THE VISCOUS AIR-FLOW PATTERN IN THE STEFAN DIFFUSION TUBE - APPLICATION TO THE MUTUAL DIFFUSION IN A POROUS-MEDIA

In this paper, we consider the problem of the binary viscous diffusion of vapour through a Stefan tube, which is the model of an elementary capillary. While some preceding results in particular cases supposed p arabolic velocity profiles and showed air recirculation, we treat here the general problem of a tube of finite length, submitted to a double viscous diffusion of vapour and air from a liquid surface. The moveme nt of gas is expressed with conservation equations and ideal gas equat ions. The following added restrictions: constant temperature, no buyoa ncy effect, no inertial forces, are compatible with a capillary. A num erical solution based on the control volume method is obtained at ever y point in the tube. The results give the vapour and air flux, describ e the circulation pattern and show that the vapour profile of concentr ation is level. In the lower part of the cylindrical tube space, over a distance of the length of a radius an important radial movement occu rs, due to the recirculation of air which changes direction once it re aches the liquid surface. The velocity profile of the gas flow then be comes parabolic in the upper part of the tube. In order to easily obta in a numerical solution, the system of dimensionless equations is expa nded to a series and transformed into a set of sub-systems. The little parameter used for this expansion is tied to the vapour concentration on the liquid surface. The solution of the sub-system of order zero, which is easier to compute, represents a good approximation of the com plete solution. These solutions are situated in comparison with the St efan diffusion and show that the influence of the viscous effect on th e vapour flux is limited to a few percents. In order to apply the resu lts to porous media where the pores are not so regular, we consider at last the diffusion in a tube including a contracted section in the mi ddle of the tube. Since the diffusion paths are longer, the vapour flu x is reduced, while the viscosity effect becomes more considerable. Th e reduction of the air flux is more significant than that of the vapou r. This part of the study provides a better understanding of the diffu sion through the pits at the wall fiber, and gives data for the air fl ux which permeates into the oak wood and produces tannin oxidation and thus discolouration.