Abstract
In this paper the authors show that fractional-order force-flux relations are obtained considering the flux of a viscous fluid across an elastic porous media. Indeed the one-dimensional fluid mass transport in an unbounded porous media with power-law variation of geometrical and physical properties yields a fractional-order relation among the ingoing flux and the applied pressure to the control section. As a power-law decay of the physical properties from the control section is considered, then the flux is related to a Caputo fractional derivative of the pressure of order 0 ≤ β≤1. If, instead, the physical properties of the media show a power-law increase from the control section, then flux is related to a fractional-order integral of order 0 ≤ β≤1. These two different behaviors may be related to different states of the mass flow across the porous media.
Original language | English (US) |
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Pages (from-to) | 940-949 |
Number of pages | 10 |
Journal | Communications in Nonlinear Science and Numerical Simulation |
Volume | 20 |
Issue number | 3 |
DOIs | |
State | Published - Mar 1 2015 |
Keywords
- Anomalous diffusion
- Anomalous scaling
- Darcy equation
- Fractional derivatives
- Porous media
ASJC Scopus subject areas
- Modeling and Simulation
- Numerical Analysis
- Applied Mathematics