Eur. Phys. J. Plus (2020) 135: 551
https://doi.org/10.1140/epjp/s13360-020-00576-5

Regular Article

New models of porous media with rotational symmetry and their application

¹ N.N. Semenov Institute of Chemical Physics, Russian Academy of Science, Moscow, Russia
² JSC “Kompozit“, Korolev, Russia

^b sergeevandrey89@gmail.com

Received: 3 February 2020
Accepted: 29 June 2020
Published online: 8 July 2020

Abstract

This study offers new models of porous media, where the pores are present in the form of a disk-shaped or a sector-shaped gap. These models are usable for representing cylindrical-symmetry porous media, given an axial loading of the media and their elastic reaction, taking into account the viscous flow in the pores. When using the disk-shaped gap model, the viscous flow problem appears to be two-dimensional, while with the sectoral gap model—three-dimensional. With the sectoral gap model, it is possible to use multiple bifurcation of the sector for any radius, thus implementing a dichotomy. Thus, the resulting solution obtained for the three-dimensional case can be multiplied by applying new boundary conditions for each dichotomy radius, changing almost nothing in the porosity and shape over the entire thickness of the cylindrical body. Analytical relationships are suggested to describe a liquid flow through a disk-shaped or a sector-shaped gap. Results of numerical simulation of a liquid flow through a disk-shaped gap are presented.