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This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.

This is the second part of the special issue on fractal geometry and its applications to the modeling of flow and transport in porous media, in which 10 original research articles and one review article are included. Combining to the first part of 11 original research articles, these two issues summarized current research on fractal models applied to porous media that will help to further advance this multidisciplinary development. This whole special issue is published also to celebrate the 70th birthday of Professor Boming Yu for his distinguished researches on fractal geometry and its application to transport physics of porous media.

We prove the existence of a pathwise weak solution to the single-phase, miscible displacement of one incompressible fluid by another in a porous medium with random forcing. Our system is described by a parabolic concentration equation driven by an additive noise coupled with an elliptic pressure equation. We use a pathwise argument combined with Schauder’s fixed point theorem.