## MBI Publications

### MBI Publications for Valveless Pumping (2)

• E. Jung, S. Lim, S. Lee and W. Lee
Computational models of valveless pumping using the immersed boundary method
Computer Methods in Applied Mechanics and EngineeringVol. 197 No. Series 25-28 (2008) pp. 2329-2339

#### Abstract

Mathematical models of valveless pumping can be represented by either a closed loop system or an open tube system. In this paper, we present a three-dimensional model of valveless pumping in a closed loop system. We also present a two-dimensional model using an open elastic cylinder contained in a rigid tank. In both models, we take the periodic compress-and-release action at the asymmetric location of the soft tube and observe the existence of a net flow and the important features of valveless pumping that have been reported in the previous models or experiments. The innovative idea of this work is that we explain the existence of a net flow by introducing the concept of the signed area of the flow-pressure loop over one cycle, which represents the power in the system. The direction and the magnitude of a net flow can also be explained by the sign and the amount of power, which is work done on the fluid by the fluid pressure and the elastic wall over one period, respectively.
• S. Lim and E. Jung
A three-dimensional model of a closed valveless pup system immersed in a viscous fluid
SIAM J. Appl. Math.Vol. 70 No. 6 (2010) pp. 1999-2010

#### Abstract

: We present a three-dimensional model of flow driven by pumping without valves (valveless pumping) in a closed loop system in which the closed loop of tubing is immersed in an incompressible viscous fluid. This closed tube consists of two parts, an open cylindrical soft tube and an open rigid tube, smoothly connected to one another. At an asymmetric location of the soft tube, a periodic compress-and-release action with a time delay between actions is taken to create a net flow. Numerical results show that the magnitude of average net flow and flow direction inside the tube depend on the pumping frequency, the amplitude of periodic forcing, the compression duration, the length of the soft tube, and the elastic properties of the tube. Fluid viscosity is also found to influence net flow. The immersed boundary method is used to investigate the interaction between the tube and the fluid and to study the valveless pumping mechanism. (A correction to the this article has been appended at the end of the pdf file.)