Behavior of a viscoelastic valveless pump: a simple theory with experimental validation

Babbs

Description

A valveless pump generates a unidirectional net flow of fluid around a closed loop of soft viscoelastic tubing that is rhythmically compressed at one point. The tubing must have at least two sections with two different stiffnesses. When a short segment of the tube is squeezed asymmetrically at certain frequencies, net flow of fluid around the loop can occur without valves. Methods Partial differential equations for the pressures, volumes, and flows define a simple one-dimensional model of such a pump, based upon elementary physical principles. Numerical computations on a personal computer can predict measured net flows. Results Net flow varies with the frequency and waveform of compression used to excite the pump, as well as with the site of compression and the stiffness and viscosity of the tubing. Net flows on the order of 1 ml/sec are obtained in a water-filled loop including 46 cm of stiffer plastic (Tygon) laboratory tubing and 70 cm of softer latex rubber tubing. Conclusions The heretofore mysterious phenomenon of valveless pumping can be described in terms of classical Newtonian physics, in which viscous damping in the walls of the pump is included. Studying valveless pumps in the laboratory and modeling their behavior numerically provides a low-cost, engaging, and instructive exercise for research and teaching in biomedical engineering.

Informations

• Publié par: biomed
• Publié le: 01 janvier 2010
• Nombre de lectures: 5
• Langue: English

Extrait

BabbsBioMedical Engineering OnLine2010,9:42 http://www.biomedicalengineeringonline.com/content/9/1/42

R E S E A R C H Behavior of a viscoelastic valveless a simple theory with experimental

Charles F Babbs

Correspondence: babbs@purdue. edu Weldon School of Biomedical Engineering and Department of Basic Medical Sciences, 1426 Lynn Hall, Purdue University, West Lafayette IN 479071246, USA

Open Access pump: validation

Abstract Background:A valveless pump generates a unidirectional net flow of fluid around a closed loop of soft viscoelastic tubing that is rhythmically compressed at one point. The tubing must have at least two sections with two different stiffnesses. When a short segment of the tube is squeezed asymmetrically at certain frequencies, net flow of fluid around the loop can occur without valves. Methods:Partial differential equations for the pressures, volumes, and flows define a simple onedimensional model of such a pump, based upon elementary physical principles. Numerical computations on a personal computer can predict measured net flows. Results:Net flow varies with the frequency and waveform of compression used to excite the pump, as well as with the site of compression and the stiffness and viscosity of the tubing. Net flows on the order of 1 ml/sec are obtained in a water filled loop including 46 cm of stiffer plastic (Tygon) laboratory tubing and 70 cm of softer latex rubber tubing. Conclusions:The heretofore mysterious phenomenon of valveless pumping can be described in terms of classical Newtonian physics, in which viscous damping in the walls of the pump is included. Studying valveless pumps in the laboratory and modeling their behavior numerically provides a lowcost, engaging, and instructive exercise for research and teaching in biomedical engineering.

Background Imagine a closed loop of flexible rubber tubing filled with water or a similar incom pressible fluid, having nonzero density. In typical laboratory experiments the loop is about 50 to 100 cm in circumference, and the tubing is about 0.5 to 1 cm in diameter. A short segment of the tube is squeezed at a frequency of 1 to 6 Hz. If the wall of the tubing is completely uniform in composition, then a small amount of fluid flows away from the compression point in both directions equally, distending the remainder of the loop slightly. When compression is released, fluid flows back again with no net flow around the loop in either direction. However, if the loop is composed of two different types of tubing with different compliances, one stiffer and one more flexible, then under certain conditions there can be unidirectional net flow around the loop[15]. When one end of the softer section of tubing is rhythmically compressed, net flow of fluid around a loop of tubing has been observed in both physical experiments[4,6] and in numerical simulations[1,35]. This phenomenon is calledvalveless pumpingbecause

© 2010 Babbs; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.