Smoothing Oscillatory Peristaltic Pump Flow with Bioinspired Passive Components

Pulsating flows are common in many industrial, scientific, and natural fluidic systems. However, because the oscillatory flow component disturbs, e.g., optical measurements, deposition, or industrial processes, it is rarely desired. Moreover, in physiological conditions, pulsation control is desired. We explore the effect of using a plant-inspired nonlinear resistor to smooth the output of a peristaltic pump. Incorporating a 3D printed millifluidic biomimetic device reduces the oscillation amplitudes by 3 orders of magnitude, from $100\mathrm{\%}$ to $0.1\mathrm{\%}$ of the output flow rate. This represents a tenfold improvement relative to a purely linear resistive-capacitive approach. The observed flow kinetics compare well to a predictive model of peristaltic transport, allowing the further development of optimized fluid-handling systems driven by pulsatile flow. Applications to particle tracking and jetting are considered.

Figure 1

Demonstration of the peristaltic pump circuit design and resulting pressure-flow rate relationship in a surrogate device. (a) Schematic of the flow configurations I, II, and III. (b) Flow rate $Q$ and pressure at the device inlet $\mathrm{\Delta }p$ as a function of time for configurations I and II. Note that the pulsation amplitude $A$ differs between the two experiments. (c) Amplitude $A/\overline{Q}$ normalized by the mean flow rate $\overline{Q}$ plotted as a function of the mean flow rate $\overline{Q}$ for configurations I and II (dots and representative error bars). The data are in reasonable accord with a hydraulic circuit model (solid lines, see Sec. 2f). The inset of (c) illustrates the linear relation between the pressure drop $\mathrm{\Delta }p$ and the flow rate $Q$ for the isolated resistor I and the device.

Figure 2

A biologically inspired passive flow controller. (a) Photographs of the top and side views of the 3D-printed fluidic device. A thin flexible polymer sheet (purple) is sandwiched between the two halves of the apparatus. Refer to Fig. 3 within the Supplemental Material [44] for further details about the geometry. (b) A diagram of the device cross section at low pressures, with an undeformed membrane (purple line). Liquid enters at the top left at pressure $p_1$ and flows through the inlet channel of height $h_1$, width $2w$, and length $L$. It then enters the outlet channel of height $h_0$, width $2w$, and length $L$. Finally, it exits the device at the pressure $p_2$. We denote the thickness of the membrane $t$. See Table S1 within the Supplemental Material [44] for parameter values. (c) Diagram of the device cross section at higher pressures, showing the deformation across the length and width of the channel. The membrane deflection becomes significant when the applied pressure $p_1-p_2$ is comparable to the stress required to bend the membrane a distance $h_0$ into the outlet channel. This occurs when $p_1-p_2\approx \mathrm{\Delta }{p}_c\sim E{h}_0{t}^3/w$, where $E$ is Young’s modulus of the membrane [Eq. (2)]. (d) Flow rate $Q$ plotted as a function of the applied pressure $\mathrm{\Delta }p=p_2-p_1$ (dots and error bars), illustrating the distinct flow plateau generated by the gradual closing of the outlet channel by the membrane deflection at $Q\approx {10}^{-7}{\mathrm{m}}^3/$s. Data are in good agreement with a fluid-structure interaction theory [solid line, Eq. (1)]. The shaded area indicates the variation in the modeled flow rate due to uncertainties in the geometric parameters using standard error propagation. The variability is predominantly affected by the errors in $h_0$, $E$, and $t$.

Figure 3

Biologically inspired passive flow controller reduces the pulsatile component of a peristaltic pump by 3 orders of magnitude. (a) Flow rate $Q$ in the optimized system III plotted as a function of time for different peristaltic frequencies. (The flow rate increases with frequency, see Sec. 2.) The oscillation amplitude decreases near the device’s flow rate plateau at $Q\approx {10}^{-7}{\mathrm{m}}^3/$s [Fig. 2]. (b) Comparative representation of the normalized amplitude $A/\overline{Q}$ as a function of the mean flow rate $\overline{Q}$ (dots with representative error bars) of systems I, II, and III (see Fig. 1). The bioinspired system III is on a par with, or outperforms, all other flow configurations examined here. The variance in the bioinspired system originates from the lack of resolution close to the flow meter noise floor (shaded region). The data are in reasonable accord with the predictions of a hydraulic circuit model (solid lines, see Sec. 2f).

Figure 4

(a) Representative demonstration of two applications where the effect of adding the smoothing components to the flow of the peristaltic pump is beneficial: jetting and constant flow of microbeads. To record the oscillatory behavior of the flow, and ascertain the impact of the flow controller, we first observe a liquid jet impacting on a sheet of paper. The top row of (b) and (c) are photographs of the spray that emerged from a nozzle upstream of configuration I (constant resistor) and III (plant-inspired flow controller), highlighting the strong pulsation attenuation in system III. See Fig. 1 for configuration details. A paper strip is translated at a constant speed of approximately equal to $0.1$ m/s normal to the jet direction to further elucidate the temporal flow variation. The middle row of (b),(c) illustrates the flows thus imprinted on paper strips. Finally, the flow is visualized in a microfluidic channel using a microscope. In the bottom row of (b),(c), the motion of fluorescent particles (dots) is illustrated in a kymograph. The slope of the lines represents the lateral velocity of the particles in the channel (i.e., a horizontal line would represent a stationary particle). In system I, particle motion is strongly time dependent. In contrast, the particles in system III move at constant speed. The translucent boxes represent the pulsation period of the pump, linking the jet and particle tracking experiments.