The Structure of Filter Curve and Methods of Its Approximation. Part 1. Darcy’s Law and the Lower Limit of Its Application. Filtration of Liquids in Microporous Media

The description of the lower limit of the application of Darcy’s law is given, which is due to the influence of a number of anomalous factors that arise during the filtration flow of liquids through low-permeability finely dispersed media. The influence of such factors as the action of the forces of intermolecular interaction is considered; boundary layers and surface wettability; concentration and electric potential gradients; the presence of impurities in the liquid; gas saturation and vaporization; changes in the structure of the porous medium, separately or in the aggregate, leading to a violation of Darcy’s law.

A Correlation for Nusselt Number of Slip Gas Flow in Confined Porous Media

A clear understanding of flow and heat transfer at pore-scale level in microporous media is a topic of concern in microcooling/heating systems. In this work, a multiple-relaxation-time lattice Boltzmann method (LBM) is employed to study flow and heat transfer of gas in microporous media. Curved boundaries are treated using an effective boundary condition, which is formed by combining nonequilibrium extrapolation with counterextrapolation methods. The method also incorporates velocity slip and temperature jump on gas–solid interface. A two-dimensional (2D) porous domain composed of microcylinders, is considered from a representative element volume (REV) for the simulation. Porosity of the domain is variated by altering diameter of microcylinders. Nusselt number is calculated by varying Knudsen number (0.0–0.1), Reynolds number (5–50) and porosity (0.4–0.8). Based on the obtained numerical predictions, a new Nusselt number correlation is proposed for the first time in this work which can accurately predict the heat transfer for slip gas flow in confined porous media.