Laminar flow through fractal porous materials: the fractional-order transport equation

The anomalous transport 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 a porous solid, then a generalized version of the Hagen-Poiseuille 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 mechanical picture for the use of generalized fractional-order relations, as recently used in scientific literature.