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.

Multivortex micromixing

“…These so-called Dean flows occur widely in nature and play an important role in a variety of applications ranging from chemical and mechanical engineering (e.g., heat exchangers, piping systems) to biomedical science (e.g., arterial blood flow, dialysis instruments) (21). The concept of Dean mixing has been explored extensively on the macroscale (22)(23)(24)(25)(26), where the use of helical tubes or pipes that extend out of a 2D plane allows curved flow trajectories to be maintained far downstream. A further adaptation of Dean effects are so-called ''twisted pipe'' designs (constructed by joining a series of planar curved segments such that each subsequent segment is oriented at a nonzero pitch angle relative to the previous one) where the inherent symmetry of the secondary flow streamlines is disrupted yielding chaotic particle trajectories (27).…”

Shear Dispersion along Circular Pipes Is Affected by Bends, but the Torsion of the Pipe Is Negligible

“…For a lower Reynolds number the qualitative deductions above vary from those of Nunge, Lin, and Gil [28] because their dispersion coefficient is different; see their equation (76). In particular, I predict that shear dispersion is frequently enhanced for gases, the reverse conclusion to that of Erdogan and Chatwin [11] and later Nunge, Lin, and Gil [28, pp.…”

“…The contaminant evolves according to the nondimensional advection-diffusion equation Here we analyze the flow and dispersion in an arbitrarily curving circular pipe. Most analysis of dispersion assumes a curved pipe is toroidal [33,28,19,8], and most experiments are performed in helical pipes [38] (see further discussion by Berger, Talbot, and Yao [3]). Neglecting molecular diffusivity, dispersion in toroidal flow has been characterized from analytic formulae by Ruthven [33] and numerical solutions by McConalogue [25] using the residence time of different streamlines.…”

Laminar dispersion at high Péclet numbers in finite-length channels: Effects of the near-wall velocity profile and connection with the generalized Leveque problem

“…The generalization of Taylor dispersion theory to Brownian particles possessing internal degrees of freedom has been developed by Frankel and Brenner. 14 Several authors considered Taylor-Aris dispersion in mildly curved channels and sinusoidal tubes, [15][16][17] in timeperiodic ͑pulsatile͒ flows, [18][19][20][21] as well as the effect of roughness on dispersion, 22 which determines a significant increase in the dispersion coefficient. A Lagrangian ͑stochastic͒ approach to Taylor dispersion has been proposed by Haber and Mauri.…”