The long cross-over dynamics of capillary imbibition

Elfego Ruiz Gutierrez, Steven Armstrong, Simon Leveque, Celestin Michel, Ignacio Pagonabarraga, Gary Wells, Aurora Hernández-Machado, Rodrigo Ledesma Aguilar*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Spontaneous capillary imbibition is a classical problem in interfacial fluid dynamics with a broad range of application, from microfluidics to agriculture. Here, we study the duration of the cross- over between an initial linear growth of the imbibition front to the diffusive-like growth limit of Washburn’s law. We show that local-resistance sources, such as the inertial resistance and the friction caused by the advancing meniscus, always limit the motion of an imbibing front. Both effects give rise to an algebraic cross-over of the growth exponent between the linear and the diffusive-like regimes. We show how this cross-over is much longer than previously thought–even longer than the time it takes the liquid to fill the porous medium. Such slowly-slowing-down dynamics is likely to cause similar long cross-over phenomena in processes governed by wetting.
Original languageEnglish
Article numberA39
Number of pages20
JournalJournal of Fluid Mechanics
Early online date31 Mar 2022
Publication statusPublished - 25 May 2022


  • Porous Media
  • low-Reynolds-number flows
  • Wetting and wicking
  • Interfacial Flows (free surface)
  • interfacial flows
  • Capillary flows


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