Propagation of viscous currents on a porous substrate with finite capillary entry pressure

Roiy Sayag, Jerome A. Neufeld

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We study the propagation of viscous gravity currents over a thin porous substrate with finite capillary entry pressure. Near the origin, where the current is deep, propagation of the current coincides with leakage through the substrate. Near the nose of the current, where the current is thin and the fluid pressure is below the capillary entry pressure, drainage is absent. Consequently the flow can be characterised by the evolution of drainage and fluid fronts. We analyse this flow using numerical and analytical techniques combined with laboratory-scale experiments. At early times, we find that the position of both fronts evolve as t1/2, similar to an axisymmetric gravity current on an impermeable substrate. At later times, the growing effect of drainage inhibits spreading, causing the drainage front to logarithmically approach a steady position. In contrast, the asymptotic propagation of the fluid front is quasi-self-similar, having identical structure to the solution of gravity currents on an impermeable substrate, only with slowly varying fluid flux. We benchmark these theoretical results with laboratory experiments that are consistent with our modelling assumption, but that also highlight the detailed dynamics of drainage inhibited by finite capillary pressure.

Original languageEnglish
Pages (from-to)65-90
Number of pages26
JournalJournal of Fluid Mechanics
StatePublished - 25 Aug 2016


  • gravity currents
  • interfacial flows (free surface)
  • porous media

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Propagation of viscous currents on a porous substrate with finite capillary entry pressure'. Together they form a unique fingerprint.

Cite this