Theory of Boundary Conditions for the Boltzmann Equation
Abstract
In preceding papers, Refs. ^{1,2}, boundary conditions were developed for transportrelaxation equations by aid of a general reciprocity postulate for the interface. The same method is now used for the linearized Boltzmann equation. A new scheme emerges: the kinetic boundary conditions consist in a linear functional relation between interfacial "forces and fluxes"  in the sense of nonequilibrium thermodynamics  which are, broadly speaking, given by the sum and the difference of the molecular distribution function and its timereversed, at the wall. The general properties of the kernels occurring in this atomistic boundary law are studied. The phenomenological surface coefficients of (generalized) linear thermohydrodynamics, as e. g. temperature jump, slip coefficients etc., can in a simple way be expressed by the kernel of the atomistic boundary law. This kernel is explicitly worked out for completely thermalizing wall collisions.
 Publication:

Zeitschrift Naturforschung Teil A
 Pub Date:
 June 1977
 DOI:
 10.1515/zna19770601
 Bibcode:
 1977ZNatA..32..521W
 Keywords:

 Boltzmann Transport Equation;
 Boundary Conditions;
 Boundary Value Problems;
 Nonequilibrium Thermodynamics;
 Transport Theory;
 Entropy;
 GasSolid Interfaces;
 Kernel Functions;
 Linear Equations;
 Rarefied Gases;
 Reciprocal Theorems;
 Thermodynamics and Statistical Physics