Limiting self-similar motion of a solid particle in a free-molecular gas flow escaping from an orifice

A problem of motion of a single spherical solid particle in the far wake of a free-molecular gas flow escaping from an orifice is considered. It is shown that the spatial distributions of macroscopic parameters of the gas are completely determined by functions of one variable: coordinate along an arbitrary straight line normal to the axis of symmetry. Based on this property, a dimensionless equation of particle motion is derived, which has self-similar solutions: trajectories of motion and particle coordinates (traces) on the target for different initial conditions. Conditions of determining the gas flow behavior on the basis of particle traces on the target are considered.