Modeling Valveless Pumping Mechanisms Public Deposited

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  • March 22, 2019
  • Baird, Austin
    • Affiliation: College of Arts and Sciences, Department of Mathematics
  • 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 ratio has a strong effect on the direction of flow when all other parameters are held fixed. The resonant frequency of the tube, based upon the elastic properties of the model and the added mass of the fluid, is also investigated. Resonance of two separate sections of the tube divided by the compression region can govern the resulting direction of flow if the tube is driven at the resonant frequency of one of the sections. Understanding the bi-directional nature of this popular pumping mechanism is important in the design of micro-fluidic pumps as well as the understanding of the structure and function of valveless hearts. In the third part of the thesis more the surrounding structures and properties of actual tubular hearts are used to improve my model of valveless pumping. I will focus on the tubular, valveless heart of the chordate, Clavelina picta. These hearts operate at a Womersley number of about 0.3. We investigate traditional impedance pumping on these small scales and show computationally and experimentally that significant flow is not achieved. We propose a different pumping mechanism that couples traveling waves of depolarization to the contraction of the boundary. Active contractile waves replace passive elastic waves, but the resulting kinematics are similar to dynamic suction pumping. This pumping mechanism can be computationally shown to drive fluid flow at the low Womersley numbers found in Clavalina picta hearts.
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Rights statement
  • In Copyright
  • Miller, Laura
  • Forest, M. Gregory
  • Mucha, Peter
  • White, Brian
  • Adalsteinsson, David
  • Waldrop, Lindsay
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2014
Place of publication
  • Chapel Hill, NC
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