Analytical solution of problem about moderately strong evaporation (condensation) for one-dimensional kinetic equation

TL;DR

This paper derives analytical solutions for one-dimensional kinetic equations describing moderately strong evaporation or condensation, providing explicit formulas for temperature and concentration jumps and distributions of key physical quantities.

Contribution

It presents the first analytical solutions for such kinetic problems under constant collision frequency, including jump conditions and distribution functions.

Findings

Explicit formulas for temperature and concentration jumps

Distributions of concentration, mass velocity, and temperature

Analytical solutions for kinetic equations with constant collision frequency

Abstract

For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function are linearize concerning the absolute Maxwellian, given far from a wall. Quantities of of temperature and concentration jumps are found. Distributions of concentration, mass velocity and temperature are constructed.