Theory of Boundary Conditions for the Boltzmann Equation

In preceding papers, Refs. ^1,2, boundary conditions were developed for transport-relaxation 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 non-equilibrium thermodynamics - which are, broadly speaking, given by the sum and the difference of the molecular distribution function and its time-reversed, at the wall. The general properties of the kernels occurring in this atomistic boundary law are studied. The phenomenological surface coefficients of (generalized) linear thermo-hydrodynamics, 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.