The dispersion of a reactive species (atomic hydrogen) in a flowing gas

Abstract

Recent studies of the dispersion of hydrogen atoms in a flowing gas have necessitated the solution of the differential equation governing the dis­persion of a very reactive species in a medium flowing along a uniform circular tube with appropriate boundary conditions. The treatment takes into account irreversible loss of the reactive species by reaction on the tube wall and also their reversible adsorption and desorption at the wall. It is also shown how first-order reaction in the moving medium, ‘slip’ of the boundary layer, and a pressure drop along the tube can be taken into account. It is found that the longitudinal distribution of the reactive species becomes gaussian eventually and that, if initially symmetrical, it will stay symmetrical. The dispersion of the reactive species is shown to increase linearly with time. Exact equations are obtained for parameters describing the rate of loss of reactive atoms or molecules by reaction on the tube wall, their average velocity and their rate of dispersion. In addition, more con­venient approximate expressions are obtained for these parameters as expansions in the (small) rate of loss of molecules on the tube wall. The precision of these expansions is confirmed numerically by using typical experimental parameters. In the limit where the rate of loss of reactive atoms or molecules on the walls is zero, the theory presented is the exact theory of open-tube chromatography.