Diffusion through the Interface between Viscous Liquids in a Laminar Flow (Diffusion in a Laminar Flow)

Studies were carried out in order to know in some detail the transport phenomena through the interface in the viscous liquid moving in laminar flow. Experiments were carried out using ca. 88% glycerin solution, one added with an acid, and the other with alkali together with a small amount of phenolphthalein. Acidic glycerin solution was supplied to a long transparent cuvette of rectangular cross section through which the liquid was made to move slowly enough to establish the laminar flow, thin cords of coloured basic solution were introduced in the direction normal to the axis of flow at regular time intervals. The so obtained patterns of bending cords shortening in regular succession were photographed also at regular time intervals. The authors attribute the origin of the changing patterns of the cords to the velocity gradient existing in the acidic solution which accelerates the diffusion by increasing the concentration gradient near the cords as well as the increase of the interfacial area, and also the decrease of the thickness of the cords. Based on these idea a mathematical analysis was carried out and was obtained an equation which gives the change of the concentration distribution of two dimensional cords. Fair agreement was obtained between the results of mathematical analysis and those of experiments. Furthermore, the influence of the thickness of the cords, and that of the velocity gradient as well as of the diffusion coefficient on the concentration at the center of the cords were discussed.