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 language | English (US) |
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Pages (from-to) | 514-559 |
Number of pages | 46 |
Journal | Journal of Fluid Mechanics |
Volume | 817 |
DOIs | |
State | Published - Apr 25 2017 |
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics
Keywords
- gravity currents
- porous media
- thin films