Net flow generation in closed-loop valveless pumping

Abstract

Net flow generation in valveless pumping, met in many physiological applications and recently in micropumping devices, constitutes an open fluid dynamics issue due to the complex interaction between the fluid medium and the flexible walls of the pump. In the context of the present experimental work, the conditions of the net flow generation are examined in a closed-loop horizontal valveless pump, which consists of a rigid and an elastic tube of equal diameters and lengths, and a pincher that forces the liquid within the tube to oscillate at Reynolds and Womersley numbers up to 7800 and 48, respectively. Pinching off as well as at the mid-length of the pump flexible tube, net flow is generated at certain pinching frequencies for which details are presented based on simultaneous recording of the pressure at the two tube junctions, the flow rate and the displacement of the pincher. Pinching off the mid-length of the pump at low pinching frequencies, net flow rate is practically null due to the almost identical pressure waveforms at the tube junctions, which vary in phase with the pincher motion. However, close to the first natural frequency of the hydraulic loop, the reflection of the pressure waves at the tube junctions combined with their increased phase difference cause high axial pressure gradients, which when they increase simultaneously with the squeezing of the tube, net flow rate maximization occurs. Pinching at the flexible tube mid-length area, nonzero net flow rates can also be generated, the sign of which changes when the pincher mid-point crosses the tube mid-length without being nullified.

Output of a valveless Liebau pump with biologically relevant vessel properties and compression frequencies

“…The physics of Liebau-type pumping is surprisingly complex since there are multiple variables involved, each having potential impact on the direction and the amplitude of the flow 6 , 7 , 9 , 15 , 34 . When recorded over broad range of frequencies, the relationship between the compression frequency and the mean flowrate has been shown to be highly non-linear 11 , 17 , 18 , 35 .…”

Building Valveless Impedance Pumps From Biological Components: Progress and Challenges

“…Yet the exact shape of the latter curve, as well as the number of flow-frequency peaks, varies dramatically across studies. In addition, while some report maximal flowrate near F n (Hickerson et al, 2005;Kozlovsky et al, 2015;Manopoulos et al, 2020), others report it being close to zero (Takagi and Takahashi, 1985;Borzì and Propst, 2003;Meier, 2011).…”

“…Frequencies at which the system resonates can be determined experimentally upon hitting the tube with a substantial force and applying a fast Fourier transform analysis to pressure signals (Manopoulos et al, 2020). There is also a simple formula to calculate the natural frequency of a tube:…”

“…When W o > 10, the velocity profile is flat or plug-like, and the flow is phase-shifted relative to the oscillating pressure gradient. Values of 1 < W o < 10 represents intermediate regimes (Manopoulos et al, 2020). For the surveyed non-biological studies of Liebau pumps listed under Table 2, typical W o values exceed 10.…”

“…These included inclusion of bends (Hiermeier and Männer, 2017), insertion of cavities (Kozlovsky et al, 2015), use of tapered connectors (Lee et al, 2017), or asymmetric arrangement of resistances between the two sides of the compliant tube (Wen and Chang, 2009). Due to its complexity and dependence on many variables, the pumping mechanism proposed by Liebau remains the subject of interest across a wide range of disciplines, including physiology, engineering, physics, and biomedical research (Hickerson et al, 2005;Rinderknecht et al, 2005;Hickerson and Gharib, 2006;Manopoulos et al, 2006Manopoulos et al, , 2020Bringley et al, 2008;Timmermann and Ottesen, 2009;Rosenfeld and Avrahami, 2010;Meier, 2011;Lee et al, 2013;Kozlovsky et al, 2016;Zislin and Rosenfeld, 2018;Li et al, 2019;Davtyan and Sarvazyan, 2021).…”