Mathematical modelling of permeability for materials composed of spherical nanoparticles

We study permeability of a compacted material consisting of spherical nanoparticles and the possibility of using this structure for separating components of natural gas. We analyze the ability of test molecules to overcome the energy barrier in gaps between rows of spherical nanoparticles. We define the tunnel of particles which is a simple structural element of a composite porous material. The ability of molecules to move closer to nanoparticles and then move in a more powerful field of repulsive forces influences filtration properties of porous materials. We consider carbon nanoparticles and bombarding molecules of helium, hydrogen, and methane. We find the geometrical dimensions of gaps providing differential permeability of natural gas components.