Yoshimoto Onishi

Kinetic Theory of Evaporation and Condensation –Hydrodynamic Equation and Slip Boundary Condition–

The steady behavior of a gas in contact with its condensed phase of arbitrary shape is investigated on the basis of kinetic theory. The Knudsen number of the system (the mean free path of the gas molecules divided by the characteristic length of the system) being assumed to be fairly small, the hydrodynamic equations for the macroscopic quantities, the velocity, temperature, and pressure, of the gas and their boundary conditions on the interface of the gas and its condensed phase are derived, and two simple examples (evaporation from a sphere, two-surface problem of evaporation and condensation) are worked out.

Kinetic Theory of Evaporation and Condensation

The behavior of a gas in contact with its condensed phase is considered on the basis of a relaxation model of the linearized Boltzmann equation. The temperature and density distributions of the gas in the Knudsen layer as well as so called slip boundary condition on the interface of the gas and its condensed phase are obtained.

Kinetic Theory of Slightly Strong Evaporation and Condensation : Hydrodynamic Equation and Slip Boundary Condition for Finite Reynolds Number

The asymptotic behavior for small mean free path of steady flow of a gas in contact with its condensed phase of arbitrary shape is investigated on the basis of kinetic theory. The hydrodynamic equations for the macroscopic quantities, the velocity, temperature, and pressure, of the gas and their boundary conditions on the interface between the gas and its condensed phase are derived up to the order of the Knudsen number squared, together with the Knudsen-layer correction near the interface. In the analysis, the perturbations from a uniform equilibrium state are assumed to be small, but their nonlinear effects are taken into account correctly so that the results obtained can be applied when the Reynolds number of the system is finite. This is an extension of the corresponding linearized theory by the same authors, which is valid only for very small Reynolds number.

Experimental Study on Instability of Natural Convection Flow above a Horizontal Line Heat Source

Experimental investigations on the stability characteristics of a natural convection plume in air above a horizontal line source of heat were performed. The results obtained experimentally confirm the predictions of the linear stability theory over an appreciably wide range of Grashof number. A slow fluctuation of a laminar plume, which is called swaying motion, was observed. Turbulent bursts in the transitional processes to turbulence were not detected but gradual and smooth breakdown of the initially regular disturbance waves were observed as the Grashof number increased.

Slightly Rarefied Gas Flow over a Body with Small Accommodation Coefficient

The asymptotic behavior (for small Knudsen number) of the steady flow of a rarefied gas over a body with a small accommodation coefficient (of the order of the Knudsen number) is investigated on the basis of the Boltzmann-Krook-Welander equation and the Maxwell-type boundary condition. It is shown that the present results provide a bridge between the cases of zero accommodation coefficient (specular reflection) and of finite one. As applications of the theory, a sphere with constant temperature in a uniform flow of gas and that in a gas at rest with a uniform temperature gradient are considered.

Kinetic Theory of Evaporation and Condensation of a Vapor Gas between Concentric Cylinders and Spheres

Evaporation and condensation of a slightly rarefied vapor gas between concentric cylinders and spheres are investigated on the basis of the linearized BKW (or BGK) equation and the diffuse reflection boundary condition. The reverse temperature gradient, negative heat and mass flows exist as in the parallel two-surface problem. The effects of the surface curvature, the normal stress other than pressure and the rarefaction on the above phenomenon as well as on the field distributions are also investigated.

Flow of Rarefied Gas over Plane Wall

Flow of a rarefied gas over an infinite plane wall is considered on the basis of a relaxation model of the Boltzmann equation. The solution is obtained in the form: Hilbert solution and boundary layer term which is appreciable only in a thin layer (with thickness of order of the mean free path) adjacent to the boundary. The Hilbert part dominates in the region away from the boundary. By using these results the asymptotic behavior (for small mean free path) of plane compressible Couette flow is investigated.

On the behavior of a noncondensable gas of a small amount in weakly nonlinear evaporation and condensation of a vapor

The steady behavior of a noncondensable gas contained in a vapor by a negligibly small amount is discussed in general terms based on kinetic theory when the Knudsen number of the system is small but the Reynolds number is finite. The macroscopic equations and the appropriate boundary conditions are derived for the description of the behavior of the noncondensable gas at the level of fluid dynamics together with the Knudsen layer corrections near the interfaces between the vapor and its condensed phases. The result shows that, in the present case, the behavior of the noncondensable gas is subject to the motion of the vapor and does not affect it at all. As expected, it indicates clearly the large variation of the number density and pressure of the noncondensable gas during the evaporation and condensation processes of the vapor. The half-space problem of evaporation and condensation is treated briefly as an example of this general analysis to show explicitly some of the qualitative nature of the noncondens...

Kinetic Theory Treatment of Nonlinear Half-Space Problem of Evaporation and Condensation

Evaporation and Condensation of a vapor gas over a plane interphase surface of its condensed phase are investigated analytically on the basis of the nonlinear Boltzmann-Krook-Welander equation and the diffuse reflection boundary condition. The distributions of temperature and pressure as well as the mass flux are explicitly obtained.

Kinetic Theory Treatment of Motion of a Spherical Condensed Phase in a Uniform Vapor Gas Flow

The behavior of a slightly rarefied vapor gas flowing around its spherical condensed phase is investigated on the basis of the linearized BKW (or BGK) equation and the diffuse reflection boundary condition. It is shown that the pressure field induced by velocity field plays an important role. The condensation occurs over the front part of the condensed phase and the evaporation over the rear due to this pressure field. This interphase transfer process reduces the total drag acting on the spherical condensed phase.