Masanari Hattori

Parabolic temperature profile and second-order temperature jump of a slightly rarefied gas in an unsteady two-surface problem

The behavior of a slightly rarefied monatomic gas between two parallel plates whose temperature grows slowly and linearly in time is investigated on the basis of the kinetic theory of gases. This problem is shown to be equivalent to a boundary-value problem of the steady linearized Boltzmann equation describing a rarefied gas subject to constant volumetric heating. The latter has been recently studied by Radtke, Hadjiconstantinou, Takata, and Aoki (RHTA) as a means of extracting the second-order temperature jump coefficient. This correspondence between the two problems gives a natural interpretation to the volumetric heating source and explains why the second-order temperature jump observed by RHTA is not covered by the general theory of slip flow for steady problems. A systematic asymptotic analysis of the time-dependent problem for small Knudsen numbers is carried out and the complete fluid-dynamic description, as well as the related half-space problems that determine the structure of the Knudsen layer ...

On the second-order slip and jump coefficients for the general theory of slip flow

The general theory of slip flow established in the late 1960s is revisited. For a long time, the complete set of data of the slip and jump coefficients up to the second order of the small Knudsen number have been available only for the Bhatnagar-Gross-Krook model. The present paper provides the complete set of data of those coefficients for a hard-sphere gas on the diffuse reflection boundary. The data are obtained by using the general identities that have been deduced from recently developed symmetry arguments. A few simple application examples are also presented.

A kinetic model of adsorption on solid surfaces

A kinetic model describing physisorption and chemisorption of gas particles on a crystal surface is introduced. A single kinetic equation is used to model gas and physisorbed particles interacting with an average potential and colliding with phonons. This equation is coupled to a kinetic equation describing localized chemisorbed species. A modified kinetic entropy is introduced for the coupled system and the H theorem is established. Using a fluid scaling and the Chapman-Enskog asymptotic method, fluid boundary conditions for the physisorbed and chemisorbed species are derived from the kinetic model.