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 6 b 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 6 b 1. These two different behaviors may be related to different states of the mass flow across the porous media. 2014 Elsevier B.V. All rights reserved.

A mechanical picture of fractional-order Darcy equation / Deseri, Luca; Massimiliano, Zingales. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 20:(2015), pp. 940-949. [10.1016/j.cnsns.2014.06.021]

A mechanical picture of fractional-order Darcy equation

Deseri, Luca;
2015

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 6 b 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 6 b 1. These two different behaviors may be related to different states of the mass flow across the porous media. 2014 Elsevier B.V. All rights reserved.
Deseri, Luca; Massimiliano, Zingales
A mechanical picture of fractional-order Darcy equation / Deseri, Luca; Massimiliano, Zingales. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 20:(2015), pp. 940-949. [10.1016/j.cnsns.2014.06.021]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/100348
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