A mathematical model of a selective nanopore

Membrane separation of mixtures is widely used in chemical, fuel and energy, pharmaceutical, food, and other industries. In particular, mixed gases are separated by porous carbon membranes of various designs. This work deals with a study of selective properties of a carbon nanopore in terms of its ability to separate helium-methane mixtures. Gaining knowledge of nanopore characteristics allows us to design nanoporous membranes that are optimal for our purposes.
The membrane composed of carbon nanoparticles has a potential energy barrier representing the summed energy of the interaction between the molecule passing through a membrane and each nanoparticle of the structure. The trajectory and velocity of the molecule are obtained when solving a system of differential equations using the Runge-Kutta fourth-order method. Permeability of the resulting filter element is determined by the molecular dynamics method as a ratio of the molecules passed through the membrane to the total number of launched ones.
Mathematical modeling of the described problem shows good selective properties of the carbon nanopore in terms of separation of a helium-methane mixture. Based on the calculated results, the most efficient pore diameter has been revealed, as well as the optimal density of the material providing the highest separation ratio for the mixtures under consideration.