Analytical solution of second Stokes problem about behaviour of gas over fluctuating surface by means of ellipsoidal statistical equation

TL;DR

This paper provides an analytical solution to the second Stokes problem for rarefied gas over a fluctuating surface using the ellipsoidal statistical kinetic model, revealing hydrodynamic behavior at low frequencies.

Contribution

It introduces an analytical approach to solve the second Stokes problem with the ellipsoidal statistical model for the first time.

Findings

Derived the distribution function of gas molecules.

Calculated the mass velocity of the gas in the half-space.

Determined the friction force on the oscillating boundary.

Abstract

Second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane limiting half-space makes harmonious fluctuations in the plane. The kinetic equation with modelling integral collisions in form of ellipsoidal statistical model is used . The case of diffusion reflexions of gas molecules from a wall is considered. Function distribution of gas molecules is constructed and mass velocity of gas also in half-space is found. Hydrodynamic character of the solution at small frequencies of fluctuation plane limiting gas is revealed. The force of a friction operating from gas on border making in the plane oscillatory movement is found.