Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-08T08:06:37.010Z Has data issue: false hasContentIssue false
  • English
  • Français

The inertial regime of drop impact on an anisotropic porous substrate

Published online by Cambridge University Press:  08 December 2011

H. Ding  and
T. G. Theofanous
H. Ding*
Affiliation:
Department of Chemical Engineering, University of California at Santa Barbara, CA 93106-5080, USA Department of Modern Mechanics, University of Science and Technology of China, Hefei, China
T. G. Theofanous
Affiliation:
Department of Chemical Engineering, University of California at Santa Barbara, CA 93106-5080, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Axisymmetric droplet impact on a hydrophilic substrate with one pore of relatively large radius is numerically studied using diffuse-interface methods. The flows above the substrate and in the capillary are fully resolved by a Navier–Stokes solver that accounts for contact-angle hysteresis. Upon impact, the infiltration of the drop into the capillary is seen to follow one or more of the three regimes identified in recent experiments (Delbos, Lorenceau & Pitois, J. Colloid Interface Sci., vol. 341, 2010, p. 171): complete penetration, partial penetration as a slug, and re-entry with bubble entrapment. The agreement on experimentally measured quantities, such as transition criteria and slug lengths, is quantitative. On this basis we reveal previously unidentified flow phenomena, investigate flow details that are not accessible experimentally, expand the parameter space considered previously, identify the key asymptotic regimes in the penetration transient, generalize the results in terms of relevant dimensionless groups, and provide a further step (using a multi-capillary arrangement as an idealization of a porous substrate) towards the ultimate purpose of such work, which is the understanding of inertial effects with porous substrates, including eccentric impacts. The significant effect of impact inertia is revealed as a spatial anchoring of a stagnation region, formed and persisting for most of the transient. As a consequence, fluid within an upright cylinder is destined to enter the capillary, and this is in agreement with the hypothesis of Delbos et al. in interpreting the amounts of liquid found inside the capillary, except that the radius of the cylinder is 30 % greater than the capillary radius. The remainder of the liquid spreads laterally on the substrate surface, and the slug regime is a consequence of this partition. Numerical experiments also indicate that after reaching the maximum-spread area, the lamella on the substrate tends to refill the capillary and entrap a bubble, unless contact-angle hysteresis hinders the radially inward motion of the lamella.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops
Type
Papers
Information
Journal of Fluid Mechanics , Volume 691 , 25 January 2012 , pp. 546 - 567
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Alleborn, N. & Raszillier, H. 2004 Spreading and sorption of a droplet on a porous substrate. Chem. Engng Sci. 59, 2071–2088.CrossRefGoogle Scholar
2. Biance, A.-L., Clanet, C. & Quéré, D. 2004 First steps in the spreading of a liquid droplet. Phys. Rev. E 69, 016301.CrossRefGoogle ScholarPubMed
3. Blanchette, F. & Bigioni, T. P. 2006 Partial coalescence of drops at liquid interfaces. Nature Phys. 2, 254–257.CrossRefGoogle Scholar
4. Clanet, C., Beguin, C., Richard, D. & Quéré, D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199–208.CrossRefGoogle Scholar
5. Clarke, A., Blake, T. D., Carruthers, K. & Woodward, A. 2002 Spreading and imbibition of liquid droplets on porous surfaces. Langmuir 18, 2980.CrossRefGoogle Scholar
6. Davis, S. H. & Hocking, L. M. 1999 Spreading and imbibition of viscous liquid on a porous base. Phys. Fluids 11, 48–57.CrossRefGoogle Scholar
7. Davis, S. H. & Hocking, L. M. 2000 Spreading and imbibition of viscous liquid on a porous base. Part II. Phys. Fluids 12, 1646–1655.CrossRefGoogle Scholar
8. Delbos, A., Lorenceau, E. & Pitois, O. 2010 Forced impregnation of a capillary tube with drop impact. J. Colloid Interface Sci. 341, 171–177.CrossRefGoogle ScholarPubMed
9. Denesuk, M., Smith, G. L., Zelinski, B. J. J., Kreidl, N. J. & Uhlmann, D. R. 1993 Capillary penetration of liquid droplets into porous materials. J. Colloid Interface Sci. 158, 114–120.CrossRefGoogle Scholar
10. Ding, H., Li, E. Q., Zhang, F., Sui, Y., Spelt, P. D. M. & Thoroddsen, S. T. 2011 Ejection of small droplets in rapid droplet spreading. Under consideration for publication in J. Fluid Mech. (submitted).Google Scholar
11. Ding, H. & Spelt, P. D. M. 2007a Inertial effects in droplet spreading: a comparison between diffuse interface and level-set simulations. J. Fluid Mech. 576, 287–296.CrossRefGoogle Scholar
12. Ding, H. & Spelt, P. D. M. 2007b Wetting condition in diffuse interface simulation of contact line motion. Phys. Rev. E 75, 046708.CrossRefGoogle ScholarPubMed
13. Ding, H. & Spelt, P. D. M. 2008 Onset of motion of a 3D droplet on a wall in shear flow at moderate Reynolds numbers. J. Fluid Mech. 599, 341–362.CrossRefGoogle Scholar
14. Ding, H., Spelt, P. D. M. & Shu, C. 2007 Diffuse interface model for incompressible two-phase flows with large density ratios. J. Comput. Phys. 226, 2078–2095.CrossRefGoogle Scholar
15. Eggers, J., Fontelos, M. A., Josser, C. & Zaleski, S. 2010 Drop dynamics after impact on a solid wall: theory and simulations. Phys. Fluids 22, 062101.CrossRefGoogle Scholar
16. Fedorchenko, A. I., Wang, A.-B. & Wang, Y.-H. 2005 Effect of capillary and viscous forces on spreading of a liquid drop impinging on a solid surface. Phys. Fluids 17, 093104.CrossRefGoogle Scholar
17. de Gennes, P. G. 1985 Wetting: statistics and dynamics. Rev. Mod. Phys. 57, 827–863.CrossRefGoogle Scholar
18. Hilpert, M. & Ben-David, A. 2009 Infitration of liquid droplets into porous media: effects of dynamic contact angle and contact angle hysteresis. Intl J. Multiphase Flow 35, 205–218.CrossRefGoogle Scholar
19. Holman, R. K., Cima, M. J., Uhland, S. A. & Sachs, E. 2002 Spreading and infiltration of inkjet-printed polymer solution droplets on a porous substrate. J. Colloid Interface Sci. 249, 432–440.CrossRefGoogle ScholarPubMed
20. Jacqmin, D. 1999 Calculation of two-phase Navier–Stokes flows using phase-field modelling. J. Comput. Phys. 155, 96–127.CrossRefGoogle Scholar
21. Jacqmin, D. 2000 Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402, 57.CrossRefGoogle Scholar
22. Kogan, V., Johnson, E. & Schumacher, P. 2008 Capillary flow of liquid under droplet impact conditions. In 22nd European Conference on Liquid Atomization Spray Systems, Lake Como, Italy. Paper ID ILASS08-A131.Google Scholar
23. Lee, M., Chang, Y. S. & Kim, H. Y. 2010 Drop impact on microwetting patterned surfaces. Phys. Fluids 22, 072101.CrossRefGoogle Scholar
24. Lembach, A. N., Tan, H. B., Roisman, I. V., Roisman, T. G., Zhang, Y., Tropea, C. & Yarin, A. L. 2010 Drop impact, spreading, splashing, and penetration into electrospun nanofibre mats. Langmuir 26, 9516–9523.CrossRefGoogle Scholar
25. Marmur, A. & Cohen, R. D. 1997 Characterization of porous media by the kinetics of liquid penetration: the vertical capillaries model. J. Colloid Interface Sci. 189, 299–304.CrossRefGoogle Scholar
26. Rioboo, R., Adao, M. H., Voué, M. & De Coninck, J. 2006 Experimental evidence of liquid drop breakup in complete wetting experiments. J. Mater. Sci. 41, 5068–5080.CrossRefGoogle Scholar
27. Rioboo, R., Marengo, M. & Tropea, C. 2002 Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33, 112–124.CrossRefGoogle Scholar
28. Roux, D. C. D. & Cooper-White, J. J. 2004 Dynamics of water spreading on a glass surface. J. Colloid Interface Sci. 277, 424–436.CrossRefGoogle ScholarPubMed
29. Seppecher, P. 1996 Moving contact lines in the Cahn–Hilliard theory. Intl J. Engng Sci. 34, 977–992.CrossRefGoogle Scholar
30. Seveno, D., Ledauphin, V., Martic, G., Vou, M. & De Coninck, J. 2002 Spreading drop dynamics on porous surfaces. Langmuir 18, 7496–7502.CrossRefGoogle Scholar
31. Sivakumar, D., Katagiri, K., Sato, T. & Nishiyama, H. 2005 Spreading behaviour of an impacting drop on a structured rough surface. Phys. Fluids 17, 100608.CrossRefGoogle Scholar
32. Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273.CrossRefGoogle Scholar
33. Xu, L. 2005 Liquid drop splashing on smooth, rough, and texture surfaces. Phys. Rev. E 75, 056316.CrossRefGoogle Scholar
34. Zhang, F. H., Li, E. Q. & Thoroddsen, S. T. 2009 Satellite formation during coalescence of unequal size drops. Phys. Rev. Lett. 102, 104502.CrossRefGoogle ScholarPubMed
35. Zhmud, B. V., Tiberg, F. & Hallstensson, K. 2000 Dynamics of capillary rise. J. Colloid Interface Sci. 228, 263–269.CrossRefGoogle ScholarPubMed