Application of Minkowski Space to Description of Anisotropic Pore Space Structure in Porous Materials

Abstract

AbstractThe subject of this note is the modelling of an anisotropic pore space structure in rigid porous materials capable of fluid flow through its pores. In this paper, the new macroscopic model of a saturated porous medium is proposed in which a fluid flow through porous skeleton of an anisotropic pore structure is considered as a motion of the material continuum in the plane anisotropic metric space ‐ Minkowski space ‐ immersed in a Euclidean one that is used as the model of the physical space. This model takes into consideration the fundamental fact, concerning kinematics of a fluid‐saturated porous solid, that the pore space of permeable skeleton forms the real space for a fluid motion and its structure imposes restrictions on that motion.The metrics of Minkowski and Euclidean spaces are applied in the paper to determine the respective measures of any line, surface, and volume elements. The new metric tensors of surface and volume elements in these spaces have been proposed that are directly related to the metric tensors of distance. This enables one to define the geometrical parameters characterising pore structure of such materials.: the tortuosity, the volume, and surface porosity. It has been shown that the structure of isotropic pore space of porous materials is described only by two independent scalar parameters.