In all high-vacuum mechanical pumps, namely molecular and turbo-molecular there is a need in sealing of inputs of the movement. A dynamic seals type find a wide application in modern industry. Protective properties and optimization of the dynamic seals at the stage of design become a relevant topic to be researched.

The aim of the work is to develop a mathematical model of gas flow in the face gap between two rotating disks. In building this model, the following assumptions are introduced: molecular gas flow, full exchange of momentum in collisions of molecules with disk surface, reflection of particles from the wall submits to the law of diffuse reflection, distribution of gas molecules according to the thermal motion speeds being described by Maxwell`s law. The calculation is based on the use of Monte Carlo method (method of test particle), which consists in the statistical modeling of processes. The article describes an algorithm to construct a mathematical model step by step. The trajectory of each molecule movement is traced from the moment of its moving in till its moving out of the system. The article defines both a probability for gas molecules to pass through the face gap of disk vacuum pump in forward and backward direction and a conductivity of the gap.

A numerical experiment based on the developed program has been conducted with considering the movement of the required number of molecules to provide a sufficient accuracy of calculation. Gas flow in the face gap of disk vacuum pump is studied. As a result of the experiment it was found that geometrical parameters of the gap and speed of disk rotation have an impact on the conductivity. With raising speed of disk rotation the probability for particles to pass in forward direction increases, accordingly increasing the conductivity, and for particles to pass in backward direction it decreases thereby improving the vacuum properties of the pump. The work carries out a process adequacy test based on the equality of the conductivity of the forward and reverse passages with disks being stationary. The accuracy does not exceed a tolerance. Results and, accordingly, recommendations, given in the article, can be used in designing a flow passage of the disk vacuum pumps, for providing a movement in high-vacuum mechanical pumps, and in calculating the overflows in the flowing passages of a similar pump design.