On the axial dispersion induced by vibrations of a flexible tube

The mechanism of shear-augmented longitudinal dispersion in a vibrating flexible thin-walled tube is investigated. An oscillatory flow in a long and longitudinally-tethered elastic tube is generated by small periodic radial displacements which form a standing-wave mode of wall vibrations. This mode of vibration arises in cylindrical shells, and for small radial displacements is consistent with the continuity equation for the fluid filling the tube. An order of magnitude analysis for the dispersion rate reveals that the effective dispersion depends on the fluid properties, the elastic and geometrical properties of the tube, and the oscillations frequency. Since no visco-elastic damping is accounted and, hence, there is no dispersion of the wave-length with the vibration frequency, the wave speed is independent of the constraining frequency. For this case (1) the dispersion induced by low-frequency wall vibrations of a gas-filled tube is almost unaffected by the frequency; (2) the effective dispersion decreases with frequency both for low-frequency wall vibrations of a liquid-filled tube, and for high-frequency wall vibrations of a tube filled with either gas or liquid. These results hold as long as dispersion induced by secondary streaming is negligible, which is true for the present long-wave mode of wall-vibrations induced flow. Monte-Carlo simulations were performed by tracking aerosol tracer point-particles in the flow field. Very high rates of dispersion were found relative to a spread resulting solely from molecular diffusion. For physiological systems as lungs and udders, enhancement of longitudinal transport by radial tube vibrations is limited due to the large wave-lengths associated with this mode of vibration. (C) 1999 Elsevier Science Ltd. All rights reserved.