Laminar dispersion in curved tubes and channels

Abstract

Dispersion in curved tubes and channels is treated analytically, using the velocity distribution of Topakoglu (1967) for tubes and that of Goldstein (1965) for curved channels. The result for curved tubes is compared with that obtained previously by Erdogan & Chatwin (1967) and it is found that the presentdispersion coefficient contains the Erdogan & Chatwin result as a limiting case.The most striking difference between the results is that Erdogan & Chatwin predict that the dispersion coefficient is always decreased by curvature if the Schmidt number exceeds 0.124, which is the ease for essentially all systems of practical interest. In contrast, the present result, equation (76), predicts that the dispersion coefficient may be increased substantially by curvature in low Reynolds number flows, particularly in liquid systems which would be of interest in biological systems.Two competing mechanisms of dispersion are present in curved systems. Curvature increases the variation in residence time across the flow in comparison with straight systems and this in turn increases the dispersion coefficient. The secondary flow which occurs in curved tubes creates a transverse mixing which decreases the dispersion coefficient. The results demonstrate that the relative importance of these two effects changes with the Reynolds number, since the dispersion coefficient first increases and then decreases as the Reynolds number increases. Since secondary flows are not present in curved channels the dispersion coefficient is increased over that in straight channels for all cases.