FRACTIONAL-ORDER GENERALIZATION OF TRANSPORT EQUATIONS IN FRACTAL POROUS MEDIA

Abstract

The anomalous flux of a viscous fluid across a porous media with power-law scaling of the geometrical features of the pores is dealt with in the paper. It has been shown that, assuming a linear force-flux relation for the motion in the porous solid, then a generalized version of the Darcy equation has been obtained with the aid of Riemann-Liouville fractional derivative. The order of the derivative is related to the scaling property of the considered media yielding an appropriate physical picture of the use fractional-order Darcy equation recently used in scientific literature.