 (2007).
  20. W. Li and S. Kumar, Three-dimensional surfactant-covered flows of thin liquid films on rotating cylinders, J. Fluid Mech. 844, 61 (2018).
  21. A. v. B. Lopes, U. Thiele, and A. L. Hazel, On the multiple solutions of coating and rimming flows on rotating cylinders, J. Fluid Mech. 835, 540 (2018).
  22. M. A. Kelmanson, On inertial effects in the Moffatt-Pukhnachov coating-flow problem, J. Fluid Mech. 633, 327 (2009).
  23. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  24. A. Oron, S. H. Davis, and S. G. Bankoff, Long-scale evolution of thin liquid films, Rev. Mod. Phys. 69, 931 (1997).
  25. M. H. Eres, D. E. Weidner, and L. W. Schwartz, Three-dimensional direct numerical simulation of surface-tension-gradient effects on the leveling of an evaporating multicomponent fluid, Langmuir 15, 1859 (1999).
  26. A. Oron and P. Rosenau, Formation of patterns induced by thermocapillarity and gravity, J. Phys. II 2, 131 (1992).
  27. T. Pham, X. Cheng, and S. Kumar, Drying of multicomponent thin films on substrates with topography, J. Polym. Sci. B 55, 1681 (2017).
  28. T. Pham and S. Kumar, Drying of droplets of colloidal suspensions on rough substrates, Langmuir 33, 10061 (2017).
  29. B. Reisfeld and S. G. Bankoff, Non-isothermal flow of a liquid film on a horizontal cylinder, J. Fluid Mech. 236, 167 (1992).
  30. S. G. Yiantsios and B. G. Higgins, A mechanism of Marangoni instability in evaporating thin liquid films due to soluble surfactant, Phys. Fluids 22, 022102 (2010).
  31. S. D. Howison, J. D. Moriarty, J. R. Ockendon, E. L. Terrill, and S. K. Wilson, A mathematical model for drying paint layers, J. Eng. Math. 32, 377 (1997).
  32. J. P. Burelbach, S. G. Bankoff, and S. H. Davis, Nonlinear stability of evaporating/condensing liquid films, J. Fluid Mech. 195, 463 (1988).
  33. L. Espín and S. Kumar, Sagging of evaporating droplets of colloidal suspensions on inclined substrates, Langmuir 30, 11966 (2014).
  34. L. Espín and S. Kumar, Forced spreading of films and droplets of colloidal suspensions, J. Fluid Mech. 742, 495 (2014).
  35. B. Tsai, M. S. Carvalho, and S. Kumar, Leveling of thin films of colloidal suspensions, J. Colloid Interface Sci. 343, 306 (2010).
  36. K. J. Ruschak and L. E. Scriven, Rimming flow of liquid in a rotating cylinder, J. Fluid Mech. 76, 113 (1976).
  37. S. H. Maron and P. E. Pierce, Application of Ree-Eyring generalized flow theory to suspensions of spherical particles, J. Colloid Sci. 11, 80 (1956).
  38. I. M. Krieger and T. J. Dougherty, A mechanism for non-Newtonian flow in suspensions of rigid spheres, Trans. Soc. Rheol. 3, 137 (1959).
  39. B. R. Duffy and S. K. Wilson, Large-Biot-number non-isothermal flow of a thin film on a stationary or rotating cylinder, Eur. Phys. J.: Spec. Top. 166, 147 (2009).
  40. E. Boujo and M. Sellier, Pancake making and surface coating: Optimal control of a gravity-driven liquid film, Phys. Rev. Fluids 4, 064802 (2019).
  41. J. M. Delhaye, Jump conditions and entropy sources in two-phase systems. local instant formulation, Int. J. Multiphase Flow 1, 395 (1974).
  42. J. C. Slattery, Interfacial Transport Phenomena, 2nd ed. (Springer, New York, 2007).
  43. C. Sodtke, V. S. Ajaev, and P. Stephan, Dynamics of volatile liquid droplets on heated surfaces: Theory versus experiment, J. Fluid Mech. 610, 343 (2008).
  44. R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, Contact line deposits in an evaporating drop, Phys. Rev. E 62, 756 (2000).
  45. W. Li and S. Kumar, Thin-film coating of surfactant-laden liquids on rotating cylinders, Phys. Fluids 27, 072106 (2015).
  46. O. E. Jensen and J. B. Grotberg, The spreading of heat or soluble surfactant along a thin liquid film, Phys. Fluids A 5, 58 (1993).
  47. L. W. Schwartz, R. V. Roy, R. R. Eley, and S. Petrash, Dewetting patterns in a drying liquid film, J. Colloid Interface Sci. 234, 363 (2001).
  48. H. Ji and T. P. Witelski, Instability and dynamics of volatile thin films, Phys. Rev. Fluids 3, 024001 (2018).
  49. T. A. Driscoll, N. Hale, and L. N. Trefethen, Chebfun Guide (Pafnuty, Oxford, 2014).
  50. C. Parrish, Ph.D. thesis, University of Minnesota (unpublished).
  51. A. K. Sahu and S. Kumar, Thin-liquid-film flow on a topographically patterned rotating cylinder, Phys. Fluids 26, 042102 (2014).
  52. W. Li, M. S. Carvalho, and S. Kumar, Liquid-film coating on topographically patterned rotating cylinders, Phys. Rev. Fluids 2, 024001 (2017).
  53. W. Li, M. S. Carvalho, and S. Kumar, Viscous free-surface flows on rotating elliptical cylinders, Phys. Rev. Fluids 2, 094005 (2017).
  54. K. Maki and S. Kumar, Fast evaporation of spreading droplets of colloidal suspensions, Langmuir 27, 11347 (2011).
  55. S. G. Yiantsios and B. G. Higgins, Marangoni flows during drying of colloidal films, Phys. Fluids 18, 082103 (2006).

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Phys. Rev. Fluids 5, 034001– Published 4 March, 2020
  • Received 16 August 2019
  • Accepted 4 February 2020
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