Sensing fluctuating airflow with spider silk

Jian Zhoua,1 and Ronald N. Milesa,1,2

aDepartment of Mechanical Engineering, Binghamton University, Binghamton, NY 13902

Edited by John G. Hildebrand, University of Arizona, Tucson, AZ, and approved September 18, 2017 (received for review June 15, 2017) The ultimate aim of flow sensing is to represent the perturbations bandwidth. Other designs seek to avoid resonances to maximize of the medium perfectly. Hundreds of millions of years of their bandwidth at the expense of sensitivity. Here we show that evolution resulted in hair-based flow sensors in terrestrial arthro- nanodimensional spider silk can overcome these adverse costs by pods that stand out among the most sensitive biological sensors following the airflow with maximum physical efficiency (Vsilk/Vair known, even better than photoreceptors which can detect a single ∼ 1) over a frequency range from infrasound to ultrasound − − photon (10 18–10 19 J) of visible light. These tiny sensory hairs can (1 Hz–50 kHz), despite the low viscosity and low density of air. move with a velocity close to that of the surrounding air at fre- The performance closely resembles that of an ideal resonant quencies near their mechanical resonance, despite the low viscos- sensor but without the usual bandwidth limitation. This finding ity and low density of air. No man-made technology to date provides a design that exceeds the performance of existing hair- demonstrates comparable efficiency. Here we show that nanodi- based flow sensors. mensional spider silk captures fluctuating airflow with maximum Results and Discussion physical efficiency (Vsilk/Vair ∼ 1) from 1 Hz to 50 kHz, providing an effective means for miniaturized flow sensing. Our mathematical To intuitively illustrate the transverse motion of spider silk due model shows excellent agreement with experimental results for to fluctuating airflow in the direction perpendicular to its long silk with various diameters: 500 nm, 1.6 μm, and 3 μm. When a axis, we record sound from the silk motion. The complex air- fiber is sufficiently thin, it can move with the medium flow per- borne acoustic signal used here contains low-frequency (100– fectly due to the domination of forces applied to it by the medium 700 Hz) wing beat of insects and high-frequency (2–10 kHz) song over those associated with its mechanical properties. These results of birds. Fig. 1 shows a schematic of our experimental setup and

suggest that the aerodynamic property of silk can provide an air- measured airborne motion of spider silk. We collect spider SCIENCES borne acoustic signal to a spider directly, in addition to the well- = A dragline silk with diameter d 500 nm (Fig. S1 ) from a female APPLIED PHYSICAL known substrate-borne information. By modifying a spider silk to spiderling, Araneus diadematus (body length of the spider is be conductive and transducing its motion using electromagnetic about 3 mm). Fig. 1A shows a spider hanging on its web. The induction, we demonstrate a miniature, directional, broadband, experimental setup is schematically shown in Fig. 1B. A strand of passive, low-cost approach to detect airflow with full fidelity over spider silk (length L = 8 mm) is supported at its two ends slackly, a frequency bandwidth that easily spans the full range of human and placed perpendicularly to the flow field. The airflow field is hearing, as well as that of many other mammals. prepared by playing sound using loudspeakers. A plane sound wave is generated at the location of the spider silk by placing the spider silk | airborne motion | flow sensing | acoustics | loudspeakers far away (3 m) from the silk in our anechoic nanodimensional fiber chamber. The silk motion is measured using a laser vibrometer (Polytec OFV-534). Detailed descriptions of the experimental iniaturized flow sensing with high spatial and temporal setups and procedures can be found in SI Methods and Fig. S2. Mresolution is crucial for numerous applications, such as The top image of Fig. 1C shows the airborne signal measured high-resolution flow mapping (1), controlled microfluidic sys- – tems (2), unmanned microaerial vehicles (3 5), boundary-layer Significance flow measurement (6), low-frequency sound-source localization (7), and directional hearing aids (8). It has important socioeco- We find nanodimensional spider silk captures airflow with nomic impacts involved with defense and civilian tasks, bio- maximum physical efficiency over an extremely wide fre- medical and healthcare, energy saving and noise reduction of quency range from infrasound to ultrasound. The aerodynamic aircraft, natural and man-made hazard monitoring and warning, – property of spider silk provides the sensitivity of an ideal res- etc (1 10). Traditional flow-sensing approaches such as laser onator but without the usual bandwidth limitation. This pro- Doppler velocimetry, particle image velocimetry, and hot-wire vides an effective means for miniaturized flow sensing, anemometry have demonstrated significant success in certain surpassing the frequency response of hair-based flow sensors applications. However, their applicability in a small space is of- of animals, which has been pursued in past decades. The re- ten limited by their large size, high power consumption, limited sults are significant because they elucidate the highly re- bandwidth, high interaction with medium flow, and/or complex sponsive nature of materials such as spider silk. This setups. There are many examples of sensory hairs in nature that bioinspired approach will be valuable to various disciplines sense fluctuating flow by deflecting in a direction perpendicular which have been pursuing miniaturized flow measurement to their long axis due to forces applied by the surrounding me- and control in various mediums (air, gas, liquid) and situations dium (11–16). The simple, efficient, and tiny natural hair-based (from steady flow to highly fluctuating flow). flow sensors provide an inspiration to address these difficulties. Miniature artificial flow sensors based on various transduction Author contributions: J.Z. and R.N.M. designed research, performed research, analyzed approaches have been created that are inspired by natural hairs data, and wrote the paper. (9, 10, 17–21). Unfortunately, their motion relative to that of the The authors declare no conflict of interest. surrounding flow is far less than that of natural hairs, signifi- This article is a PNAS Direct Submission. cantly limiting their performance (9, 10). Published under the PNAS license. An ideal sensor should represent the measured quantity with 1J.Z. and R.N.M. contributed equally to this work. full fidelity. All dynamic mechanical sensors have resonances, a 2To whom correspondence should be addressed. Email: [email protected]. fact which is exploited in some sensor designs to achieve suffi- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. cient sensitivity. This comes with the cost of limiting their 1073/pnas.1710559114/-/DCSupplemental.

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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.

using a probe microphone (B&K type 4182) and the silk motion the fluctuating airflow, and V is the velocity amplitude). We use shown in the bottom image is measured by the laser vibrometer. a long (L = 3.8 cm) and loose spider silk strand to avoid possible As shown in the waveform and spectrogram, the motion of the nonlinear stretching when the deflection is relatively large at very silk (bottom image) clearly captures the broadband acoustic low frequencies. The measured silk velocity relative to the air signals (top image) with high fidelity. More detailed laser signals particle velocity at the middle of the silk strand is presented in can be found in Movie S1, which contains a time-domain trace, Fig. 2A. It shows that the nanodimensional spider silk can follow frequency-dependent spectrogram, and audio. the airflow with maximum physical efficiency (Vhair/Vair ∼ 1) in While the geometric forms (cobweb, orb web, and single the measured frequency range from 1 Hz to 50 kHz. Fig. 2B strand), size, and tension of the spider silk shape the ultimate shows 50-ms-long time-domain data of the silk motion due to a time and frequency responses, this intrinsic aerodynamic prop- 10,000-Hz airflow. The velocity and displacement amplitude of erty of silk to represent the motion of the medium suggests that it the flow field are 0.83 mm/s and 13.2 nm, respectively. This can provide the acoustic information propagated through air to shows that the silk motion accurately tracks the air velocity at the spiders. This may allow them to detect and discriminate potential initial transient as well as when the motion becomes periodic in nearby prey and predators (22, 23), which is different from the the steady state. The 500-nm spider silk can thus follow the well-known substrate-borne information transmission induced by medium flow with high temporal and amplitude resolution. animals making direct contact with the silk (24–27). We then characterize the motion of a 500-nm silk strand (L = Knowing that the spider silk can capture the broadband fluc- 8 mm) at various locations along its length. The measured silk tuating airflow, we characterize its frequency and time response velocity relative to the air particle velocity at various silk loca- at the middle of a silk strand. We use three loudspeakers of tions is presented in Fig. 2C. The location is measured relative to different bandwidths to generate broadband fluctuating airflow the left fixed end as shown in Fig. 1B. Although the fixed ends of from 1 to 50,000 Hz. Detailed experimental setups and proce- the silk cannot move with air, over most of the length, the silk dures can be found in SI Methods and Figs. S2–S4. Note that the motion closely resembles that of the airflow over a broad amplitude of air particle deflections X at low frequencies are frequency range. much larger than those at high frequencies for the same air While our present purpose is to report the experimental particle velocity V (X = V/ω, where ω = 2πf, f is the frequency of finding, insight can be gained by considering a highly simplified

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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.

mathematical model of the silk’s response. If we consider the It should be noted that the first term on the left side of Eq. 1 silk and the surrounding medium to behave as a continuum, a accounts for the fact that thin fibers will surely bend as they model for the silk motion can be expressed in the form of a are acted on by a flowing medium. This differs from previous simple partial differential equation. While this approach ne- studies of the flow-induced motion of thin hairs which assume glects molecular interactions that are important at small scale, that the hair moves as a rigid rod supported by a torsional it can guide our understanding of the effects of certain key spring at the base (12–14, 17, 18). The motion of a rigid hair system parameters. This simple approximate analytical model can be described by a single coordinate such as the angle of is presented in Eq. 1 to examine the dominant forces and re- rotation about the pivot. In our case, the deflection depends sponse of a thin fiber in the sound field. on a continuous variable x describing the location along the length. Eq. 1 is then a partial differential equation, unlike the ∂4wðx, tÞ ∂2wðx, tÞ dv ðtÞ ordinary differential equation used when the hair does not EI + ρA = Cv ðtÞ + M r . [1] ∂x4 ∂t2 r dt bend or flex. It is evident that the terms on the left side of Eq. 1 are The left term gives the mechanical force due to bending of the proportional to either d4 or d2. The dependence on the di- ’ fiber per unit length, where E is Young s modulus of elasticity, ameter d of the terms on the right side of this equation is more = π 4 I d /64 is the area moment of inertia, w(x, t) is the fiber difficult to calculate owing to the complex mechanics of fluid transverse displacement, which depends on both position x and forces. It can be shown, however, that these fluid forces tend to time t. The second term on the left accounts for the inertia of the ρ = π 2 depend on the surface area of the fiber, which is proportional fiber where is volume density and A d /4 is the cross-section π area. The right term estimates the viscous force due to the rel- to its circumference d. As d becomes sufficiently small, the ative motion of the fiber and the surrounding fluid. C and M are terms proportional to C and M will clearly dominate over those damping and added mass per unit length which, for a continuum ontheleftsideofEq.1. For sufficiently small values of the fluid, were determined by Stokes (28). vr(t) = vair(t) − vsilk(t) is diameter d, the governing equation of motion of the fiber the relative velocity between the air movement and fiber motion. becomes approximately

Zhou and Miles PNAS Early Edition | 3of6 Downloaded by guest on October 1, 2021 the fiber motion becomes independent of its material and geo- dvrðtÞ 0 ≈ CvrðtÞ + M . [2] metric properties when it is sufficiently thin. dt The fiber motion can be transduced to an electric signal using For small values of d, Eq. 1 is then dominated by terms that are various methods depending on various application purposes. Because the fiber curvature is substantial near each fixed end as proportional to vr(t), the relative motion between the solid fiber C and the medium. Since v (t) = v (t) − v (t), the solution of Eq. shown in Fig. 2 , sensing bending strain can be a promising r air silk approach. If nanowires are stacked into a rigid three-dimension 2 may be approximated by vair(t) ∼ vsilk(t). According to this highly simplified continuum view of the medium, the fiber will nanolattice (31), capacitive transduction is also possible. When thus move with the medium fluid instantaneously and with the sensing steady or slowly changing flows for applications such as same amplitude if the fiber is sufficiently thin. controlled microfluidics, the transduction of fiber displacement To examine the validity of the approximate analysis above, we may be preferred over velocity. Having an electric output that is measure the velocity response of dragline silks (L = 3.8 cm) from proportional to the velocity of the silk is advantageous when detecting broadband flow fluctuations such as sound. While the A. diadematus having various diameters (Fig. S1): 0.5, 1.6, and μ detailed transduction approach (for example piezoresistive, pi- 3 m. All silks are measured at the middle position. Fig. 3 shows ezoelectric, capacitive, magnetic, and optical sensing) may be predicted and measured velocity transfer functions of silks using different depending on the applications, the fact that the fiber the air particle velocity as the reference. Predictions are obtained motion is nearly identical to that of the medium in its vicinity will by solving Eq. 1. In the prediction model, Young’s modulus E always prove beneficial. Advances in nanotechnology make the and volume density ρ are 10 Gpa (29) and 1,300 kg/m3 (30), flow sensor fabrication possible (31–33). respectively. The measured responses of the silks are in close Here we demonstrate fiber motion transduction using elec- agreement with the predicted results. While all three of the tromagnetic induction. The motion of the fiber is transduced measured silks can follow the air motion in a broad frequency to an open-circuit voltage output E directly based on Faraday’s law, E = BLV , where B is the magnetic flux density and L is range, the thinnest silk can follow air motion closely (Vsilk/Vair ∼ fiber 1) at extremely high frequencies up to 50 kHz. These results the fiber length. To examine the feasibility of this approach, a suggest that when a fiber is sufficiently thin (diameter in nano- 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 dimensional scale), the fiber motion can be dominated by forces to obtain a freestanding conductive nanofiber. The conductive associated with the surrounding medium, causing the fiber to fiber is aligned in a magnetic field with flux density B = 0.35 T. represent the air particle motion accurately. We also show pre- The orientation of the fiber axis, the motion of the fiber, and the dictions of the flow-induced fiber responses of various materials magnetic flux density are all approximately orthogonal. The [poly(methyl methacrylate) (PMMA), aluminum, and carbon measured E/Vair is shown in Fig. 4A. Because the fiber accurately = = nanotube fibers] with diameter d 500 nm and length L follows the airflow (Vfiber/Vair ∼ 1) over most of the length, and 3.8 cm in Fig. S5. Remarkably, over a wide range of frequencies, the fiber motion is transduced linearly to a voltage signal, E/Vair

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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.

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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.

2 2 is approximately equal to the product of B and L in the measured power per unit volume can be expressed as P/Ѵ = B V /ρe.IfB= 1 −8 3 frequency range 1 Hz–10 kHz. T, V = 1cm/s,ρe = 2.44 × 10 Ωm, then P/Ѵ is 4.1 mW/cm . This provides a directional, passive, and miniaturized ap- The results presented here offer a simple, low-cost alternative proach to detect broadband fluctuating airflow with excellent to methods for measuring fluctuating flows that require seeding fidelity and high resolution. Our results suggest it could be in- the fluid with flow tracer particles such as laser Doppler corporated in a system for passive sound-source localization, velocimetry or particle image velocimetry (PIV). While good even for infrasound monitoring and localization despite its small fidelity can be obtained by careful choice of tracer particles size. Fig. 4B shows the directional sensor response to a 3-Hz (35), these methods employ rather complicated optical systems infrasound flow with wavelength λ ∼ 114 m. The sensor is sen- to track the tracer particle motions. In the present study, a sitive to the flow direction with relationship e(t) = e (t)cos(θ), velocity-dependent voltage is obtained using simple electrody- 0 namic transduction by measuring the open-circuit voltage be- where e0(t) is the voltage output when the flow is perpendicular to the fiber direction (θ = 0°). As infrasound waves have large tween the two ends of the fiber when it is in the presence of a magnetic field. wavelength λ (λ = c/f, c is speed of sound), at least two pressure Because we have used three unrelated measurement methods sensors should normally be used and placed at large separation (one with our fiber motion sensed with a laser vibrometer, one distances (on the order of meters to kilometers) to determine the with a microphone, and one with our sensor voltage output), wave direction. Since velocity is a vector, in contrast to the scalar each based on altogether different physical principles, close pressure, flow sensing inherently contains the directional infor- agreement between them bolsters confidence in each. Additional mation. This is very beneficial if one wishes to localize a source. confidence in our result derives from the fact that our analytical The device can also work as a nanogenerator to harvest broad- model provides very close agreement with the measurements. band flow energy with high power density (34). For a conductive fiber (of length L, cross-section area A, volume Ѵ = LA, resistivity Conclusion ρe, velocity amplitude V), the maximum generated voltage E0 = In summary, the motion of a fiber having a diameter at the BLV, the fiber resistance R = ρeL/A, the maximum short-circuit nanodimensional scale can closely resemble that of the flow of

Zhou and Miles PNAS Early Edition | 5of6 Downloaded by guest on October 1, 2021 the surrounding air, providing an accurate and simple approach examined here, we use three different experimental setups, each designed to detect complicated airflow. This is a result of the dominance to cover a portion of the frequency range. The fluctuating airflow from of applied forces from the surrounding medium over internal 100 Hz to 50 kHz near the silk is determined using a measure of the spatial forces of the fiber such as those associated with bending and gradient of the pressure, ∂p(x, t)/∂x (36). Knowing the sound-pressure gra- dient, the acoustic particle velocity va(x, t) is calculated using Euler’s equa- inertia at these small diameters. This study was inspired by nu- −∂ ∂ = ρ ∂ ∂ ρ merous examples of acoustic flow sensing by animals (12–16). tion: p(x, t)/ x 0 va(x, t)/ t, where 0 is the air density. The pressure is measured using a calibrated reference microphone. Our results indicate that this biomimetic device responds to Spider silks used in the measurement are dragline silks collected from subtle air motion over a broader range of frequencies than has female orb-weaver spiders A. diadematus. The silk motion shown in Figs. 1–3 been observed in natural flow sensors. The miniature fiber-based was measured using a Polytec OFV-534 laser vibrometer. The silk used to approach of flow sensing has potential applications in various obtain the data of Fig. 4 was made to be conductive by evaporating it with disciplines which have been pursuing precise flow measurement 80-nm-thickness gold using electron beam evaporation. The open-circuit and control in various mediums (air, gas, liquid) and situations voltage across the silk is detected using a low-noise preamplifier, SRS (from steady flow to highly fluctuating flow). model SR560. Methods Detailed descriptions of the methods are provided in Supporting Information. All measurements were performed in the anechoic chamber at Binghamton ACKNOWLEDGMENTS. The authors thank Prof. R. R. Hoy of the Department University. The fluctuating airflow was created using loudspeakers, as shown of Neurobiology and Behavior at Cornell University for his comments on an in Figs. S2 and S3. To obtain measurements over the broad frequency range earlier draft of this paper.

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