Illustration of the multilayer impedance pumping mechanism.
(Top) 3D view of the physical model of the gelatinous impedance pump. (Bottom) 2D view in the longitudinal cross section.
Schematic of the boundary conditions.
2D axisymmetric view of the mesh and pinching of imposed displacement of a series of nodes at the outer surface of the tube.
Impulse response: (top) Exit flow rate variation in time under triangular impulse excitation; (bottom) the associated power spectrum density (PSD). The Fourier transform was calculated using 4096 points and a time resolution of .
Typical exit flow rate history plot. Excitation frequency is . Periodicity is achieved after 15 pinching cycles and mean flow at steady state is . The solid line is a filtered curve of the flow rate using a moving average window of one cycle.
Mean exit flow rate as a function of the excitation frequency .
Gelatin maximum positive radial strain in time and space vs frequency of excitation .
Illustration of the propagating waves in the multilayer impedance pump. Example for . Selected frames at time as a fraction of the period time . Top frame: Outline of the model, walls position against longitudinal axis. Middle frame: Corresponding snapshots of the axial velocity fluid field. Bottom frame: Axial pressure longitudinal distribution.
(Top) Cross-sectional view of the impedance pump and the fixed control volume (solid line box) used to compute the energy balance, and the moving wall (dashed line). The fixed control volume is delimited by the input and output cross sections, the axis of symmetry, and a closure line outside the pump. The input and output cross sections delimit the passive portion of the tube for which mechanical work is calculated. We use a fixed control volume that encloses the moving wall so that to consider the wall motion as a shaft work. (Bottom) Schematic of the energy contributions to the fluid for the control volume considered. Pumping work defined as shaft work minus the losses is balanced by the differential of energy between the output and input of the system.
Pumping work of the elastic tube (, ) vs frequency of excitation .
The different test cases (mesh and time steps refinements) and the associated error with respect to the finest mesh.
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