Artificial Whisker Sensor with Undulated Morphology and Self-Spread Piezoresistors for Diverse Flow Analyses

Abstract

Harbor seal whiskers possess an undulated surface morphology that can effectively modify the vortex street behind the whiskers and suppress vortex-induced vibrations (VIVs). In this study, we propose a novel piezoresistive flow sensor that mimics the function of seal whiskers. The sensor consists of a bionic whisker with an undulated morphology and integrated out-of-plane piezoresistors. The piezoresistors are formed using a novel directional liquid spreading method to deliver a conductive nanocomposite ink into four Ω-shaped microchannels. Steady flow experiments indicate that the undulated morphology of the artificial whisker significantly reduces the drag forces and VIVs of the whisker at an angle of attack of 0°. Moreover, the whisker sensor can measure the oscillatory flow, which reaches a threshold detection limit of 8 mm/s. In addition, we demonstrate the function of the artificial whisker sensor to distinguish various wakes induced by upstream cylinders. Therefore, the facile fabrication and preliminary experiments of the artificial whisker sensor demonstrate its potential application in diverse flow analyses.

Introduction

With the rapid development of unmanned underwater vehicles and soft robots, miniaturized and flexible flow sensors have become crucial for attitude control and flow-field analysis. Hair-like flow sensors inspired by the highly sensitive flow receptors of fish, insects, and harbor seals have been extensively studied in the literature.^1–5 For instance, Kottapalli et al. developed a hair-like sensor consisting of a liquid crystal polymer membrane with metal piezoresistors and a cylindrical rod for flow sensing.¹ Gul et al. proposed a fully 3D printed whisker sensor by integrating a polyurethane rod with piezoresistive graphene stripes.² However, vortex shedding also occurs when the incoming flow on cylindrical rod-structured sensors is uniform; this flow exerts a suction force on the rod and results in strong vibrations.^6–8 Such vortex-induced vibrations (VIVs) cause considerable noise and deteriorate the signal-to-noise ratio of the flow sensor.

Blindfolded harbor seals use their whiskers to track vortex wakes induced by mobile animals.^9–12 While scanning the water for these hydrodynamic signals, the seals generally align their long and flexible whiskers perpendicular to the swimming direction.¹³ Interestingly, the morphology of the harbor seal whisker differs significantly from that of terrestrial mammals: the cross-section is elliptical, with its long axis aligned with the incoming flow, and the ratio of the long and short axes changes along the whisker. Therefore, the flattened whiskers have an undulated surface structure.^14–16 This unique morphology probably allows the seal whisker to suppress the VIVs and self-induced noise from these VIVs.^17–21

Inspired by the morphology of harbor seal whiskers, Beem and Triantafyllou presented an artificial seal whisker sensor with four piezoresistive beams.²¹ Both cross-flow and in-line vibration amplitudes of the whiskers were ∼90% smaller than those of the cylinder rod. Alvarado et al. proposed a whisker-like sensor by mounting a bionic whisker on a flexible membrane with four flexible variable potentiometers.²² However, these artificial whisker sensors^21–23 were based on discrete strain gauges or displacement sensors, which made them bulky and resulted in a cumbersome assembly. Therefore, the development of seal whisker-inspired flexible flow sensors with a facile fabrication technique and optimized morphology for enhanced sensitivity, suppressed noise, and miniaturized size remains a technological challenge.

In this article, we report a novel design and fabrication method for an artificial whisker sensor that consists of a 3D-printed bionic whisker and a polydimethylsiloxane (PDMS) base rod integrated with four Ω-shaped microchannels (Fig. 1). A directional liquid spreading (DLS) method was used to form out-of-plane piezoresistors in the microchannels, in which carbon nanotubes and silver nanoparticles (CNT/AgNPs) ink was filled. Compared to direct printing methods, DLS is a much more facile and high-speed approach to form well-defined piezoresistors with complicated out-of-plane structures. This artificial whisker sensor exhibited good sensitivity for intricate flow details, including vortex-induced vibrations, oscillating flow, and upstream wakes.

FIG. 1.

Schematic structure of the seal whisker-inspired flow sensor.

Materials and Methods

Sensor design

The sensor consists of a bionic whisker and a PDMS base with piezoresistors near the fixed end, as illustrated in Figure 1. The bionic whisker was 35-mm long and had an undulatory, asymmetrical, and elliptical geometry. The geometrical dimensions of the bionic whisker in this study were twice that of the biological whisker reported by Hanke et al.¹⁷ The PDMS base comprises of a base plate (10 mm × 10 mm × 2 mm) and a base rod (Ø 1.4 mm × 7 mm). Four microchannels (5 mm × 200 μm × 80 μm) with inclined pitted grooves²⁴ extended from the pads on the base plate to the cylindrical base rod. The depth of the overlaid microgrooves was 30 μm, the length of the overlaid microgrooves along the channel direction was 60 μm, and the angle between the leading edge of the microgroove was 120° (Supplementary Fig. S1).

CNT/AgNPs were used as the sensing material deposited on the microchannel surface. The four CNT/AgNP-based piezoresistors on the surface of the PDMS rod enabled the whisker sensor to detect deflections in any direction.

Fabrication

The fabrication process is illustrated in Figure 2and Supplementary Figure S2. The bionic whisker and two pieces of molds for the PDMS base were fabricated from a resin using a microscale 3D printing system (nanoArch P130; BMF, China). Commercially available PDMS (Sylgard 184; Dow Corning) was cast into the molds (Fig. 2a) to obtain a PDMS base with microchannels on the surface of the rod. The monomer curing agent of the PDMS solution was mixed at a weight ratio of 10:1, degassed inside a vacuum chamber to remove any air bubbles, and finally poured into the molds. The poured solution was then cured at 60°C for 4 h, and then the solid PDMS structure was peeled off.

FIG. 2.

Schematic diagram of the fabrication steps: (a) PDMS casting through the 3D-printed mold. (b) CNT/AgNP ink filling. (c–f) High-speed images of the DLS process. CNT/AgNPs, carbon nanotubes and silver nanoparticles; DLS, directional liquid spreading; PDMS, polydimethylsiloxane.

The ink of the piezoresistive strain gauges was prepared by mixing the CNT paste (MW095; Kaina, China) and AgNP ink (CON-INK550; BroadTeko, China). After an oxygen plasma treatment of the PDMS base, ∼0.5 μL of the ink was filled into the pads using a micropipette (Fig. 2b). Subsequently, it readily flowed into the microchannels in 13 s using the DLS mechanism²⁵ with CNT/AgNPs coated on the microchannel walls. A high-speed video recorder (I-speed LT; Olympus, Japan) was used to observe the liquid spreading process (Figs. 2c–f). Finally, a PDMS layer was deposited evenly over the structure by spray coating for waterproofing.

Characterization of piezoresistors

To calibrate the gauge factors (GFs) of the piezoresistors, we measured the variation in resistance, which was induced by the strain of the bionic whisker. While the bionic whisker deflected, a strain was introduced owing to the bending radian of the curved PDMS rod, which led to a variation in the resistance of the piezoresistor. Subsequently, a microstage was used to shift the tip of the bionic whisker, and a SourceMeter (Keithley 2400; Tektronix) was used to record the resistance simultaneously.

Experimental setup

The sensor was placed in a water tunnel to calibrate its VIV suppression and drag reduction capabilities. A velocimeter (SLD300-A; SENLOD, China) was used to monitor the flow velocity in the water tunnel. The output of the sensor was filtered using a low-pass filter with a cutoff frequency of 45 Hz. These data were then collected by a USB data acquisition system (USB-4711; Advantech, China) at a data sampling rate of 2000 Hz. The average normalized resistance change was used to estimate the flow velocity. To determine the amplitude and frequency of the VIV, the output from the sensor was additionally bandpass filtered at 3 to 45 Hz.

To evaluate the sensing performance of the whisker for an oscillatory flow, we used a dipole vibration source, in which a sphere with a diameter of 2.5 cm was entirely submerged below the water surface and driven at a constant frequency of 10 Hz by a mini shaker to generate oscillatory dipole stimuli. The whisker was placed horizontally at the same depth as that of the dipole. For vortex detection, hydrodynamic wakes were generated upstream of the whisker using a vertically mounted cylinder with different base diameters, which shed a Kármán vortex street.

Results and Discussion

Fabrication result of artificial whisker sensor

The artificial whisker was successfully fabricated as shown in Figure 3a. Figure 3b shows the photograph of a PDMS rod after the molding process, and Figure 3c depicts the cross sectional scanning electron microscope (SEM) image of microgrooves in a microchannel. With the DLS process, a thin layer of CNT/AgNPs with a thickness of 500 nm was formed as shown in Figure 3d. 3D printing is an alternative technique to fabricate out-of-plane piezoresistors on a bionic whisker as reported by Gul et al.² However, the feature size of their sensors is relatively larger compared with our device. In addition, 3D printing of piezoresistors is applicable to very limited choice of piezoresistive materials.

FIG. 3.

Fabrication result of artificial whisker sensor. (a) Overall appearance of whisker sensor. (b) Enlarged view of PDMS rod. (c) Cross-sectional view of microchannel with microgrooves. (d) SEM image of CNT/AgNP layer deposited by DLS method. SEM, scanning electron microscope.

Sensitivity of self-spread piezoresistors

As shown in Figure 4a, the relationships between the deflection of the whisker tip (x) and bending radian (φ) can be expressed as follows:

FIG. 4.

Characterization of the out-of-plane piezoresistors. (a) Schematic illustration of deflection of whisker sensor. (b) Resistance change of a piezoresistor (R4) for a tip displacement of 10 mm. (c) Resistance changes in variation with displacement at the tip of the whisker. (d) Normalized resistance variation of four piezoresistors with the rotating angles.

x = L_{w} sin φ + (1 - cos φ) \frac{L_{r}}{φ},

(1)

where L_w and L_r are the lengths of the bionic whiskers and PDMS rod, respectively. Thereafter, the GF of the sensor can be calculated as $G F = \frac{Δ R}{R} \frac{2 L_{r}}{D_{r} φ},$ (2)

where R is the initial resistance, ΔR is the resistance change, and D_r is the diameter of the PDMS rod.

Figure 4b shows the resistance change of a piezoresistor, while whisker tip is pushed repeatedly to a displacement of 10 mm. It indicates that the piezoresistor was repeatable in measuring the tip displacement of the whisker. When the sensor was held for a fixed tip displacement of 8 mm, the output is stable as shown in Supplementary Figure S3. The four piezoresistors on the PDMS rod are illustrated in the inset of Figure 4c, denoted as R1, R2, R3, and R4. Figure 4c shows the ratio of the resistance change variation with the tip displacement of the four piezoresistors.

The resistance of the piezoresistors at each displacement was measured thrice, and the average value was used to calculate the ratio of resistance change. Through linear fitting of the data for tip displacements from 0 to 6 mm, the GFs of the four piezoresistors (R1, R2, R3, and R4) were calculated to be 1.02, 1.72, 0.45, and 1.43, respectively. It should be noted that the out-of-plane piezoresistors were well formed and that the GF values were reasonable for all the four piezoresistors although the sensitivity consistency cannot be compared with that of silicon piezoresistors.

To calibrate the response of the bionic whisker to forces from different directions, the sensor was characterized on a manual rotation microstage. We simultaneously recorded the changes in resistance of the four piezoresistors while rotating the whisker from 0° to 180° in increments of 30°. For comparison, normalization was applied in this experiment. When rotating the whisker from 0° to 180°, the normalized resistance variation of each piezoresistor demonstrated a near-sinusoidal signal to the rotation angle, as shown in Figure 4b. For instance, when the sensor was applied in the 90° direction, R4 was stretched and R2 was compressed with large resistance changes, while R1 and R3 were relaxed with marginal resistance change.

Deflection and VIVs in steady flow

Harbor seal whiskers are extremely sensitive at frequencies lower than 100 Hz,⁹ matching the properties of the hydrodynamic signals generated by prey fish.^26,27 However, the frequency of vortex shedding from the whiskers at the swim speed of the harbor seal may lie in the same range.²⁸ Therefore, it is essential to mitigate the drag forces and suppress the VIVs.

We quantified and collected the response of the bionic whisker (deflection and vibration) at various flow speeds in the range of 0–0.25 m/s in a water tunnel, as shown in Figure 5a. The corresponding Reynolds number, Re, varies between 27 and 255 based on the average cross-flow diameter d_w (∼1.06 mm) at an angle of attack α = 0°. The deflection of the whisker and VIV-induced noise is schematically illustrated in Figure 5b. The amplitude was determined by calculating the normalized root-mean-square (RMS) amplitude of the sensor's output, and the vibration frequency was obtained from the fast Fourier transform (FFT) of the output signal.

FIG. 5.

Characterization of the artificial whisker sensor in a steady flow field. (a) Schematic illustration of the experimental setup. Angle of attack (α) refers to the angle between the direction of the incoming flow and long axis of the elliptical cross-section. (b) Schematic illustration of whisker's deflection and VIVs in the flow direction. (c) Normalized resistance changes in the whisker sensor as a function of flow velocity at α = 0° and α = 90°, respectively. (d) Amplitude and (e) frequency of whisker's VIV-induced oscillatory voltage output variation with the flow velocity. DAQ, data acquisition; PC, personal computer; VIVs, vortex-induced vibrations.

Figure 5c shows the response of the whisker sensor to different flow velocities. The normalized resistance changes in the whisker sensor for α = 0° were ∼5.1 times lower compared with α = 90°. This indicates that the drag forces acting on the bionic whisker can be significantly reduced at a small angle of attack.²⁹ In fact, harbor seals maintain their whiskers at an angle of attack of ∼0° as they swim, which considerably reduces the tendency of the whiskers to bend backwards.^15,30

Figure 5d and e shows the vibration amplitude and frequency of the whisker mounted at α = 0° and α = 90°, respectively. In the case of α = 0° the RMS amplitude of the whisker sensor increased from 0.024% to 0.043% when the flow velocity changed from 0.048 to 0.25 m/s, whereas the RMS amplitude of whisker sensor at α = 90° increased from 0.411% to 0.687%. This indicates that the whisker experienced very low VIVs for α = 0° compared to that at α = 90°. It is consistent with previous reported theory that the undulatory morphology of bionic seal whisker could suppress the VIVs at small angle of attacks.³¹

For the same incident flow velocity, the whisker at α = 0° showed a significantly higher vibration frequency (f = 192U, where U refers to the flow speed) compared to the whisker at α = 90° (f = 84U). The result was highly consistent with the theoretical VIV frequency, which obeys the Strouhal relation, $f = S t \frac{U}{D},$ (3)

where D is the average cross-flow diameter of the whisker, U is the flow speed, and Strouhal number St ≈ 0.20 for Reynolds numbers Re <200,000. Since the average cross-flow diameter of whisker at α = 0° (1.06 mm) was smaller than the cross-flow diameter at α = 90° (2.14 mm), the VIV frequency was much higher at α = 0°.

This indicates that the undulated surface morphology of seal whiskers can significantly reduce the drag forces and VIVs at a small angle of attack. For harbor seal whiskers a lower angle of attack is likely to sustain the VIVs at a higher frequency, thus avoiding interference from the objective signals and VIV noise. By reducing the drag forces and amplitude of the vibrations and shifting the frequency of VIVs away from the frequency of the prey, the seal whisker can retain high sensitivity during flow detection while predation.

Oscillatory flow detection

To obtain different oscillatory flow velocities at the tip of the whisker sensor, the distance L between the tip of the whisker and the center of the dipole was set to 2, 3, 4, and 5 cm. The oscillatory flow velocity v_z in the horizontal direction at the position of the whisker tip can be calculated as follows^30,32: $v_{z} = \frac{1}{4} π f_{s} s a^{3} L^{- 3},$ (4)

where a is the diameter of the sphere; f_s and s are the frequency and amplitude of the vibration, respectively.

FFT operations were performed on the sensor output to determine the peak amplitude. Figure 6a shows the FFT result of the sensor output when the distance between the tip of the whisker and the center of the dipole was 2 cm, corresponding to an oscillatory flow velocity of 0.123 m/s. As the distance increased to 5 cm, a peak with an amplitude of 0.013% was still clearly visible, as shown in the inset of Figure 6b. In this case, the calculated oscillatory flow velocity is as low as 8 mm/s. As shown in Figure 6b, the sensor exhibited a linear response to the oscillatory flow velocity. Therefore, a linear regression fit was obtained in the linear velocity range of 8.0 to 123 mm/s to determine the oscillatory flow sensitivity of the sensor, which was 0.0076%/ms⁻¹ in the linear regime.

FIG. 6.

Experiment for an oscillatory flow. (a) Output of whisker sensor in frequency domain, when the dipole sphere was 2 cm away from the tip of the whisker. (b) FFT amplitude of the sensor output variation with the oscillatory flow velocity. FFT, fast Fourier transform.

Vortex detection

As the seal whisker is a natural vortex receptor, the artificial whisker was characterized for the function of vortex detection. The artificial whisker sensor was mounted vertically at α = 0° in the water tunnel, as shown in Figure 7a. Three different cylinder diameters (d = 2.5, 3.5, and 5 cm) for vortex generation and three different downstream distances (l = 15, 20, and 25 cm) were investigated, ranging from the near wake to the far wake. To determine the mechanism of vortex street detection, we used a particle image velocimetry system to visualize the whisker interaction with the cylinder wake.³³ Figure 7b and c shows the flow velocity distribution of the Kármán vortex street in the cross-flow direction (Y direction) and along the flow direction (X direction), respectively. The semicircle represents the position of the upstream cylinder, and the square refers to the position of the whisker sensor.

FIG. 7.

Experimental setup and results of vortex detection. (a) Schematic illustration of the experimental setup. (b, c) The flow velocity distribution of the Kármán vortex street downstream of the cylinder. (d) Frequency-domain signals of whisker sensor in flow direction (dashed line) and cross-flow direction (solid line) for vortex street induced by an upstream cylinder with a diameter of 5 cm in different distances. (e) Frequency-domain signals of whisker sensor variation in flow direction (dashed line) and cross-flow direction (solid line) with the diameter of the upstream cylinder at a distance of 20 cm. The dash-dotted line represents the theoretical Karmen vortex street frequency.

The flow velocity in the Y direction of the Kármán vortex street varies from −0.12 to 0.16 m/s, which is much larger than the velocity variation in the X direction (0.02 to 0.15 m/s). Therefore, the piezoresistor located on the cross-flow side of the PDMS rod (R1) was used for wake detection for higher output signals.

In the first trial, the sensor was placed 15, 20, and 25 cm downstream of the cylinder (d = 5 cm). Figure 7d shows the spectra of the whisker output with exposure to the Kármán vortex shedding of the cylinder at a water flow velocity of 145 mm/s. The solid line represents the output of piezoresistor on the cross-flow direction (R1), and the dashed line shows the output of the piezoresistor facing the flow (R2). It should be noted that the output of the piezoresistor facing the flow is not sensitive enough to detect the vortex. Time-domain result is shown in Supplementary Figure S4. When the downstream distance was 15 cm, a strong peak at 0.63 Hz was dominant. This closely matches the expected frequency (∼0.61 Hz) of the vortex shedding of the cylinder based on Equation (3). Even for a distance of 25 cm, a clear peak at 0.67 Hz could still be observed.

Similarly, in the cases where cylinders with a diameter of 2.5 and 3.5 cm were placed 20 cm upstream from the whisker sensor at a flow velocity of 145 mm/s, the sensor showed a peak amplitude at 1.30 and 0.77 Hz, respectively (Fig. 7e), which closely matched the theoretical shedding frequencies (1.22 and 0.87 Hz). When the whisker was placed at α = 0°, minor VIV oscillations were stimulated by a uniform incoming flow. However, as the whisker locked into the shedding frequency of the cylinder ahead, wake-induced vibrations rapidly emerged. The whisker's lock-in to the dominant frequency of the wake and significant passive suppression of VIV endow the whisker with superior ability to detect a wave from a far distance.^31,34

In this experiment, the vortex shedding frequencies of the cylinder with a diameter of 5 cm (∼47d_w) were detected at the largest distance of 25 cm (∼235d_w) within a 10% error margin. This result is consistent with that reported by Beem and Triantafyllou in 2015,²¹ who obtained close accuracy at a distance of 17d_w for a cylinder with a diameter of 4d_w. A key challenge in wake detection is to identify the dominant frequency of small fluctuations of the wake in high-speed water flow. In this study, the flow velocity (∼145 mm/s) was 18 times the threshold limit for the oscillatory flow (∼8 mm/s) of the sensor. In contrast, seals can detect flow velocities as low as 245 μm/s, and the ratio of the whisker's own forward velocity to the minimum detectable velocity can be of the order of 1000, which is called exquisite sensitivity.

We thus experimentally confirmed that the undulated shape of the seal whiskers facilitates the suppression of VIVs in the inline direction and has a high sensitivity for wave detection in the cross-flow direction. With further optimization of geometric parameters and structural stiffness, the artificial whisker sensor can be expected to achieve the same level of exquisite sensitivity as harbor seal whiskers.

As shown in Table 1, by combining the microscale 3D printing and DLS method, we obtained a much smaller whisker sensor with the function of VIV suppression. Compared to specific flow analysis reported in literatures, we demonstrated the sensing performances for diverse flow analyses, such as steady flow, oscillating flow, and upstream wakes.

Table 1.

Comparison of the State-of-the-Art Piezoresistive Seal Whisker Sensors

Whisker sensors	Whisker length	Fabrication method	VIV suppression	Functions of flow analyses
Gul et al.²	160 mm	3D printing	No	Vortex
Beem and Triantafyllou²¹	275 mm	Assembly	Yes	Steady flow Vortex
Alvarado et al.²²	250 mm	Assembly	Yes	Steady flow
This work	42 mm	DLS	Yes	Steady flow Oscillating flow Vortex

DLS, directional liquid spreading; VIV, vortex-induced vibration.

Conclusion

In this study, we presented an artificial whisker sensor fabricated using a facile technique by novel DLS method. The surface of the whisker sensor emulated the undulatory and asymmetric geometry of the harbor seal whiskers. The biomimetic morphology substantially reduced the drag forces and VIVs at small angles of attack; thus, the sensor could distinguish self-induced vibrations from the vibrations induced by the oncoming wake features. Therefore, the artificial whisker sensor was able to perceive intricate flow details, including flow velocity, vortex-induced vibrations, and oscillating flow. Further experiments demonstrated that the whisker sensor could distinguish upstream vortex wakes. Although the consistency in sensor sensitivity should be optimized in the future work, the facile fabrication and excellent sensing performance of the artificial whisker sensor have paved a way for large-scale fabrication and future applications in intelligent flow analysis.

Footnotes

Acknowledgments

The authors are grateful to Mr. Zheng Gong and Mr. Qipei He from Beihang University for useful discussions in sensor development. The authors thank Editage for English language editing.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the National Natural Science Foundation of China (Nos. 52022008, 51975030).

Supplementary Material

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