TY - JOUR
T1 - A mechanical picture of fractional-order Darcy equation
AU - Deseri, Luca
AU - Zingales, Massimiliano
N1 - Funding Information:
The authors are grateful to financial support provided in the course of the study. Massimiliano Zingales acknowledge the PRIN2010-2011 with national coordinator Prof. A. Luongo; Luca Deseri acknowledges the Department of Mathematical Sciences and the Center for Nonlinear Analysis, Carnegie Mellon University through the NSF Grant No. DMS-0635983 and the financial support from Grant PIAP-GA-2011-286110-INTERCER2 “Modelling and optimal design of ceramic structures with defects and imperfect interfaces”.
Publisher Copyright:
© 2014 Elsevier B.V.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2015/3/1
Y1 - 2015/3/1
N2 - 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.
AB - 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.
KW - Anomalous diffusion
KW - Anomalous scaling
KW - Darcy equation
KW - Fractional derivatives
KW - Porous media
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U2 - 10.1016/j.cnsns.2014.06.021
DO - 10.1016/j.cnsns.2014.06.021
M3 - Article
AN - SCOPUS:84908658827
VL - 20
SP - 940
EP - 949
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
IS - 3
ER -