Studying permeability of nanostructures obtained from polyethylene threads

The paper studies process of interaction of a moving molecule with structure atoms. The mathematical description is based on application of Hamiltonian systems model and numerical methods for solving the basic problem of molecular dynamics. The interaction between individual atoms and the simplest molecules is cared out using the classical Lennard-Jones potential. Polyethylene nanostructures are considered as filtering elements for selective separation of natural gas mixtures, in particular, their light components: hydrogen and helium. The influence of geometric dimensions and geometric features of a nanostructure on selectivity of gas mixtures separation is studied

The mathematical model of the chevron-arch gearing transmitter

The teeth of herringbone transmission wheels are obtained by docking two helical wheels with an opposite arrangement of teeth, which can solve the problem of the axial force. The mathematical model of coupling chevron teeth of the driving wheel in the area of their docking using the arch tooth fragment is developed. The conjugacy area surface of the driven wheel chevron teeth is obtained as the envelope of the surfaces family formed by the arched tooth during the process of the parts motion

Permeability of ultra-thin amorphous carbon films

The present paper deals with defining the energy of interaction between an ultra-thin hydrocarbon layer and helium molecules using a modification of the LJ-potential and the continual approach. The suggested approach allows determination of the statistically average motion of a test molecule through material layers under consideration. The obtained results made it possible to localize global sorption zones both inside the layer and at its external borders and to identify the parameters which are responsible for permeability of the layer

Separation of gases using ultra-thin porous layers of monodisperse nanoparticles

The present paper deals with a numerical solution of the two-dimensional problem of helium and methane molecules motion through an ultra-thin layer of a porous material composed of spherical nanoparticles of the same size. The interaction potential “nanoparticle-molecule” is obtained by integrating paired molecular interactions over the nanoparticle volume. Using the method of classical molecular dynamics, permeability of a layer having the size of about 10−8 m is studied

Penetration of particles through multi-barrier systems

The paper gives a theoretical justification for the effect of increasing permeability of ultra-thin membranes by altering their internal material structure, namely through the process of creating one or two energy voids within the permeable layer. An effective computing technology for solving the stationary Schrödinger equation is also described

Simple energy barrier for component mixture of natural gases

This paper investigates the ability of a test molecule to overcome the energy barrier being in the gap between spherical nanoparticles. Three particles make a primitive structural element of composite porous material. The ability of molecules to converge with nanoparticles and then to move through more powerful repulsion field defines the filtration properties of porous materials. This paper presents the investigation of carbon nanoparticles and molecules of helium and methane bombarding them. Calculations proved that methane molecules can not get through three particles if the gap equals to 3.5 nm. For helium molecules this value makes 1.02 nm. These gaps remain the same when the size of nanoparticles increases. Therefore filters for helium separated from natural gas are to have nanopores within the range from 1.02 nm to 3.5 nm

The interaction potential of an open nanotube and its permeability: molecular dynamics simulation

The integration of the modified LJ-potential allowed revealing the universal effect of the open carbon tube on the molecular objects moving within or proximate to the tube. There has been established that there are modes of the molecule motion without the energy exchange with the atoms of the carbon framing, under which the moving molecules are subjected to the considerable activation in the tube. The potential holes being the sorption zones in fact are localized

Permeability of the regular structure from spherical nanoparticles

This paper presents a theoretical study on permeability of a regular structure composed of twenty spherical nanoparticles of the same size. The numerical solution is constructed using turn-based schemes of higher-order accuracy. The interaction between structure elements and moving molecules is determined by the V.Y. Rudyak and S.L. Krasnolutsky potential. It was found, that the tested model structure has the helium permeability to four times more than for methane

Ability of fullerene to accumulate hydrogen

In the present paper, using a modification of the LJ-potential and the continuum approach, we define С60-H2 (He) potentials, as well as interaction energy of two fullerene particles. The proposed approach allows to calculate interactions between carbon structures of any character (wavy graphenes, nanotubes, etc.). The obtained results allowed to localize global sorption zones both inside the particle and on the outer surface of the fullerene

Numerical simulation of oil pool boundary evolution

The study of spatial distribution of hydrocarbon resources and forecasting their geographical location is of great importance for the most complete recovery of hydrocarbons from deposits. The present study gives new mathematical results in the theory of stratified fluid flow in a porous medium. This paper analyzes the evolution of oil pool boundary basing on vortex numerical model for movement of the boundary separating fluids of different densities. It presents the investigation of how the location of light fluid regarding the heavier fluid influences on the changes in the boundary between two media in case of various shifting of the well