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Advances in Mathematical Physics
Volume 2016, Article ID 1234642, 16 pages
http://dx.doi.org/10.1155/2016/1234642
Research Article

Slug Self-Propulsion in a Capillary Tube Mathematical Modeling and Numerical Simulation

1Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand
2Department of Electrical and Computer Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand

Received 1 February 2016; Accepted 20 June 2016

Academic Editor: Xavier Leoncini

Copyright © 2016 M. I. Khodabocus et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Bico and D. Quéré, “Self-propelling slugs,” Journal of Fluid Mechanics, vol. 467, pp. 101–127, 2002. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Thomson, “On certain curious motions observable at the surfaces of wine and other alcoholic liquors,” Philosophical Magazine, vol. 10, pp. 330–333, 1855. View at Google Scholar
  3. C. Marangoni, On the Expansion of Liquid Floating on the Surface of Another Liquid, Tipographia dei Fratelli Fusi, Pavia, Italy, 1865.
  4. L. E. Scriven and C. V. Sternling, “The marangoni effects,” Nature, vol. 187, no. 4733, pp. 186–188, 1960. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Bico and D. Quéré, “Liquid trains in a tube,” Europhysics Letters, vol. 51, no. 5, pp. 546–550, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. D. K. N. Sinz and A. A. Darhuber, “Self-propelling surfactant droplets in chemically-confined microfluidics—Cargo transport, drop-splitting and trajectory control,” Lab on a Chip—Miniaturisation for Chemistry and Biology, vol. 12, no. 4, pp. 705–707, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. H. Bouasse, Capillarit, Phnomnes Superficiel, Delagrave, Paris, France, 1924.
  8. M. M. Weislogel, “Steady spontaneous capillary flow in partially coated tubes,” AIChE Journal, vol. 43, no. 3, pp. 645–654, 1997. View at Publisher · View at Google Scholar · View at Scopus
  9. F. D. Dos Santos and T. Ondarçuhu, “Free-running droplets,” Physical Review Letters, vol. 75, no. 16, pp. 2972–2975, 1995. View at Publisher · View at Google Scholar · View at Scopus
  10. P. G. De Gennes, “The dynamics of reactive wetting on solid surfaces,” Physica A: Statistical Mechanics and Its Applications, vol. 249, no. 1–4, pp. 196–205, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. F. Hauksbee, “An account of an experiment touching the direction of oil of oranges, between two glass planes, towards any side of them that is nearest press'd together,” Philosophical Transactions, vol. 27, pp. 395–396, 1712. View at Google Scholar
  12. S. K. Cho and H. Moon, “Electrowetting on dielectric (EWOD): new tool for bio/micro fluids handling,” Biochip Journal, vol. 2, no. 2, pp. 79–96, 2009. View at Google Scholar · View at Scopus
  13. L. Y. Yeo and H.-C. Chang, “Static and spontaneous electrowetting,” Modern Physics Letters B, vol. 19, no. 12, pp. 549–569, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. T. B. Jones, K.-L. Wang, and D.-J. Yao, “Frequency-dependent electromechanics of aqueous liquids: electrowetting and dielectrophoresis,” Langmuir, vol. 20, no. 7, pp. 2813–2818, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. S. K. Cho, H. Moon, and C.-J. Kim, “Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits,” Journal of Microelectromechanical Systems, vol. 12, no. 1, pp. 70–80, 2003. View at Publisher · View at Google Scholar · View at Scopus
  16. M. G. Pollack, R. B. Fair, and A. D. Shenderov, “Electrowetting-based actuation of liquid droplets for microfluidic applications,” Applied Physics Letters, vol. 77, no. 11, pp. 1725–1726, 2000. View at Publisher · View at Google Scholar · View at Scopus
  17. J. Lee and C.-J. Kim, “Surface-tension-driven microactuation based on continuous electrowetting,” Journal of Microelectromechanical Systems, vol. 9, no. 2, pp. 171–180, 2000. View at Publisher · View at Google Scholar · View at Scopus
  18. T. B. Jones, M. Gunji, M. Washizu, and M. J. Feldman, “Dielectrophoretic liquid actuation and nanodroplet formation,” Journal of Applied Physics, vol. 89, no. 2, pp. 1441–1448, 2001. View at Publisher · View at Google Scholar · View at Scopus
  19. M. L. Ford and A. Nadim, “Thermocapillary migration of an attached drop on a solid surface,” Physics of Fluids, vol. 6, no. 9, pp. 3183–3185, 1994. View at Publisher · View at Google Scholar · View at Scopus
  20. M. K. Smith, “Thermocapillary migration of a two-dimensional liquid droplet on a solid surface,” Journal of Fluid Mechanics, vol. 294, pp. 209–230, 1995. View at Publisher · View at Google Scholar · View at Scopus
  21. A. A. Darhuber, J. M. Davis, S. M. Troian, and W. W. Reisner, “Thermocapillary actuation of liquid flow on chemically patterned surfaces,” Physics of Fluids, vol. 15, no. 5, pp. 1295–1304, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. A. A. Darhuber, J. P. Valentino, S. M. Troian, and S. Wagner, “Thermocapillary actuation of droplets on chemically patterned surfaces by programmable microheater arrays,” Journal of Microelectromechanical Systems, vol. 12, no. 6, pp. 873–879, 2003. View at Publisher · View at Google Scholar · View at Scopus
  23. A. Renaudin, P. Tabourier, V. Zhang, J. C. Camart, and C. Druon, “SAW nanopump for handling droplets in view of biological applications,” Sensors and Actuators B: Chemical, vol. 113, no. 1, pp. 389–397, 2006. View at Publisher · View at Google Scholar · View at Scopus
  24. L. Y. Yeo and J. R. Friend, “Ultrafast microfluidics using surface acoustic waves,” Biomicrofluidics, vol. 3, no. 1, Article ID 012002, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. J. Pfahler, J. Harley, H. Bau, and J. Zemel, “Liquid transport in micron and submicron channels,” Sensors and Actuators A, vol. 22, no. 1–3, pp. 431–434, 1989. View at Publisher · View at Google Scholar · View at Scopus
  26. P. G. De Gennes, “Wetting: statics and dynamics,” Reviews of Modern Physics, vol. 57, no. 3, pp. 827–863, 1985. View at Publisher · View at Google Scholar · View at Scopus
  27. P. G. De Gennes, “Eponges filantes,” Comptes Rendus de l'Académie des Sciences, vol. 323, pp. 663–667, 1996. View at Google Scholar
  28. M. E. R. Shanahan and P. G. De Gennes, “The motion of long bubbles in tubes,” Comptes Rendus de l'Académie des Sciences (Paris) IIb, vol. 324, p. 261, 1997. View at Google Scholar
  29. M. Sellier, V. Nock, and C. Verdier, “Self-propelling, coalescing droplets,” International Journal of Multiphase Flow, vol. 37, no. 5, pp. 462–468, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. M. Sellier, V. Nock, C. Gaubert, and C. Verdier, “Droplet actuation induced by coalescence: experimental evidences and phenomenological modeling,” European Physical Journal: Special Topics, vol. 219, no. 1, pp. 131–141, 2013. View at Publisher · View at Google Scholar · View at Scopus
  31. S. Karpitschka and H. Riegler, “Quantitative experimental study on the transition between fast and delayed coalescence of sessile droplets with different but completely miscible liquids,” Langmuir, vol. 26, no. 14, pp. 11823–11829, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. S. Karpitschka and H. Riegler, “Noncoalescence of sessile drops from different but miscible liquids: hydrodynamic analysis of the twin drop contour as a self-stabilizing traveling wave,” Physical Review Letters, vol. 109, no. 6, Article ID 066103, 5 pages, 2012. View at Google Scholar
  33. A. A. Darhuber, J. P. Valentino, J. M. Davis, S. M. Troian, and S. Wagner, “Microfluidic actuation by modulation of surface stresses,” Applied Physics Letters, vol. 82, no. 4, pp. 657–659, 2003. View at Publisher · View at Google Scholar · View at Scopus
  34. A. A. Darhuber, J. P. Valentino, J. M. Davis, and S. M. Troian, “Principles of microuidic actuation by modulation of surface stresses,” Annual Review of Fluid Mechanics, vol. 37, pp. 425–455, 2005. View at Publisher · View at Google Scholar
  35. I. Lunati and D. Or, “Gravity-driven slug motion in capillary tubes,” Physics of Fluids, vol. 21, no. 5, Article ID 052003, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. J. Bico and D. Quéré, “Falling slugs,” Journal of Colloid and Interface Science, vol. 243, no. 1, pp. 262–264, 2001. View at Publisher · View at Google Scholar · View at Scopus
  37. P. Carles and A. M. Cazabat, “Spreading involving the marangoni effect: some preliminary results,” Colloids and Surfaces, vol. 41, pp. 97–105, 1989. View at Publisher · View at Google Scholar · View at Scopus
  38. P. Carles and A. M. Cazabat, “Spreading of oil drops under a solvent vapor: inuence of marangoni effect,” Progress in Colloid and Polymer Science, vol. 82, pp. 76–81, 1990. View at Google Scholar
  39. P. Yue, C. Zhou, and J. J. Feng, “Sharp-interface limit of the Cahn-Hilliard model for moving contact lines,” Journal of Fluid Mechanics, vol. 645, pp. 279–294, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. D. Jacqmin, “Calculation of two-phase Navier-Stokes flows using phase-field modeling,” Journal of Computational Physics, vol. 155, no. 1, pp. 96–127, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. O. K. Matar and R. V. Craster, “Models for Marangoni drying,” Physics of Fluids, vol. 13, no. 7, pp. 1869–1883, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. S. B. G. M. O'Brien, “On Marangoni drying: nonlinear kinematic waves in a thin film,” Journal of Fluid Mechanics, vol. 254, pp. 649–670, 1993. View at Publisher · View at Google Scholar · View at Scopus
  43. K. Piroird, C. Clanet, and D. Quéré, “Detergency in a tube,” Soft Matter, vol. 7, no. 16, pp. 7498–7503, 2011. View at Publisher · View at Google Scholar · View at Scopus
  44. K. Piroird, C. Clanet, and D. Queźreź, “Capillary extraction,” Langmuir, vol. 27, no. 15, pp. 9396–9402, 2011. View at Publisher · View at Google Scholar · View at Scopus