- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Modeling the dynamics of partially wetting droplets on fibers

Raymond Christianto1, Yudi Rahmawan2, Ciro Semprebon3,*, and Halim Kusumaatmaja1,†

  • 1Department of Physics, Durham University, DH1 3LE, United Kingdom
  • 2Department of Mechanical Engineering, Universitas Pertamina, Jakarta 12220, Indonesia
  • 3Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle-upon-Tyne NE1 8ST, United Kingdom

  • *ciro.semprebon@northumbria.ac.uk
  • †halim.kusumaatmaja@durham.ac.uk
PDF

Phys. Rev. Fluids 7, 103606 – Published 24 October, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.103606

Abstract

We simulate gravity-driven dynamics of partially wetting droplets moving along a fiber using the lattice Boltzmann method. For the so-called clamshell morphology, we find three possible dynamic regimes upon varying the droplet Bond number and the fiber radius: compact droplet, droplet breakup, and droplet oscillation. For small Bond numbers, in the compact droplet regime, the droplet reaches a steady state and its velocity scales linearly with the driving body force. We find two scaling laws depending on whether the droplet size is smaller or larger compared to the fiber radius. In addition, we further identify a scaling law applicable for the barrel morphology. For higher Bond numbers, in the droplet breakup regime, satellite droplets are formed trailing the initial moving droplet. We find such droplet satellite formation is easier with increasing fiber curvature (smaller fiber radius). Finally, in the droplet oscillation regime, favored in the midrange of fiber radius, the droplet shape periodically extends and contracts along the fiber.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (46)

  1. J. Ju, H. Bai, Y. Zheng, T. Zhao, R. Fang, and L. Jiang, A multi-structural and multi-functional integrated fog collection system in cactus, Nat. Commun. 3, 1247 (2012).
  2. H. Bai, J. Ju, Y. Zheng, and L. Jiang, Functional fibers with unique wettability inspired by spider silks, Adv. Mater. 24, 2786 (2012).
  3. B. J. Carroll, Droplet formation and contact angles of liquids on mammalian hair fibers, J. Chem. Soc., Faraday Trans. 1: Phys. Chem. Condensed Phases 85, 3853 (1989).
  4. F. Weyer, M. Lismont, L. Dreesen, and N. Vandewalle, Compound droplet manipulations on fiber arrays, Soft Matter 11, 7086 (2015).
  5. T. Gilet, D. Terwagne, and N. Vandewalle, Digital microfluidics on a wire, Appl. Phys. Lett. 95, 014106 (2009).
  6. R. M. Von Spreckelsen, M. T. Harris, J. M. Wigzell, R. C. Fraser, A. Carletto, D. P. Mosquin, D. Justice, and J. P. S. Badyal, Bioinspired breathable architecture for water harvesting, Sci. Rep. 5, 16798 (2015).
  7. K.-C. Park, S. S. Chhatre, S. Srinivasan, R. E. Cohen, and G. H. McKinley, Optimal design of permeable fiber network structures for fog harvesting, Langmuir 29, 13269 (2013).
  8. R. Ghosh, C. Patra, P. Singh, R. Ganguly, R. P. Sahu, I. Zhitomirsky, and I. K. Puri, Influence of metal mesh wettability on fog harvesting in industrial cooling towers, Appl. Therm. Eng. 181, 115963 (2020).
  9. L. Rayleigh, On the instability of jets, Proc. London Math. Soc. s1-10, 4 (1878).
  10. N. K. Adam, Detergent action and its relation to wetting and emulsification, J. Soc. Dyers Colour. 53, 121 (1937).
  11. H. B. Eral, J. De Ruiter, R. De Ruiter, J. M. Oh, C. Semprebon, M. Brinkmann, and F. Mugele, Drops on functional fibers: From barrels to clamshells and back, Soft Matter 7, 5138 (2011).
  12. G. McHale and M. Newton, Global geometry and the equilibrium shapes of liquid drops on fibers, Colloids Surf., A 206, 79 (2002).
  13. T.-H. Chou, S.-J. Hong, Y.-E. Liang, H.-K. Tsao, and Y.-J. Sheng, Equilibrium phase diagram of drop-on-fiber: Coexistent states and gravity effect, Langmuir 27, 3685 (2011).
  14. R. de Ruiter, J. de Ruiter, H. B. Eral, C. Semprebon, M. Brinkmann, and F. Mugele, Buoyant droplets on functional fibers, Langmuir 28, 13300 (2012).
  15. É. Lorenceau and D. Quéré, Drops on a conical wire, J. Fluid Mech. 510, 29 (2004).
  16. T. Gilet, D. Terwagne, and N. Vandewalle, Droplets sliding on fibers, Eur. Phys. J. E 31, 253 (2010).
  17. B. J. Mullins, R. D. Braddock, I. E. Agranovski, and R. A. Cropp, Observation and modelling of barrel droplets on vertical fibers subjected to gravitational and drag forces, J. Colloid Interface Sci. 300, 704 (2006).
  18. P.-B. Bintein, H. Bense, C. Clanet, and D. Quéré, Self-propelling droplets on fibers subject to a crosswind, Nat. Phys. 15, 1027 (2019).
  19. B. D. Texier and S. Dorbolo, Droplets climbing a rotating helical fiber, Eur. Phys. J. E 38, 1 (2015).
  20. J. Ju, K. Xiao, X. Yao, H. Bai, and L. Jiang, Bioinspired conical copper wire with gradient wettability for continuous and efficient fog collection, Adv. Mater. 25, 5937 (2013).
  21. Y.-E. Liang, H.-K. Tsao, and Y.-J. Sheng, Drops on hydrophilic conical fibers: Gravity effect and coexistent states, Langmuir 31, 1704 (2015).
  22. J. McCarthy, D. Vella, and A. A. Castrejón-Pita, Dynamics of droplets on cones: Self-propulsion due to curvature gradients, Soft Matter 15, 9997 (2019).
  23. J. Van Hulle, F. Weyer, S. Dorbolo, and N. Vandewalle, Capillary transport from barrel to clamshell droplets on conical fibers, Phys. Rev. Fluids 6, 024501 (2021).
  24. M. Davoudi, J. Fang, and G. Chase, Barrel shaped droplet movement at junctions of perpendicular fibers with different orientations to the air flow direction, Separat. Purif. Technol. 162, 1 (2016).
  25. F. Weyer, A. Duchesne, and N. Vandewalle, Switching behavior of droplets crossing nodes on a fiber network, Sci. Rep. 7, 13309 (2017).
  26. A. Sauret, F. Boulogne, D. Cébron, E. Dressaire, and H. A. Stone, Wetting morphologies on an array of fibers of different radii, Soft Matter 11, 4034 (2015).
  27. H. Aziz and H. V. Tafreshi, Competing forces on a liquid bridge between parallel and orthogonal dissimilar fibers, Soft Matter 15, 6967 (2019).
  28. F. Wang and U. D. Schiller, Hysteresis in spreading and retraction of liquid droplets on parallel fiber rails, Soft Matter 17, 5486 (2021).
  29. T. Podgorski, J.-M. Flesselles, and L. Limat, Corners, Cusps, and Pearls in Running Drops, Phys. Rev. Lett. 87, 036102 (2001).
  30. N. Le Grand, A. Daerr, and L. Limat, Shape and motion of drops sliding down an inclined plane, J. Fluid Mech. 541, 293 (2005).
  31. I. Peters, J. H. Snoeijer, A. Daerr, and L. Limat, Coexistence of two Singularities in Dewetting flows: Regularizing the Corner Tip, Phys. Rev. Lett. 103, 114501 (2009).
  32. S. Engelnkemper, M. Wilczek, S. V. Gurevich, and U. Thiele, Morphological transitions of sliding drops: Dynamics and bifurcations, Phys. Rev. Fluids 1, 073901 (2016).
  33. J. Yang, X. Ma, L. Fei, X. Zhang, K. H. Luo, and S. Shuai, Effects of hysteresis window on contact angle hysteresis behaviour at large Bond number, J. Colloid Interface Sci. 566, 327 (2020).
  34. T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen, The Lattice Boltzmann Method—Principles and Practice (Springer International Publishing, Cham, 2016).
  35. T. Inamuro, S. Tajima, and F. Ogino, Lattice Boltzmann simulation of droplet collision dynamics, Int. J. Heat Mass Transf. 47, 4649 (2004).
  36. M. Wöhrwag, C. Semprebon, A. Mazloomi Moqaddam, I. Karlin, and H. Kusumaatmaja, Ternary Free-Energy Entropic Lattice Boltzmann Model with a High Density Ratio, Phys. Rev. Lett. 120, 234501 (2018).
  37. N. Bala, M. Pepona, I. Karlin, H. Kusumaatmaja, and C. Semprebon, Wetting boundaries for a ternary high-density-ratio lattice Boltzmann method, Phys. Rev. E 100, 013308 (2019).
  38. A. Dupuis and J. Yeomans, Modeling droplets on superhydrophobic surfaces: Equilibrium states and transitions, Langmuir 21, 2624 (2005).
  39. A. Mazloomi M, S. S. Chikatamarla, and I. V. Karlin, Entropic Lattice Boltzmann Method for Multiphase Flows, Phys. Rev. Lett. 114, 174502 (2015).
  40. A. Kupershtokh, D. Medvedev, and D. Karpov, On equations of state in a lattice Boltzmann method, Comput. Math. Appl. 58, 965 (2009).
  41. S. Khirevich, I. Ginzburg, and U. Tallarek, Coarse- and fine-grid numerical behavior of MRT/TRT lattice-Boltzmann schemes in regular and random sphere packings, J. Comput. Phys. 281, 708 (2015).
  42. Y. Liu, M. Andrew, J. Li, J. M. Yeomans, and Z. Wang, Symmetry breaking in drop bouncing on curved surfaces, Nat. Commun. 6, 10034 (2015).
  43. R. N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem. 28, 988 (1936).
  44. H.-Y. Kim, H. J. Lee, and B. H. Kang, Sliding of liquid drops down an inclined solid surface, J. Colloid Interface Sci. 247, 372 (2002).
  45. B. A. Puthenveettil, V. K. Senthilkumar, and E. J. Hopfinger, Motion of drops on inclined surfaces in the inertial regime, J. Fluid Mech. 726, 26 (2013).
  46. R. Sahu, S. Sinha-Ray, A. Yarin, and B. Pourdeyhimi, Blowing drops off a filament, Soft Matter 9, 6053 (2013).

Outline

Information

Phys. Rev. Fluids 7, 103606– Published 24 October, 2022
  • Received 5 July 2022
  • Accepted 26 September 2022
Crossmark - Check for updates button

©2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation