Valveless pumping in a fluid-filled closed elastic tube-system: one-dimensional theory with experimental validation
Related Experiment Video
Updated: Sep 26, 2026

Protocol for Relative Hydrodynamic Assessment of Tri-leaflet Polymer Valves
Published on: October 17, 2013
1Department of Mathematics and Physics, P.O. Box 260, Roskilde University, Denmark. Johnny@ruc.dk
Abstract:
An elastic rubber tube is connected with a stiffer rubber tube forming two halves of a torus and filled with water. Compressing one of the rubber tubes symmetrically and periodic at a point of asymmetry creates a remarkable unidirectional mean flow in the system. The size and the direction of the mean flow depend on the frequency of compression, the elasticity of the tubes, the compression ratio, and the type of compression with respect to time in a complicated manner. The system is modelled using a one-dimensional theory derived by averaging the Navier-Stokes equations ignoring higher order terms in a certain small quantity. The one-dimensional model is analysed partly analytically and partly numerically. A series of experiments on a physical realisation of the system are described. The theoretical findings and experimental results are compared; They show a remarkable agreement between the experiments and the predictions of the model. Frequencies at which the mean flow change direction are predicted numerically as well as analytically and the two results are compared.
Related Concept Videos
Steady, Laminar Flow in Circular Tubes
Typical Model Studies
Bernoulli's Principle
Bernoulli's principle has several applications. It is used...
Pascal's Law
Steady, Laminar Flow Between Parallel Plates
Bernoulli's Principle: Applications
Entrainment devices use a high fluid speed to create low pressures and, thus, entrain one fluid into another. Some examples of these devices are given below:

