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Spreading of rinsing liquids across a horizontal rotating substrate

Daniel J. Walls1,*,†, Andrew S. Ylitalo1,*,‡, David S. L. Mui2, John M. Frostad1,†,§, and Gerald G. Fuller1,∥

  • 1Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA
  • 2Lam Research Corporation, Fremont, California 94538, USA

  • *D.J.W. and A.S.Y. contributed equally to this work.
  • †Present address: Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z3, Canada.
  • ‡Present address: Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States.
  • §jfrostad@mail.ubc.ca; Present address: Food Science, University of British Columbia, Vancouver, British Columbia V6T 1Z3, Canada.
  • ∥ggf@stanford.edu
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Phys. Rev. Fluids 4, 084102 – Published 7 August, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.084102

Abstract

‘‘Rinsing” liquids and their dynamics are interesting both fundamentally in the interaction of several classic modes of spreading, and industrially in a variety of cleaning applications, such as in the manufacturing of silicon wafers. In this paper, we investigate the time-dependent spreading behavior of a rinsing liquid across a horizontal, rotating substrate; the rinsing liquid is applied to the center of the rotating substrate as an orthogonal impinging jet of constant volumetric flow. We present experimental findings on the azimuthally averaged outer radius of the spreading liquid, in which we observed four distinct growth behaviors in time. We use lubrication theory to explain these phenomena and to define boundaries within the explored parameter space where each was observed. In the absence of rotation, capillarity dominates and the spreading radius grows as t4/10. When centrifugal forces dominate the spreading process, several time dependencies of the spreading radius are possible, with lubrication theory predicting exponential growth as well as power laws of t3/4 and t3/2.

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References (38)

  1. C. Huh and L. E. Scriven, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, J. Colloid Interface Sci. 35, 85 (1971).
  2. O. V. Voinov, Hydrodynamics of wetting, Fluid Dyn. 11, 714 (1976).
  3. L. H. Tanner, The spreading of silicone oil drops on horizontal surfaces, J. Phys. D 12, 1473 (1979).
  4. R. G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow, J. Fluid Mech. 168, 169 (1986).
  5. N. Didden and T. Maxworthy, The viscous spreading of plane and axisymmetric gravity currents, J. Fluid Mech. 121, 27 (1982).
  6. H. E. Huppert, The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface, J. Fluid Mech. 121, 43 (1982).
  7. A.-M. Cazabat, How does a droplet spread?, Contemp. Phys. 28, 347 (1987).
  8. J.-F. Joanny and D. Andelman, Steady-state motion of a liquid/liquid/solid contact line, J. Colloid Interface Sci. 119, 451 (1987).
  9. L. M. Pismen and J. Eggers, Solvability condition for the moving contact line, Phys. Rev. E 78, 056304 (2008).
  10. A. Eddi, K. G. Winkels, and J. H. Snoeijer, Short time dynamics of viscous drop spreading, Phys. Fluids 25, 013102 (2013).
  11. D. J. Walls, S. J. Haward, A. Q. Shen, and G. G. Fuller, Spreading of miscible liquids, Phys. Rev. Fluids 1, 013904 (2016).
  12. D. J. Walls, E. Meiburg, and G. G. Fuller, The shape evolution of liquid droplets in miscible environments, J. Fluid Mech. 852, 422 (2018).
  13. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  14. A. G. Emslie, F. T. Bonner, and L. G. Peck, Flow of a viscous liquid on a rotating disk, J. Appl. Phys. 29, 858 (1958).
  15. F. Melo, J.-F. Joanny, and S. Fauve, Fingering Instability of Spinning Drops, Phys. Rev. Lett. 63, 1958 (1989).
  16. S. M. Troian, E. Herbolzheimer, S. A. Safran, and J.-F. Joanny, Fingering instabilities of driven spreading films, Europhys. Lett. 10, 25 (1989).
  17. N. Fraysse and G. M. Homsy, An experimental study of rivulet instabilities in centrifugal spin coating of viscous Newtonian and non-Newtonian fluids, Phys. Fluids 6, 1491 (1994).
  18. M. A. Spaid and G. M. Homsy, Stability of Newtonian and viscoelastic dynamic contact lines, Phys. Fluids 8, 460 (1996).
  19. M. A. Spaid and G. M. Homsy, Stability of viscoelastic dynamic contact lines: An experimental study, Phys. Fluids 9, 823 (1997).
  20. S. K. Wilson, R. Hunt, and B. R. Duffy, The rate of spreading in spin coating, J. Fluid Mech. 413, 65 (2000).
  21. I. S. McKinley, S. K. Wilson, and B. R. Duffy, Spin coating and air-jet blowing of thin viscous drops, Phys. Fluids 11, 30 (1999).
  22. I. S. McKinley and S. K. Wilson, The linear stability of a drop of fluid during spin coating or subject to a jet of air, Phys. Fluids 14, 133 (2002).
  23. K. E. Holloway, P. Habdas, N. Semsarillar, K. Burfitt, and J. R. de Bruyn, Spreading and fingering in spin coating, Phys. Rev. E 75, 046308 (2007).
  24. T. T. Hsu, T. W. Walker, C. W. Frank, and G. G. Fuller, Role of fluid elasticity on the dynamics of rinsing flow by an impinging jet, Phys. Fluids 23, 033101 (2011).
  25. T. W. Walker, T. T. Hsu, C. W. Frank, and G. G. Fuller, Role of shear-thinning on the dynamics of rinsing flow by an impinging jet, Phys. Fluids 24, 093102 (2012).
  26. L. Rayleigh, On the theory of long waves and bores, Proc. Royal Soc. Lond. A 90, 324 (1914).
  27. E. J. Watson, The radial spread of a liquid jet over a horizontal plane, J. Fluid Mech. 20, 481 (1964).
  28. A. D. D. Craik, R. C. Latham, M. J. Fawkes, and P. W. F. Gribbon, The circular hydraulic jump, J. Fluid Mech. 112, 347 (1981).
  29. R. I. Bowles and F. T. Smith, The standing hydraulic jump: Theory, computations and comparisons with experiments, J. Fluid Mech. 242, 145 (1992).
  30. X. Liu and J. H. Lienhard, The hydraulic jump in circular jet impingement and in other thin liquid films, Exp. Fluids 15, 108 (1993).
  31. F. J. Higuera, The hydraulic jump in a viscous laminar flow, J. Fluid Mech. 274, 69 (1994).
  32. C. Ellegaard, A. E. Hansen, A. Haaning, K. Hansen, A. Marcussen, T. Bohr, J. L. Hansen, and S. Watanabe, Creating corners in kitchen sinks, Nature (London) 392, 767 (1998).
  33. K. Yokoi and F. Xiao, Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps, Phys. Rev. E 61, R1016 (2000).
  34. J. W. M. Bush, J. M. Aristoff, and A. E. Hosoi, An experimental investigation of the stability of the circular hydraulic jump, J. Fluid Mech. 558, 33 (2006).
  35. J. W. M. Bush and J. M. Aristoff, The influence of surface tension on the circular hydraulic jump, J. Fluid Mech. 489, 229 (2003).
  36. L. G. Leal, Advanced Transport Phenomena (Cambridge University Press, Cambridge, 2007).
  37. A. S. Ylitalo, D. J. Walls, D. S. L. Mui, J. M. Frostad, and G. G. Fuller, Evolution of rivulets during spreading of an impinging water jet on a rotating, precoated substrate, Phys. Fluids 31, 082104 (2019).
  38. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967).

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Phys. Rev. Fluids 4, 084102– Published 7 August, 2019
  • Received 6 December 2018
Article part of CHORUS
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