Modeling Valveless Pumping Mechanisms

Austin J Baird: Modeling valveless pumping mechanisms (Under the direction of Laura Miller) Several mechanisms of valveless pumping are studied numerically. The discussion begins with an introduction into the two well-known driving mechanisms of flow in valveless tubes: impedance pumping and peristalsis. Flow generated from peristalsis and impedance pumping is examined using the immersed boundary method. Previous research has shown that impedance pumping, also known as dynamic suction pumping, produces bidirectional flows. This change in direction is dependent upon pumping frequency, the position of the actuation point, and several other parameters. In this thesis, I investigate the direction and magnitude of flow as a function of the Womersley number and the diameter to length ratio of the flexible portion of the tube. The diameter to length ratio has a significant effect on the overall net flow rate and direction. This type of sensitivity is not seen in peristalsis where the average net flow is determined by direction and speed of the contraction wave. Variations in Womersley number are used to determine at what scales peristalsis and dynamic suction pumping are effective. For the parameters considered, valveless suction pumping does not generate significant flow for Womersley numbers less than 1. In the second part of the thesis, the flow direction of impedance pumping as a function of tube diameter and pumping frequency is examined in more detail. Impedance pumping, is a mechanism that has been speculated to be the driving force behind the uni-directional flow present in the vertebrate embryonic heart. Although the bidirectional nature of this mechanism is something that has been described in experimental and computational studies, no well established explanation has been offered for why changes in flow direction are seen for certain parameters choices. We will address the bidirectional nature of this mechanism by investigating flow direction as a function of the ratio of the tube diameter to length and the elastic properties of the tube. Direct numerical simulations of the fully-coupled fluid-structure interaction problem will be used to determine the magnitude and direction of fluid flow as a function of these parameters. The diameter to length