Mass transfer in ideal and geometrically deformed open tubes. : I. Ideal and coiled tubes with circular cross-section

Abstract

A summary of the hydrodynamics relevant to open tubes is presented. The band broadening of unretained samples in ideal and coiled tubes with circular cross-sections (0.25–4 mm I.D.) was measured with n-heptane and water as eluents. The lack of any appreciable interference from instrumental factors is substantiated by the experimentally determined diffusion coefficients and critical Reynold's numbers. It is shown that carefully prepared copper tubes behave as ideally as the corresponding glass tubes. With decreasing tube diameter, wall roughness leads to greater radial mass transfer. This effect is evident in 0.25-mm I.D. copper tubes and 0.5-mm (or even 0.75-mm) I.D. stainless-steel tubes, and can be used to advantage in constructing heat exchangers, connecting tubes or reaction detectors in liquid chromatography. It is shown for the first time that the onset of turbulence can be detected with considerably higher sensitivity by means of h versus u curves than by the K versus u curves used previously. It is shown that at the onset of turbulence the specific permeability decreases by a factor of about 3. Band broadening in the turbulent region was found to be ten times greater than that calculated on the basis of the friction theory of Taylor, apparently because laminar conditions prevail in a substantial portion of the tube cross-section. If an ideal tube is coiled, its specific permeability decreases with increasing velocity. Furthermore, coiling stabilizes “laminar” flow and the beginning of the turbulent region is shifted to higher Reynold's number ( i. e., higher velocities). It is shown that, as the inner diameter of the open tube decreases, higher linear velocities are required in order to decrease band broadening substantially ( e. g., by a factor of 5) for coiled tubes than for ideal tubes. For example, a linear velocity of 250 cm/sec is necessary to achieve this factor of 5 with 0.25-mm I.D. tubing, even though the presence of secondary flow is indicated by the K versus u curve at u > 10 cm/sec. For liquid chromatographic separations tubes narrower than 0.25 mm I.D. are essential. Therfore, at acceptable linear velocities (<50 cm/sec), the coiling of an