Resonant pumping in a multilayer impedance pump

Abstract

This paper introduces the concept of multilayer impedance pump, a novel pumping mechanism inspired by the embryonic heart structure. The pump is a composite two-layer fluid-filled elastic tube featuring a thick gelatinous internal. Pumping is based on the impedance pumping mechanism. In an impedance pump, elastic waves are generated upon external periodic compressions of the elastic tube. These waves propagate along the tube's walls, reflect at the tube's extremities, and drive the flow in a preferential direction. The originality in the multilayer impedance pump design relies on the use of the thick internal gelatinous layer to amplify the elastic waves responsible for the pumping. As a consequence, only small excitations are needed to produce significant flow. This fully coupled fluid-structure interaction problem is solved for the flow and the structure using the finite element method over a relevant range of frequencies of excitation. Results show that the multilayer impedance pump is a complex system that exhibits a resonant response. Flow output and inner wall motion are maximal when the pump is actuated at the resonant frequency. The wave interaction mechanism present in an impedance pump is described here in details for the case of a multilayer impedance pump. Using energy balance for the passive portion of the elastic tube, we show that the elastic tube itself works as a pump and that at resonance maximum energy transmission between the elastic tube and the fluid occurs. Finally, the pump is especially suitable for many biomedical applications.

How does the tubular embryonic heart work? Looking for the physical mechanism generating unidirectional blood flow in the valveless embryonic heart tube

“…The thick gelatinous layer was found to amplify the elastic waves responsible for Liebau effect-driven pumping, so that only small excitations of the active compression side (10% external radius) were needed to produce significant flow (Loumes et al, 2008). The presence of a thick layer of cardiac jelly obviously seems to be advantageous for the pumping function of both kinds of tubular hearts; those working as peristaltic pumps (Barry, 1948) as well as those working as Liebau pumps (Loumes et al, 2008). Therefore, the presence of a thick layer of cardiac jelly cannot be regarded as supporting evidence for either of the two competing theories of early cardiac pumping mechanism.…”

“…However, recent studies on Liebau pumps have shown that this must not be the case. Inspired by the multilayered structure of embryonic heart tubes, engineers have constructed a multilayered Liebau pump in which a thick gelatinous layer acts as cardiac jelly (Loumes et al, 2008). The thick gelatinous layer was found to amplify the elastic waves responsible for Liebau effect-driven pumping, so that only small excitations of the active compression side (10% external radius) were needed to produce significant flow (Loumes et al, 2008).…”

“…Inspired by the multilayered structure of embryonic heart tubes, engineers have constructed a multilayered Liebau pump in which a thick gelatinous layer acts as cardiac jelly (Loumes et al, 2008). The thick gelatinous layer was found to amplify the elastic waves responsible for Liebau effect-driven pumping, so that only small excitations of the active compression side (10% external radius) were needed to produce significant flow (Loumes et al, 2008). The presence of a thick layer of cardiac jelly obviously seems to be advantageous for the pumping function of both kinds of tubular hearts; those working as peristaltic pumps (Barry, 1948) as well as those working as Liebau pumps (Loumes et al, 2008).…”

Computational studies of resonance wave pumping in compliant tubes

“…For further study of the pumping power transferred to the fluid by the elastic tube, an energy calculation was performed based on the method described in Loumes, Avrahami & Gharib (2008). The control volume (∀) selected for the calculation is defined as the long passive region (illustrated in figure 13a), bounded by the elastic tube and the cross-sections z = 4 cm (input) and z = 14 cm (output).…”

“…The input and output energy fluxes through the control surface were calculated from their kinetic and potential components (for further details refer to Loumes et al 2008):…”