Description of anisotropic pore space structure of permeable materials based on Minkowski metric space

Abstract

This paper contains an extended presentation of a new approach to the macroscopic description of anisotropic pore space structure of rigid permeable material, utilizing the concept of Minkowski metric space. The metrics of the Minkowski and Euclidean spaces are used to determine double measures of any line, surface and volume elements, and to define geometrical macro-parameters characterizing anisotropic pore space structure: the volume and surface porosities, and the tortuosity of the pores. It is shown that the metric tensor of the Minkowski space can be interpreted as a tensor of the pore tortuosity, and its inverse as a tensor of the surface porosity. This means that the pore tortuosity has a pure geometrical character and is of fundamental importance for description of anisotropic pore space structure and for all physical processes taking place in the pore space. The approach presented in this paper allows a description of fluid dynamics in the anisotropic pore space in the framework of rational mechanics.