The influence of capillary effects on the drainage of a viscous gravity current into a deep porous medium

Ying Liu, Zhong Zheng, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The drainage of a viscous gravity current into a deep porous medium driven by both the gravitational and capillary forces is considered in two steps. We first study the one-dimensional case where a layer of fluid drains vertically into an infinitely deep porous medium. We determine a transition from the capillary-driven regime to the gravity-driven regime as time proceeds. Second, we solve the coupled spreading and drainage problem. There are no self-similar solutions of the problem for the entire time period, so asymptotic analyses are developed for the height, depth and front location in both the early-time and the late-time periods. In addition, we present numerical results of the governing partial differential equations, which agree well with the self-similar solutions in the appropriate asymptotic limits.

Original languageEnglish (US)
Pages (from-to)514-559
Number of pages46
JournalJournal of Fluid Mechanics
Volume817
DOIs
StatePublished - Apr 25 2017

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • gravity currents
  • porous media
  • thin films

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