We study numerically the tortuosity-porosity relation in a microscopic model of a porous medium arranged as a collection of freely overlapping squares. It is demonstrated that the finite-size, slow relaxation and discretization errors, which were ignored in previous studies, may cause significant underestimation of tortuosity. The simple tortuosity calculation method proposed here eliminates the need for using complicated, weighted averages. The numerical results presented here are in good agreement with an empirical relation between tortuosity (T) and porosity (varphi) given by T-1 proportional, variantlnvarphi , that was found by others experimentally in granule packings and sediments. This relation can be also written as T-1 proportional, variantRSvarphi with R and S denoting the hydraulic radius of granules and the specific surface area, respectively. Applicability of these relations appears to be restricted to porous systems of randomly distributed obstacles of equal shape and size.

Tortuosity (T ) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate T directly from the fluid velocity field, without the need of determining streamlines, which greatly simplifies determination of tortuosity in complex geometries, including those found in experiments or 3D computer models. Numerical results obtained with this method suggest that (a) the hydraulic tortuosity of an isotropic fibrous medium takes on the form T = 1 + p √ 1 − ϕ, where ϕ is the porosity and p is a constant and (b) the exponent controlling the divergence of T with the system size at percolation threshold is related to an exponent describing the scaling of the most probable traveling length at bond percolation.

Nitrogen (N) loss rates were determined in permeable sediments of the Wadden Sea using a combination of stable N isotope incubation experiments and model simulation approaches during three seasons. Three different incubation methods that employed the isotope pairing technique were used: intact core incubations simulating either (1) diffusive or (2) advective transport conditions and (3)

Tortuosity is one of the key parameters describing the geometry and transport properties of porous media. It is defined either as an average elongation of fluid paths or as a retardation factor that measures the resistance of a porous medium to the flow. However, in contrast to a retardation factor, an average fluid path elongation is difficult to compute numerically and, in general, is not measurable directly in experiments. We review some recent achievements in bridging the gap between the two formulations of tortuosity and discuss possible method of numerical and an experimental measurements of the tortuosity directly from the fluid velocity field.

Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power-exponential law controlled by an exponent γ and a shift parameter u_{0} and examine how these parameters depend on the porosity. We find that γ has a universal value 1/2 at the percolation threshold and grows with the porosity, but never exceeds 2.