Inertia onset in disordered porous media flow.

We investigate the onset of the inertial regime in the fluid flow at the pore level in three-dimensional, disordered, highly porous media. We analyze the flow structure in a wide range of Reynolds numbers starting from 0.01 up to 100.

Deep learning for diffusion in porous media.

We adopt convolutional neural networks (CNN) to predict the basic properties of the porous media. Two different media types are considered: one mimics the sand packings, and the other mimics the systems derived from the extracellular space of biological tissues. The Lattice Boltzmann Method is used to obtain the labeled data necessary for performing supervised learning.

Pushing Droplet Through a Porous Medium.

Unlabelled: I use a mechanical model of a soft body to study the dynamics of an individual fluid droplet in a random, non-wettable porous medium. The model of droplet relies on the spring-mass system with pressure. I run hundreds of independent simulations.

Predicting porosity, permeability, and tortuosity of porous media from images by deep learning.

Convolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ([Formula: see text]), permeability (k), and tortuosity (T). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method.

Power-exponential velocity distributions in disordered porous media.

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.

Anisotropy of flow in stochastically generated porous media.

Models of porous media are often applied to relatively small systems, which leads not only to system-size-dependent results, but also to phenomena that would be absent in larger systems. Here we investigate one such finite-size effect: anisotropy of the permeability tensor. We show that a nonzero angle between the external body force and macroscopic flux vector exists in three-dimensional periodic models of sizes commonly used in computer simulations and propose a criterion, based on the ratio of the system size to the grain size, for this phenomenon to be relevant or negligible.

Hydraulic tortuosity in arbitrary porous media flow.

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 three-dimensional computer models.

Finite-size anisotropy in statistically uniform porous media.

Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes in transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is a/L , being the ratio of the obstacle to system size.

Tortuosity-porosity relation in porous media flow.

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.