Sensing fluctuating airflow with spider silk

Jian Zhou; Ronald N. Miles

doi:10.1073/pnas.1710559114

Edited by John G. Hildebrand, University of Arizona, Tucson, AZ, and approved September 18, 2017 (received for review June 15, 2017)

Significance

We find nanodimensional spider silk captures airflow with maximum physical efficiency over an extremely wide frequency range from infrasound to ultrasound. The aerodynamic property of spider silk provides the sensitivity of an ideal resonator but without the usual bandwidth limitation. This provides an effective means for miniaturized flow sensing, surpassing the frequency response of hair-based flow sensors of animals, which has been pursued in past decades. The results are significant because they elucidate the highly responsive nature of materials such as spider silk. This bioinspired approach will be valuable to various disciplines which have been pursuing miniaturized flow measurement and control in various mediums (air, gas, liquid) and situations (from steady flow to highly fluctuating flow).

Abstract

The ultimate aim of flow sensing is to represent the perturbations of the medium perfectly. Hundreds of millions of years of evolution resulted in hair-based flow sensors in terrestrial arthropods that stand out among the most sensitive biological sensors known, even better than photoreceptors which can detect a single photon (10⁻¹⁸–10⁻¹⁹ J) of visible light. These tiny sensory hairs can move with a velocity close to that of the surrounding air at frequencies near their mechanical resonance, despite the low viscosity and low density of air. No man-made technology to date demonstrates comparable efficiency. Here we show that nanodimensional spider silk captures fluctuating airflow with maximum physical efficiency (V_silk/V_air ∼ 1) from 1 Hz to 50 kHz, providing an effective means for miniaturized flow sensing. Our mathematical model shows excellent agreement with experimental results for silk with various diameters: 500 nm, 1.6 µm, and 3 µm. When a fiber is sufficiently thin, it can move with the medium flow perfectly due to the domination of forces applied to it by the medium over those associated with its mechanical properties. These results suggest that the aerodynamic property of silk can provide an airborne acoustic signal to a spider directly, in addition to the well-known substrate-borne information. By modifying a spider silk to be conductive and transducing its motion using electromagnetic induction, we demonstrate a miniature, directional, broadband, passive, low-cost approach to detect airflow with full fidelity over a frequency bandwidth that easily spans the full range of human hearing, as well as that of many other mammals.

Miniaturized flow sensing with high spatial and temporal resolution is crucial for numerous applications, such as high-resolution flow mapping (1), controlled microfluidic systems (2), unmanned microaerial vehicles (3 ⇓–5), boundary-layer flow measurement (6), low-frequency sound-source localization (7), and directional hearing aids (8). It has important socioeconomic impacts involved with defense and civilian tasks, biomedical and healthcare, energy saving and noise reduction of aircraft, natural and man-made hazard monitoring and warning, etc (1 ⇓⇓⇓⇓⇓⇓⇓⇓–10). Traditional flow-sensing approaches such as laser Doppler velocimetry, particle image velocimetry, and hot-wire anemometry have demonstrated significant success in certain applications. However, their applicability in a small space is often limited by their large size, high power consumption, limited bandwidth, high interaction with medium flow, and/or complex setups. There are many examples of sensory hairs in nature that sense fluctuating flow by deflecting in a direction perpendicular to their long axis due to forces applied by the surrounding medium (11 ⇓⇓⇓⇓–16). The simple, efficient, and tiny natural hair-based flow sensors provide an inspiration to address these difficulties. Miniature artificial flow sensors based on various transduction approaches have been created that are inspired by natural hairs (9, 10, 17 ⇓⇓⇓–21). Unfortunately, their motion relative to that of the surrounding flow is far less than that of natural hairs, significantly limiting their performance (9, 10).

An ideal sensor should represent the measured quantity with full fidelity. All dynamic mechanical sensors have resonances, a fact which is exploited in some sensor designs to achieve sufficient sensitivity. This comes with the cost of limiting their bandwidth. Other designs seek to avoid resonances to maximize their bandwidth at the expense of sensitivity. Here we show that nanodimensional spider silk can overcome these adverse costs by following the airflow with maximum physical efficiency (V_silk/V_air ∼ 1) over a frequency range from infrasound to ultrasound (1 Hz–50 kHz), despite the low viscosity and low density of air. The performance closely resembles that of an ideal resonant sensor but without the usual bandwidth limitation. This finding provides a design that exceeds the performance of existing hair-based flow sensors.

Results and Discussion

To intuitively illustrate the transverse motion of spider silk due to fluctuating airflow in the direction perpendicular to its long axis, we record sound from the silk motion. The complex airborne acoustic signal used here contains low-frequency (100–700 Hz) wing beat of insects and high-frequency (2–10 kHz) song of birds. Fig. 1 shows a schematic of our experimental setup and measured airborne motion of spider silk. We collect spider dragline silk with diameter d = 500 nm (Fig. S1A) from a female spiderling, Araneus diadematus (body length of the spider is about 3 mm). Fig. 1A shows a spider hanging on its web. The experimental setup is schematically shown in Fig. 1B. A strand of spider silk (length L = 8 mm) is supported at its two ends slackly, and placed perpendicularly to the flow field. The airflow field is prepared by playing sound using loudspeakers. A plane sound wave is generated at the location of the spider silk by placing the loudspeakers far away (3 m) from the silk in our anechoic chamber. The silk motion is measured using a laser vibrometer (Polytec OFV-534). Detailed descriptions of the experimental setups and procedures can be found in SI Methods and Fig. S2. The top image of Fig. 1C shows the airborne signal measured using a probe microphone (B&K type 4182) and the silk motion shown in the bottom image is measured by the laser vibrometer. As shown in the waveform and spectrogram, the motion of the silk (bottom image) clearly captures the broadband acoustic signals (top image) with high fidelity. More detailed laser signals can be found in Movie S1, which contains a time-domain trace, frequency-dependent spectrogram, and audio.

Fig. 1.

Airborne motion of spider silk. (A) A spider hanging on its web. (B) Schematic diagram showing the motion measurement of spider silk. A loose spider silk (length = 8 mm, diameter = 500 nm) is placed perpendicularly to the flow field in our anechoic chamber. The flow field is generated by speakers. The motion of the silk strand at the middle point is measured using a laser vibrometer. A more detailed description of the setup is provided in SI Methods and Fig. S2. (C) Measured time-domain signals and spectrograms. The airborne signal (top image) is measured by a pressure microphone and the silk motion (bottom image) is measured by the laser vibrometer. The acoustic signal contains low-frequency (100–700 Hz) wing beat of insects and high-frequency (2–10 kHz) song of birds. The silk motion clearly captures the airborne signal.

While the geometric forms (cobweb, orb web, and single strand), size, and tension of the spider silk shape the ultimate time and frequency responses, this intrinsic aerodynamic property of silk to represent the motion of the medium suggests that it can provide the acoustic information propagated through air to spiders. This may allow them to detect and discriminate potential nearby prey and predators (22, 23), which is different from the well-known substrate-borne information transmission induced by animals making direct contact with the silk (24 ⇓⇓–27).

Knowing that the spider silk can capture the broadband fluctuating airflow, we characterize its frequency and time response at the middle of a silk strand. We use three loudspeakers of different bandwidths to generate broadband fluctuating airflow from 1 to 50,000 Hz. Detailed experimental setups and procedures can be found in SI Methods and Figs. S2–S4. Note that the amplitude of air particle deflections X at low frequencies are much larger than those at high frequencies for the same air particle velocity V (X = V/ω, where ω = 2πf, f is the frequency of the fluctuating airflow, and V is the velocity amplitude). We use a long (L = 3.8 cm) and loose spider silk strand to avoid possible nonlinear stretching when the deflection is relatively large at very low frequencies. The measured silk velocity relative to the air particle velocity at the middle of the silk strand is presented in Fig. 2A. It shows that the nanodimensional spider silk can follow the airflow with maximum physical efficiency (V_hair/V_air ∼ 1) in the measured frequency range from 1 Hz to 50 kHz. Fig. 2B shows 50-ms-long time-domain data of the silk motion due to a 10,000-Hz airflow. The velocity and displacement amplitude of the flow field are 0.83 mm/s and 13.2 nm, respectively. This shows that the silk motion accurately tracks the air velocity at the initial transient as well as when the motion becomes periodic in the steady state. The 500-nm spider silk can thus follow the medium flow with high temporal and amplitude resolution.

Fig. 2.

Velocity response characterization of 500-nm spider silk. (A) Measured silk velocity relative to the air particle velocity at silk middle position (length L = 3.8 cm). For comparison, the frequency responses of a cricket cercal hair and an artificial hair sensor are also shown (10). (B) Silk time response to the 10,000-Hz low-amplitude airflow at middle position. The signal duration is 50 ms. Zoomed-in views are provided to show the initial transient and the steady-state responses. (C) Measured silk velocity relative to the air particle velocity at various silk locations (L = 8 mm). This shows that the silk moves with nearly the same velocity amplitude as the air over most of its length.

We then characterize the motion of a 500-nm silk strand (L = 8 mm) at various locations along its length. The measured silk velocity relative to the air particle velocity at various silk locations is presented in Fig. 2C. The location is measured relative to the left fixed end as shown in Fig. 1B. Although the fixed ends of the silk cannot move with air, over most of the length, the silk motion closely resembles that of the airflow over a broad frequency range.

While our present purpose is to report the experimental finding, insight can be gained by considering a highly simplified mathematical model of the silk’s response. If we consider the silk and the surrounding medium to behave as a continuum, a model for the silk motion can be expressed in the form of a simple partial differential equation. While this approach neglects molecular interactions that are important at small scale, it can guide our understanding of the effects of certain key system parameters. This simple approximate analytical model is presented in Eq. 1 to examine the dominant forces and response of a thin fiber in the sound field.EI∂4w(x,t)∂x4+ρA∂2w(x,t)∂t2=Cvr(t)+Mdvr(t)dt.[1]The left term gives the mechanical force due to bending of the fiber per unit length, where E is Young’s modulus of elasticity, I = πd⁴/64 is the area moment of inertia, w(x, t) is the fiber transverse displacement, which depends on both position x and time t. The second term on the left accounts for the inertia of the fiber where ρ is volume density and A = πd²/4 is the cross-section area. The right term estimates the viscous force due to the relative motion of the fiber and the surrounding fluid. C and M are damping and added mass per unit length which, for a continuum fluid, were determined by Stokes (28). v_r(t) = v_air(t) − v_silk(t) is the relative velocity between the air movement and fiber motion.

It should be noted that the first term on the left side of Eq. 1 accounts for the fact that thin fibers will surely bend as they are acted on by a flowing medium. This differs from previous studies of the flow-induced motion of thin hairs which assume that the hair moves as a rigid rod supported by a torsional spring at the base (12 ⇓–14, 17, 18). The motion of a rigid hair can be described by a single coordinate such as the angle of rotation about the pivot. In our case, the deflection depends on a continuous variable x describing the location along the length. Eq. 1 is then a partial differential equation, unlike the ordinary differential equation used when the hair does not bend or flex.

It is evident that the terms on the left side of Eq. 1 are proportional to either d⁴ or d². The dependence on the diameter d of the terms on the right side of this equation is more difficult to calculate owing to the complex mechanics of fluid forces. It can be shown, however, that these fluid forces tend to depend on the surface area of the fiber, which is proportional to its circumference πd. As d becomes sufficiently small, the terms proportional to C and M will clearly dominate over those on the left side of Eq. 1. For sufficiently small values of the diameter d, the governing equation of motion of the fiber becomes approximately0≈Cvr(t)+Mdvr(t)dt.[2]For small values of d, Eq. 1 is then dominated by terms that are proportional to v_r(t), the relative motion between the solid fiber and the medium. Since v_r(t) = v_air(t) − v_silk(t), the solution of Eq. 2 may be approximated by v_air(t) ∼ v_silk(t). According to this highly simplified continuum view of the medium, the fiber will thus move with the medium fluid instantaneously and with the same amplitude if the fiber is sufficiently thin.

To examine the validity of the approximate analysis above, we measure the velocity response of dragline silks (L = 3.8 cm) from A. diadematus having various diameters (Fig. S1): 0.5, 1.6, and 3 µm. All silks are measured at the middle position. Fig. 3 shows predicted and measured velocity transfer functions of silks using the air particle velocity as the reference. Predictions are obtained by solving Eq. 1. In the prediction model, Young’s modulus E and volume density ρ are 10 Gpa (29) and 1,300 kg/m³ (30), respectively. The measured responses of the silks are in close agreement with the predicted results. While all three of the measured silks can follow the air motion in a broad frequency range, the thinnest silk can follow air motion closely (V_silk/V_air ∼ 1) at extremely high frequencies up to 50 kHz. These results suggest that when a fiber is sufficiently thin (diameter in nanodimensional scale), the fiber motion can be dominated by forces associated with the surrounding medium, causing the fiber to represent the air particle motion accurately. We also show predictions of the flow-induced fiber responses of various materials [poly(methyl methacrylate) (PMMA), aluminum, and carbon nanotube fibers] with diameter d = 500 nm and length L = 3.8 cm in Fig. S5. Remarkably, over a wide range of frequencies, the fiber motion becomes independent of its material and geometric properties when it is sufficiently thin.

Fig. 3.

Predicted and measured silk velocity relative to the air particle velocity for silks (L = 3.8 cm) of various diameters: 500 nm, 1.6 µm, 3 µm. The measured velocity response of the various silks is in close agreement with the prediction.

The fiber motion can be transduced to an electric signal using various methods depending on various application purposes. Because the fiber curvature is substantial near each fixed end as shown in Fig. 2C, sensing bending strain can be a promising approach. If nanowires are stacked into a rigid three-dimension nanolattice (31), capacitive transduction is also possible. When sensing steady or slowly changing flows for applications such as controlled microfluidics, the transduction of fiber displacement may be preferred over velocity. Having an electric output that is proportional to the velocity of the silk is advantageous when detecting broadband flow fluctuations such as sound. While the detailed transduction approach (for example piezoresistive, piezoelectric, capacitive, magnetic, and optical sensing) may be different depending on the applications, the fact that the fiber motion is nearly identical to that of the medium in its vicinity will always prove beneficial. Advances in nanotechnology make the flow sensor fabrication possible (31 ⇓–33).

Here we demonstrate fiber motion transduction using electromagnetic induction. The motion of the fiber is transduced to an open-circuit voltage output E directly based on Faraday’s law, E = BLV_fiber, where B is the magnetic flux density and L is the fiber length. To examine the feasibility of this approach, a 3.8-cm-long loose spider silk with a 500-nm diameter is coated with an 80-nm-thick gold layer using electron beam evaporation to obtain a freestanding conductive nanofiber. The conductive fiber is aligned in a magnetic field with flux density B = 0.35 T. The orientation of the fiber axis, the motion of the fiber, and the magnetic flux density are all approximately orthogonal. The measured E/V_air is shown in Fig. 4A. Because the fiber accurately follows the airflow (V_fiber/V_air ∼ 1) over most of the length, and the fiber motion is transduced linearly to a voltage signal, E/V_air is approximately equal to the product of B and L in the measured frequency range 1 Hz–10 kHz.

Fig. 4.

Frequency and directional response of the flow sensor. (A) Sensor voltage output E relative to the air particle velocity. A spider silk (L = 3.8 cm) is evaporated with 80-nm gold to be a freestanding conductive fiber. The fiber is aligned in a magnetic field with flux density B = 0.35 T. The motion of the fiber is transduced to open-circuit voltage output directly based on electromagnetic induction. The sensor is passive and can work as a nanogenerator. (B) Measured effect on response due to the propagation direction of a 3-Hz infrasound flow with wavelength λ ∼ 114 m. The voltage output e(t) to the infrasound from various directions (0°, 60°, 90°) is measured. The sensor is sensitive to the flow direction with relationship e(t) = e₀(t)cos(θ), where e₀(t) is the voltage output at θ = 0°. A more detailed description of the measurement is provided in SI Methods and Fig. S3.

This provides a directional, passive, and miniaturized approach to detect broadband fluctuating airflow with excellent fidelity and high resolution. Our results suggest it could be incorporated in a system for passive sound-source localization, even for infrasound monitoring and localization despite its small size. Fig. 4B shows the directional sensor response to a 3-Hz infrasound flow with wavelength λ ∼ 114 m. The sensor is sensitive to the flow direction with relationship e(t) = e₀(t)cos(θ), where e₀(t) is the voltage output when the flow is perpendicular to the fiber direction (θ = 0°). As infrasound waves have large wavelength λ (λ = c/f, c is speed of sound), at least two pressure sensors should normally be used and placed at large separation distances (on the order of meters to kilometers) to determine the wave direction. Since velocity is a vector, in contrast to the scalar pressure, flow sensing inherently contains the directional information. This is very beneficial if one wishes to localize a source. The device can also work as a nanogenerator to harvest broadband flow energy with high power density (34). For a conductive fiber (of length L, cross-section area A, volume Ѵ = LA, resistivity ρ_e, velocity amplitude V), the maximum generated voltage E₀ = BLV, the fiber resistance R = ρ_eL/A, the maximum short-circuit power per unit volume can be expressed as P/Ѵ = B²V²/ρ_e. If B = 1 T, V = 1 cm/s, ρ_e = 2.44 × 10⁻⁸ Ωm, then P/Ѵ is 4.1 mW/cm³.

The results presented here offer a simple, low-cost alternative to methods for measuring fluctuating flows that require seeding the fluid with flow tracer particles such as laser Doppler velocimetry or particle image velocimetry (PIV). While good fidelity can be obtained by careful choice of tracer particles (35), these methods employ rather complicated optical systems to track the tracer particle motions. In the present study, a velocity-dependent voltage is obtained using simple electrodynamic transduction by measuring the open-circuit voltage between the two ends of the fiber when it is in the presence of a magnetic field.

Because we have used three unrelated measurement methods (one with our fiber motion sensed with a laser vibrometer, one with a microphone, and one with our sensor voltage output), each based on altogether different physical principles, close agreement between them bolsters confidence in each. Additional confidence in our result derives from the fact that our analytical model provides very close agreement with the measurements.

Conclusion

In summary, the motion of a fiber having a diameter at the nanodimensional scale can closely resemble that of the flow of the surrounding air, providing an accurate and simple approach to detect complicated airflow. This is a result of the dominance of applied forces from the surrounding medium over internal forces of the fiber such as those associated with bending and inertia at these small diameters. This study was inspired by numerous examples of acoustic flow sensing by animals (12 ⇓⇓⇓–16). Our results indicate that this biomimetic device responds to subtle air motion over a broader range of frequencies than has been observed in natural flow sensors. The miniature fiber-based approach of flow sensing has potential applications in various disciplines which have been pursuing precise flow measurement and control in various mediums (air, gas, liquid) and situations (from steady flow to highly fluctuating flow).

Methods

All measurements were performed in the anechoic chamber at Binghamton University. The fluctuating airflow was created using loudspeakers, as shown in Figs. S2 and S3. To obtain measurements over the broad frequency range examined here, we use three different experimental setups, each designed to cover a portion of the frequency range. The fluctuating airflow from 100 Hz to 50 kHz near the silk is determined using a measure of the spatial gradient of the pressure, ∂p(x, t)/∂x (36). Knowing the sound-pressure gradient, the acoustic particle velocity v_a(x, t) is calculated using Euler’s equation: −∂p(x, t)/∂x = ρ₀∂v_a(x, t)/∂t, where ρ₀ is the air density. The pressure is measured using a calibrated reference microphone.

Spider silks used in the measurement are dragline silks collected from female orb-weaver spiders A. diadematus. The silk motion shown in Figs. 1–3 was measured using a Polytec OFV-534 laser vibrometer. The silk used to obtain the data of Fig. 4 was made to be conductive by evaporating it with 80-nm-thickness gold using electron beam evaporation. The open-circuit voltage across the silk is detected using a low-noise preamplifier, SRS model SR560.

Detailed descriptions of the methods are provided in Supporting Information.

Acknowledgments

The authors thank Prof. R. R. Hoy of the Department of Neurobiology and Behavior at Cornell University for his comments on an earlier draft of this paper.

Footnotes

↵¹J.Z. and R.N.M. contributed equally to this work.
↵²To whom correspondence should be addressed. Email: miles{at}binghamton.edu.

Author contributions: J.Z. and R.N.M. designed research, performed research, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1710559114/-/DCSupplemental.

Published under the PNAS license.

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[1] ↵
Birch JM,
Dickinson MH
(2001) Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412:729–733.
OpenUrl CrossRef PubMed

[2] Birch JM,

[3] Dickinson MH

[4] ↵
Atencia J,
Beebe DJ
(2005) Controlled microfluidic interfaces. Nature 437:648–655.
OpenUrl CrossRef PubMed

[5] Atencia J,

[6] Beebe DJ

[7] ↵
Floreano D,
Wood RJ
(2015) Science, technology and the future of small autonomous drones. Nature 521:460–466.
OpenUrl CrossRef PubMed

[8] Floreano D,

[9] Wood RJ

[10] ↵
Sterbing-D’Angelo S, et al.
(2011) Bat wing sensors support flight control. Proc Natl Acad Sci USA 108:11291–11296.
OpenUrl Abstract/FREE Full Text

[11] Sterbing-D’Angelo S, et al.

[12] ↵
Fuller SB,
Straw AD,
Peek MY,
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