Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T23:45:12.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Droplet spreading and absorption on rough, permeable substrates

Published online by Cambridge University Press:  06 November 2015

Leonardo Espín  and
Satish Kumar
Leonardo Espín
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Satish Kumar*
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Wetting of permeable substrates by liquids is an important phenomenon in many natural and industrial processes. Substrate heterogeneities may significantly alter liquid spreading and interface shapes, which in turn may alter liquid imbibition. A new lubrication-theory-based model for droplet spreading on permeable substrates that incorporates surface roughness is developed in this work. The substrate is assumed to be saturated with liquid, and the contact-line region is described by including a precursor film and disjoining pressure. A novel boundary condition for liquid imbibition is applied that eliminates the need for a droplet-thickness-dependent substrate permeability that has been employed in previous models. A nonlinear evolution equation describing droplet height as a function of time and the radial coordinate is derived and then numerically solved to characterize the influence of substrate permeability and roughness on axisymmetric droplet spreading. Because it incorporates surface roughness, the new model is able to describe the contact-line pinning that has been observed in experiments but not captured by previous models.

JFM classification

Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 784 , 10 December 2015 , pp. 465 - 486
Check for updates
Copyright
© 2015 Cambridge University Press 

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

Alleborn, N. & Raszillier, H. 2004 Spreading and sorption of a droplet on a porous substrate. Chem. Engng Sci. 59, 2071–2088.CrossRefGoogle Scholar
Anderson, D. M. 2005 Imbibition of a liquid droplet on a deformable porous substrate. Phys. Fluids 17, 087104.CrossRefGoogle Scholar
Arora, D., Deshpande, A. P. & Chakravarthy, S. R. 2006 Experimental investigation of fluid drop spreading on heterogeneous and anisotropic porous media. J. Colloid Interface Sci. 293, 496–499.CrossRefGoogle ScholarPubMed
Bacri, L. & Brochard-Wyart, F. 2000 Droplet suction on porous media. Eur. Phys. J. E 93, 87–97.CrossRefGoogle Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.CrossRefGoogle Scholar
Berg, J. C. 2009 An Introduction to Interfaces and Colloids: The Bridge to Nanoscience. World Scientific.CrossRefGoogle Scholar
Brown, P. N., Hindmarsh, A. C. & Petzold, L. R. 1994 Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15, 1467–1488.Google Scholar
Clarke, A., Blake, T. D., Carruthers, K. & Woodward, A. 2002 Spreading and imbibition of liquid droplets on porous surfaces. Langmuir 18, 2980–2984.Google Scholar
Davis, S. H. & Hocking, L. M. 1999 Spreading and imbibition of viscous liquid on a porous base. Phys. Fluids 11, 48–57.Google Scholar
Davis, S. H. & Hocking, L. M. 2000 Spreading and imbibition of viscous liquid on a porous base. II. Phys. Fluids 12, 1646–1655.CrossRefGoogle Scholar
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.Google Scholar
Espín, L. & Kumar, S. 2014 Sagging of evaporating droplets of colloidal suspensions on inclined substrates. Langmuir 30, 11966–11974.Google Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.Google Scholar
Kumar, S. M. & Deshpande, A. P. 2006 Dynamics of drop spreading on fibrous porous media. Colloids Surf. A 277, 157–163.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.Google Scholar
Popescu, M. N., Oshanin, G., Dietrich, S. & Cazabat, A.-M. 2012 Precursor films in wetting phenomena. J. Phys.: Condens. Matter 24, 243102.Google Scholar
Ruckenstein, E. & Jain, R. K. 1974 Spontaneous rupture of thin liquid films. J. Chem. Soc. Faraday Trans. 2 70, 132–147.Google Scholar
Savva, N. & Kalliadasis, S. 2009 Two-dimensional droplet spreading over topographical substrates. Phys. Fluids 21, 092102.Google Scholar
Savva, N. & Kalliadasis, S. 2011 Dynamics of moving contact lines: A comparison between slip and precursor film models. Europhys. Lett. 94, 64004.Google Scholar
Savva, N. & Kalliadasis, S. 2012 Influence of gravity on the spreading of two-dimensional droplets over topographical substrates. J. Engng Maths 73, 3–16.CrossRefGoogle Scholar
Savva, N. & Kalliadasis, S. 2013 Droplet motion on inclined heterogeneous substrates. J. Fluid Mech. 725, 462–491.Google Scholar
Savva, N., Kalliadasis, S. & Pavliotis, G. A. 2010 Two-dimensional droplet spreading over random topographical substrates. Phys. Rev. Lett. 104, 084501.Google Scholar
Schwartz, L. W. 1998 Hysteretic effects in droplet motions on heterogeneous substrates: direct numerical simulation. Langmuir 14, 3440–3453.CrossRefGoogle Scholar
Schwartz, L. W. & Eley, R. R. 1998 Simulation of droplet motion on low-energy and heterogeneous surfaces. J. Colloid Interface Sci. 202, 173–188.Google Scholar
Schwartz, L. W., Roux, D. & Cooper-White, J. J. 2005 On the shapes of droplets that are sliding on a vertical wall. Physica D 209, 236–244.Google Scholar
Sodtke, C., Ajaev, V. S. & Stephan, P. 2008 Dynamics of volatile liquid droplets on heated surfaces: theory versus experiment. J. Fluid Mech. 610, 343–362.Google Scholar
Spannuth, M. J., Neufeld, J. A., Wettlaufer, J. S. & Worster, M. G. 2009 Axisymmetric viscous gravity currents flowing over a porous medium. J. Fluid Mech. 622, 135–144.CrossRefGoogle Scholar
Starov, V. M., Kostvintsev, S. R., Sobolev, V. D., Velarde, M. G. & Zhdanov, S. A. 2002a Spreading of liquid drops over dry porous layers: complete wetting case. J. Colloid Interface Sci. 252, 397–408.Google Scholar
Starov, V. M., Kosvintsev, S. R., Sobolev, V. D., Velarde, M. G. & Zhdanov, S. A. 2002b Spreading of liquid drops over saturated porous layers. J. Colloid Interface Sci. 246, 372–379.CrossRefGoogle ScholarPubMed
Talbott, K., Xu, A., Anderson, D. M. & Seshaiyer, P. 2015 Modelling the evaporation of a tear film over a contact lens. Math. Med. Biol. 32, 209–238.Google Scholar
Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D 12, 1473–1484.Google Scholar
Teletzke, G. F., Davis, H. T. & Scriven, L. E. 1987 How liquids spread on solids. Chem. Engng Commun. 55, 41–82.Google Scholar
Zadražil, A., Stepanek, F. & Matar, O. K. 2006 Droplet spreading, imbibition and solidification on porous media. J. Fluid Mech. 562, 1–33.Google Scholar
Zosel, A. 1993 Studies of the wetting kinetics of liquid drops on solid surfaces. Colloid Polym. Sci. 271, 680–687.CrossRefGoogle Scholar