Investigations on some diffusion problems in rarefied gases

• Main Author: Chu, Frank I-chien
• Format: Others
• Published: 1969
• Online Access: https://thesis.library.caltech.edu/3956/1/Chu_f_1969.pdf; Chu, Frank I-chien (1969) Investigations on some diffusion problems in rarefied gases. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SAKW-WA48. https://resolver.caltech.edu/CaltechETD:etd-10072002-143841 <https://resolver.caltech.edu/CaltechETD:etd-10072002-143841>

This is a theoretical study of diffusion problems in transitional rarefied gases with surface dissociation and recombination reactions. The method of composite solution, which is a simplified version of the exact composite expansion theory with similarity to the mean free path method, has proved to be very successful. Both the methods of Lester Lees and of composite solution have been used to solve the problem of simultaneous heat and mass transfer of a partially dissociated diatomic gas of transitional rarefaction from a hot fine wire to a surrounding cylinder. We have employed a sticking probability to describe the dissociation reaction of the diatomic gas at the wire but have used continuum type boundary conditions at the outer cylinder. We have also assumed a small total temperature variation and a small mole fraction of the dissociated atoms. The results obtained by both methods are identical and agree very well with the existing formulas in many limiting cases. Owing to its simplicity, the method of composite solution was applied to the problem of a subsonic viscous flow past a sphere for small Mach number but arbitrary Knudsen number. This problem was considered both as a prerequisite for the investigation of mass transfer from a sphere to a stream of gas mixtures and as a means to acquire familiarity with the matching procedures. The result for the drag force agrees with the known formulas in both the free molecular flow limit and the continuum limit. The agreement with experimental data in the transitional flow regimes is less satisfactory. The method of composite solution was then applied to the problem of mass transfer from a sphere to a partially dissociated diatomic gas. Surface recombination reaction was assumed to take place at the sphere while the flow conditions were the same as those in the previous problem. Small mole fraction of the dissociated atoms was also assumed, with the implication of a uniform temperature field. The concentration and flux of the dissociated atoms were found in terms of the sticking probability of the recombination reaction. The problem of simultaneous diffusion and reaction of dissociated atoms in the interior of a sphere is also very interesting and practically important. We have studied the special case of a very fast reaction where the concentration of atoms at the surface of the sphere is given. A new method of solving this unsteady state diffusion problem with moving boundary was proposed and has proved to be more advantageous than the existing ones. Finally, the sticking probabilities employed in the previous problems were obtained for various mechanisms of dissociation and recombination reactions. These sticking probabilities turn out to be constant over a wide range of Knudsen number and vanish in the continuum limit.