- Volume 49 Issue 5
DOI QR Code
VALVELESS PUMPING IN OPEN TANK SYSTEM USING ENERGY CONSERVING COMPARTMENT MODEL
- Jung, Eun-Ok (Department of Mathematics Konkuk University) ;
- Kim, Do-Wan (Department of Mathematics Inha University)
- Received : 2011.05.12
- Published : 2012.09.30
A compartment model of the flow driven by pumping without valves (valveless pumping) in an open tank system is proposed. By the open tank system, we mean that two rigid cylindrical tanks are connected with an elastic tube. An incompressible fluid fills this system up to a certain level in tanks under the gravity. The compartment model for analyzing such open system is derived from the energy principle which will be called the energy conserving compartment model or shortly the ECCM. Based on this ECCM of valveless pumping, we explore the occurrence of directional net flow or directional net power by a specific excitation at an asymmetric part of the elastic tube. The interaction between deformable elastic tube and the fluid inside is considered in the ECCM. The reliability of the ECCMis investigated through some physical examples. The ECCM shows the existence of directional net power of the valveless pump system with open tanks and confirms that the direction and magnitude of the net power depend on the pumping frequency as well. Furthermore, the phase synchronization in time between the fluid pressure difference and the external pinching force over the pumping region is highly related to the direction of energy storing or net power.
- D. Auerbach, W. Moehring, and M. Moser, An analytic approach to the Liebau problem of valveless pumping, Cardiovasc. Eng. 4 (2004), 201-207. https://doi.org/10.1023/B:CARE.0000031549.13354.5e
- I. Avrahami and M. Gharib, Computational studies of resonance wave pumping in compliant tube, J. Fluid Mech. 608 (2008), 139-160.
- A. Borzi and G. Propst, Numerical investigation of the Liebau phenomenon, Z. Angew. Math. Phys. 54 (2003), no. 6, 1050-1072. https://doi.org/10.1007/s00033-003-1108-x
- T. T. Bringley, S. Childress, N. Vandenberghe, and J. Zhang, An experimental investigation and a simple model of a valveless pump, Phys. Fluids 20 (2008), 033602. https://doi.org/10.1063/1.2890790
- H.-T. Chang, C.-Y. Lee, and C.-Y. Wen, Design and modeling of a MEMS-based valveless pump driven by an electromagnetic force, DTIP of MEMS & MOEMS, Stresa, Italy, 26-28 April 2006.
- H.-T. Chang, C.-Y. Lee, C.-Y. Wen, and B.-S. Hong, Theoretical analysis and optimization of electromagnetic actuation in a valveless microimpedance pump, Microelectron. J. 38 (2007), 791-799. https://doi.org/10.1016/j.mejo.2007.04.013
- A. I. Hickerson, An Experimental Analysis of the Characteristic Behaviors of an Impedance Pump, Thesis, California Institute of Technology Pasadena, California, 2005.
- A. I. Hickerson, D. Rinderknecht, and M. Gharib, Experimental study of the behavior of a valveless impedance pump, Exps. Fluids 38 (2005), 534-540. https://doi.org/10.1007/s00348-005-0946-z
- E. Jung, A mathematical model of valveless pumping: A lumped model with timedependent compliance, resistance, and inertia, Bull. Math. Biol. 69 (2007), no. 7, 2181- 2198. https://doi.org/10.1007/s11538-007-9208-y
- T. Kenner, Biological asymmetry and cardiovascular blood transport, Cardiovasc. Eng. 4 (2004), 209-218. https://doi.org/10.1023/B:CARE.0000031550.14659.06
- J. Koo and C. Kleinstreuer, Viscous dissipation effects in microtubes and microchannels, Int. J. Heat Mass Tran. 47 (2004), 3159-3169. https://doi.org/10.1016/j.ijheatmasstransfer.2004.02.017
- S. Lee and E. Jung, A two-chamber model of valveless pumping using the immersed boundary method, Appl. Math. Comput. 206 (2008), no. 2, 876-884. https://doi.org/10.1016/j.amc.2008.09.047
- W. Lee, E. Jung, and S. Lee, Simulations of valveless pumping in an open elastic tube, SIAM J. Sci. Comput. 31 (2009), no. 3, 1901-1925. https://doi.org/10.1137/08071613X
- G. Liebau, Prinzipien Kombinierter Ventilloser Pumpen, Abgeleitet Vom Menschlichen Blutkreislauf, Naturwissenschaften 42 (2008), 339.
- Y. Y. Lin Wang, W.-B. Chiu, M.-Y. Jan, J.-G. Bau, S.-P. Li, and W.-K. Wang, Analysis of transverse wave as a propagation mode for the pressure pulse in large arteries, J. Appl. Phys. 102 (2007), 064702. https://doi.org/10.1063/1.2783979
- L. Loumes, I. Avrahami, and M. Gharib, Resonant pumping in a multilayer impedance pump, Phys. Fluids 20 (2008), 023103. https://doi.org/10.1063/1.2856528
- C. G. Manopoulos, D. S. Mathioulakis, and S. G. Tsangaris, One-dimensional model of valveless pumping in a closed loop and a numerical solution, Phys. Fluids 18 (2006), 017106. https://doi.org/10.1063/1.2165780
- C. G. Manopoulos and S. Tsangaris, Modelling of the blood flow circulation in the human foetus by the end of the third week of gestation, Cardiovasc. Eng. 5 (2005), 29-35. https://doi.org/10.1007/s10558-005-3071-y
- A. Olsson, G. Stemme, and E. Stemme, A numerical design study of the valveless diffuser pump using a lumped-mass model, J. Micromech. Microeng. 9 (1999), 34-44. https://doi.org/10.1088/0960-1317/9/1/004
- J. T. Ottesen, Valveless pumping in a fluid-filled closed elastic tube-system: onedimensional theory with experimental validation, J. Math. Biol. 46 (2003), no. 4, 309-332. https://doi.org/10.1007/s00285-002-0179-1
- G. Propst, Pumping effects in models of periodically forced flow configurations, Phys. D 217 (2006), no. 2, 193-201. https://doi.org/10.1016/j.physd.2006.04.007
- D. Rinderknecht, A. I. Hickerson, and M. Gharib, A valveless micro impedance pump driven by electromagnetic actuation, J. Micromech. Microeng. 15 (2005), 861-866. https://doi.org/10.1088/0960-1317/15/4/026
- S. Takagi and K. Takahashi, Study of a piston pump without valves, Bull. JSME 28 (1985), 831-836. https://doi.org/10.1299/jsme1958.28.831
- S. Timmermann and J. T. Ottesen, Novel characteristics of valveless pumping, Phys. Fluids 21 (2009), 053601. https://doi.org/10.1063/1.3114603
- A. Ullmann and I. Fono, The Piezoelectric Valve-Less Pump-Improved Dynamic Model, J. Microelectromech. Syst. 11 (2002), 655-664. https://doi.org/10.1109/JMEMS.2002.805048