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Abstract
Inspired by superficial neuromasts in the lateral line of fish for the sensing of flow rate, we report a bionic optical microfiber flow rate sensor by embedding a U-shaped microfiber into a thin PDMS film. When immersed into liquid, the PDMS film is deflected by the flowing liquid, resulting in a bending-dependent transmittance change of the embedded microfiber which is directly related to the flow rate of the liquid. The flow rate sensor exhibits a low detection limit (< 0.05 L/min), a high resolution (0.005 L/min), and a fast response time (12 ms). In addition, the sensitivity and working range of the sensor are tunable in a wide range via adjusting the thickness of PDMS film, the microfiber diameter, and/or the working wavelength.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the development of chemical, pharmacy, and energy engineering, there exists a trend of miniaturization of industrial systems. Real-time and accurate liquid flow rate measurement in the millimeter-scale pipeline have become more and more important [1,2]. Usually, conventional liquid flowmeters with electric signal outputs are operated by the combination of electrical sensing elements and mechanical components. However, the application of these flowmeters may be restricted by factors such as harsh environment, electromagnetic interference, hysteresis in response, and complexity in fabrication [3–5]. Compared with above mentioned electrical flowmeters, fiber-optic flow rate sensors [6–9] have attracted increasing attention due to the inherent advantages of fiber-optic sensors, such as immunity to electromagnetic interference, resistance to corrosion, and capability to remote sensing.
Recently, a large number of novel fiber-optic flow rate sensors [10–23] have been demonstrated with enhanced performance in sensitivity, dynamic range, and footprint. Note that the flow rate sensors based on standard optical fiber cantilever [15,21] usually work nicely in the high flow rate range (typically larger than 10 L/min) while show very low or no response in the low flow rate range, which is due to the relatively large stiffness of standard optical fibers and protective casings. Although the flow rate sensors based on microcantilever [7,11] have demonstrated high sensitivity in low flow rate range owing to their high flexibility, it is impractical to employ these sensors to measure liquid in the millimeter-scale pipeline. Different from the laminar flow in microchannels, vortices or bubbles often appear in millimeter-scale pipelines, leading to a complicated flow pattern. Owing to the small size of the microcantilever, one can only obtain the flow information at one specific position, not the whole cross-section of the pipeline. In addition, because the microcantilevers are directly immersed in liquid, adsorption of microparticle and/or surface contamination may result in performance degradation. “Hot-wire” flow rate sensor, which is based on heat-transfer, provides an alternative approach to measure liquid at low flow rate range. Nevertheless, its response time is highly relying on the heat-transfer rate, typically, at tens of seconds level [12,16]. Notably, optical microfibers with diameters close to or below the wavelength of the guided light are capable of guiding light with low optical loss, offering unique properties, including tight optical confinement, strong evanescent fields, and high mechanical flexibility [24,25], which are attractive for developing compact flow rate sensors with fast response and high sensitivity. However, unpackaged optical microfibers are highly sensitive to flow disturbance (e.g., vortices or bubbles in liquid) or contamination (e.g., small particle adsorption), which may lead to unpredictable variations of guided signals of the microfiber flow rate sensors [7,26]. Meanwhile, they tend to get saturated or damaged easily while working at relatively large flow rate range. Overall, despite the promising prospects, fiber-optic flow rate sensors for accurate flow rate measurement in millimeter-scale pipelines remain challenging.
Nature has always been a source of inspiration for researchers and a guide for the technical developments. As a spatially distributed directional flow rate sensing system, the lateral line of fish plays an indispensable role in sensing the external water flow. It is found that superficial neuromasts (SNs) in the lateral line of eel have a linear response to the stimulus of different flow rates [27]. This is because the SNs consist of hundreds of hair cells encapsulated in a gelatinous cupula which can feel the water flow [28].
To address the issues faced by the optical flow rate sensors and provide a cost-effective scheme for millimeter-scale pipeline flow rate sensing, we propose a bio-inspired optical flow rate sensor by embedding a U-shaped microfiber in a thin layer of polydimethylsiloxane (PDMS). The PDMS film is analogous to a cupula of an SN while the microfiber enveloped in it is equivalent to a hair cell in the cupula. In this case, microfiber was effectively protected from environmental interference, and the sensing area of the microfiber was dramatically enlarged by the PDMS film. When inserted into an 8-mm-diameter pipeline, the PDMS film is deflected by the flowing liquid, resulting in a bending-dependent transmittance change of the microfiber which is directly related to the flow rate of the liquid. By optimizing the thickness of the PDMS film, the microfiber diameter, and/or the working wavelength, an SN-like optical flow rate sensor with low detection limit (<0.05 L/min), high resolution (0.005 L/min) and fast response (12 ms) is realized. Although the sensitivity and dynamic range of our sensor are not the best among the reported microfluidic flow rate sensors, its excellent reversibility, fast response, adjustable working range as well as the potential for assembling cost-effective systems are attractive for a number of applications, including microreactors, pharmacy, and energy engineering.
2. Fabrication of flow rate sensors and experimental set-up
Figure 1(a) shows a schematic diagram of an optical microfiber flow rate sensor. When a microfiber was embedded into a PDMS film, we define the sensory area as the part of PDMS film that embedded microfiber with a uniform diameter. For a microfiber with a uniform waist diameter of 1 cm in length, when it was bent to a U-shape with a bending radius of 1 mm, the length of the sensory area indicated in the Fig. 1(a) was about 3.5 mm. In this sensory area, the variation in microfiber diameter can be neglected. Typically, the bottom PDMS film is 0.5 mm in thickness. When the U-shape microfiber was fixed onto the bottom PDMS film, a top PDMS film coated with a thin layer of uncured PDMS (∼5 µm in thickness) was attached to the bottom PDMS to embed the U-shape microfiber. The PDMS film is analogous to a gelatinous cupula of an SN which has an excellent flexibility to deflect under water flow, while the microfiber enveloped in it is equivalent to a hair cell in the cupula as shown in Fig. 1(b). It is worth to mention that the PDMS film not only provides a low refractive index (n = 1.40 environment for the holding of silica microfibers but also protects them from the undesired interferences from measured liquids (e.g., unrecoverable degradation of optical properties by contaminations [29], or absorption by liquids) in practical applications. Experimentally, the silica microfibers used in this work were obtained by flame-heated taper drawing [30] of standard optical fibers. As-fabricated microfiber shows excellent flexibility, which allows for a much smaller bending radius than that of standard optical fibers. As shown in Fig. 1(c), the radius of a U-turn can be as small as 100 µm, providing a potential for fabricating a compact flow rate sensor. Benefitted from the high flexibility of the silica microfiber and the thin PDMS film, an as-fabricated optical microfiber flow rate sensor can withstand a large degree of bending, and show an obvious red light scattering in the film when the microfiber is guiding a 633-nm-wavelength light (Fig. 1(d)). This is due to the bending induced energy leakage of the embedded silica microfiber [31,32], which forms the operation principle of optical microfiber flow rate sensors.
Fig. 1. (a) Schematic diagram of an optical microfiber flow rate sensor; d represents the distance between the U-turn and the end of the PDMS film; (b) Schematic diagrams of an SN and an optical microfiber flow rate sensor; (c) SEM image of a 1.5-µm-diameter silica microfiber with a bending radius of 100 µm; (d) Photograph of the bending of a microfiber flow rate sensor guiding a 633-nm-wavelength light.
When a microfiber flow rate sensor is immersed into a liquid, it can be deflected by the flowing liquid, resulting in a bending-dependent transmittance change of the microfiber which is directly related to the flow rate of the liquid. In the case of a flexible film inserted in a liquid environment, the drag force experienced by the film is given as [33]:
where CD is the drag force coefficient, ρ is the liquid density, V is the flow velocity (m/s), and S is the film area. It is clear that in the same liquid environment the drag force experienced by the film only depends on the flow rate of the liquid. Thus, the bending angle (θ) of a PDMS film under a drag force of FD is given by [34]: where E is the Young’s modulus of PDMS, L and I are the length and the area moment of inertia of a PDMS film, respectively. Since the flow rate of the liquid in the pipeline is not uniform, finite element analysis is used to investigate the behavior of liquid and the deflection of a PDMS film in the pipeline. Figures 2(a and b) show the deflection of a PDMS film in a pipeline under different initial flow rates (1° vs. 20° of bending). It is clearly seen that the increase of liquid flow rate causes an increased deflection of the PDMS film (Fig. 2(c)), accompanied by the bending of the embedded microfiber. To investigate the effect of bending on the waveguiding of an optical microfiber, finite difference time domain (FDTD) was applied to simulate the cross-sectional electric field intensity distributions of a 1-µm-diameter microfiber with a 1°(Fig. 2(d)) and 20° (Fig. 2(e)) bending in the PDMS film. As expected, under a slight bending, an obvious energy leakage is observed, confirming the flow rate sensing capability of the optical microfiber flow rate sensors. The bending angles of the PDMS film with different sizes in an 8-mm-diameter pipeline were also simulated. We found that a PDMS film with a longer immersed length and width tends to achieve a greater bending angle (due to the increased pressure difference exerted on the PDMS film), as a result, a higher sensitivity. However, an increased inserted PDMS film area leads to a greater flow resistance for a millimeter-scale pipeline, which is undesired for flow rate sensing. By trading off the sensitivity and flow resistance, both immersed length and width of the PDMS film were set as 4 mm for an 8-mm-diameter pipeline in this work. To investigate the effect of thickness on the sensor performance, the top PDMS film with three different thickness (0.25 mm, 0.5 mm, 0.75 mm) was used to bond with the bottom PDMS film. The distance between the U-turn and the package end (d indicated in Fig. 1(a)) is another key factor that has a great impact on the sensing performance. In this work, the inner diameter of the pipeline was 8 mm, and a typical immersed length of the PDMS film was 4 mm, the length of the sensory area embedded uniform microfiber is about 3.5 mm. If the distance between the U-turn and the package end is less than 0.5 mm, non-uniform microfiber may be involved in the flow rate sensing, leading to a decrease in sensitivity. When the distance between U-turn and the package end is greater than 3 mm, the main part of the U-shape microfiber will locate in the package pipe, making the sensor insensitive to the variation of flow rate. In order to transduce mechanical stimuli of the fluid into microfiber deformation with a high fidelity, the distance between the U-turn and the package end was set as 1.5 mm. In this case, the immersed length of the PDMS film can be varied in the range of 2.5 to 5 mm.Fig. 2. (a, b) Deflection of a flow rate sensor packaged in an 8-mm-diameter pipeline with a PDMS film of 0.75-mm thickness, 4-mm width and 4-mm length under an entrance flow rate of 0.6 (a) and 3.0 L/min (b), respectively; The black line indicates an embedded U-shaped microfiber with a diameter of 1 µm; (c) Measured and simulated bending angle of a 0.75-mm-thickness, 4-mm-width and 4-mm-length PDMS film under different flow rates; (d, e) Electric field intensity distributions of the embedded microfiber at the positions indicated by the red dashed lines in (a) and (b) corresponding to a bending angle of 1 (d) and 20 (e) degrees respectively. The wavelength of the guided light is 700 nm.
To test the sensing performance, an optical microfiber flow rate sensor was packaged into a section of water pipe as a holder and then inserted into a tee coupling for the easy connection with water pipelines, as shown in Fig. 3(a). In order to fix the U-shape microfiber embedded PDMS film in a water pipe, we developed a three-step process. (1) Cutting the U-shape microfiber embedded PDMS film to a patch (4 mm in width, 4 cm in length) ∼1.5 mm away from the microfiber U-turn; (2) Inserting the PDMS patch into a package pipe (5 mm in inner diameter), and making the immersed PDMS (sensory area) outside the package pipe; (3) Fixing the PDMS patch in the center of the package pipe by silicone sealant. After curing overnight, the water pipe packaged sensor can be inserted into a tee coupling as shown in Fig. 3(a) for flow rate measurement. Figure 3(b) shows a schematic diagram of the experimental set-up for water flow rate measurement. Water in a storage tank was pumped into a pipeline with a constant flow rate of 16.7 L/min, which was then split into two channels. The water flow rates in the channels were regulated by two valves connected to each channel. An optical fiber flow rate sensor in a tee coupling was connected to the upper channel after a commercial hall flowmeter which was used for the calibration of flow rate. To obtain a broadband spectral response of the optical microfiber flow rate sensor, white light from a halogen tungsten lamp (SLS201L, Thorlabs) was coupled into the sensor. The transmitted light was guided into a spectrometer (Maya2000-Pro, Ocean Optics) for the spectral analysis.
Fig. 3. (a) Schematic diagram of the integration of an optical microfiber flow rate sensor with a tee coupling; Inset: photograph of an integrated microfiber flow rate sensor; (b) Schematic diagram of the experimental set-up.
3. Experimental results and discussion
Figure 4(a) shows the transmission spectra of a flow rate sensor with a 1.7-µm-diameter microfiber embedded in a 1-mm-thickness PDMS film measured under water flow rates from 0 to 2.06 L/min. With the increase of the water flow rate, the intensity of the transmitted light decreases gradually, together with the blue shift of the peak wavelength. Figure 4(b) provides the dependence of the transmittance of the sensor on the flow rate at light wavelengths of 600, 650, 700, 750, and 850 nm, respectively. With the increase of the guided light wavelength, the sensitivity of the microfiber flow rate sensor increases gradually, along with the shift of the detection range to lower flow rates. This is due to the weaker confinement of guided modes in the microfiber at longer wavelength [31]. The broadband wavelength-dependent response offers an opportunity for tuning the sensitivity and working range in the same sensor using different wavelengths, and thus broadens the dynamic range without sacrificing sensitivity. For reference, the transmittance at 850 nm shows an approximately linear response to flow rate in the range of 0.25-0.87 L/min with an equation of Transmittance = -1.35 Flow rate + 1.34 (R2 = ±0.998). Since the system noise in the experiment is about 0.24%, the flow rate resolution is estimated to be around 0.005 L/min (0.002 m/s), which is one order of magnitude better than that of fiber-optic flowmeter based on bending loss (e.g., 0.05 m/s [35]) and hot-wire flowmeter based on a metallic coated hybrid long period grating/fiber Bragg grating structure (0.08 m/s [36]), and comparable with that of flowmeter based on an FBG heated by Co2+-doped fiber (0.005 m/s [20]) and surface-mountable flowmeter based on piezoelectric sensor arrays (0.003 m/s [37]).
Fig. 4. (a) Transmission spectra of a flow rate sensor (1.7-µm-diameter microfiber, 1-mm-thickness PDMS film) measured at different water flow rates from 0 to 2.06 L/min; (b) Transmittance of the sensor at different wavelengths as a function of flow rate; (c) Dynamic responses of averaged transmitted light intensity of a flow rate sensor (1.7-µm-diameter microfiber, 0.75-mm-thickness PDMS film) at the spectral ranges of 500-600 and 700-800 nm to continuously switched flow rates (0, 0.05, 0.36, 0.56, 0.68, 0.81, 0.93,1.18, 1.37, 1.75, 2.12 L/min); (d) Time-dependent response of the sensor tested by attaching it on an oscillator shaking at a speed of 2400 rpm at 650 nm wavelength;(e) Reversible response of the sensor tested by alternatively switching the flow rate between 0 and 1.34 L/min at the spectral ranges of 600-700 nm.
The wavelength-dependent response offers an approach for the development of flow rate sensors with adjustable flow rate measurement range. As shown in Fig. 4(c), the response of a flow rate sensor with a 1.7-µm-diameter microfiber embedded in a 0.75-mm-thickness PDMS film shows a dramatic difference at different flow rate ranges when working at different spectral ranges. The transmittance of the sensor measured in the wavelength region of 700-800 nm is more sensitive for relatively low flow rates (0-0.56 L/min), with a detection limit below 0.05 L/min. On the contrary, at the working wavelength range of 500-600 nm, the sensor shows a higher sensitivity at high flow rates between 0.68-2.12 L/min. By fixing the flow rate sensor onto an oscillator to introduce a fast vibration on the PDMS film, the response time of the sensor is determined to be as short as ∼12 ms (Fig. 4(d)), which is an order of magnitude faster than many other types of flow rate sensors [4,7,16]. Figure 4(e) presents the response of the sensor when the flow rate of water is switched alternatively between 0 and 1.34 L/min, which shows an excellent reversibility.
In addition to working wavelengths, the performance of microfiber flow rate sensors is also highly dependent on the thickness of PDMS film and the diameter of the microfiber. Figures 5(a-c) show the bending of PDMS film with different thickness under a constant flow rate of 3.0 L/min. As expected, the thinner the PDMS film, the greater the bending angle. This result suggests that a flow rate sensor with a thinner PDMS tends to achieve a higher sensitivity at a low flow rate range. Experimentally, Fig. 5(d) shows flow-rate-dependent transmittance at 700-nm-wavelength of flow rate sensors using microfibers with the same diameter (1.7 µm) while PDMS films with different thicknesses. It can be seen clearly that, at low liquid flow rates, the thinner the PDMS film, the higher the sensitivity of the sensor. For example, the sensor using a 0.75-mm-thickness PDMS film has a good response at flow rates below 0.85 L/min, while the sensor with a 1.25-mm-thickness PDMS film is highly sensitive to flow rates above 1.35 L/min. This is understandable due to the easier bending of a PDMS film with thinner thickness under the action of a water flow which is also consistent with our simulation results in Figs. 5(a-c). Figure 5(d) presents flow-rate-dependent transmittance at 700-nm wavelength of flow rate sensors using PDMS films with the same thickness (1 mm) while microfibers with different diameters. To investigate the impact of microfiber diameter on the sensing performance, we compared the responses of two microfiber flow rate sensors with the same PDMS thickness (1 mm) and operation wavelength while different microfiber diameters (1.2 and 1.7 µm, respectively). As shown in Fig. 5(e), while the sensor using a 1.7-µm-diameter microfiber shows a better performance at larger flow rates (0.63-1.70 L/min), the one using a 1.2-µm-diameter microfiber gives a higher sensitivity at lower flow rates (0-0.5 L/min). This is due to the lower optical confinement of guided modes in the thinner microfiber (inset of Fig. 5(e)), which leads to a higher bending loss of the guided modes and consequently a higher sensitivity to a slight bending of the PDMS film [31]. Owing to the high flexibility of PDMS and microfiber as shown in Fig. 1(d), (a) microfiber embedded PDMS film can be bent in a range of 0° to 90° in the tee coupling. By optimizing the thickness of the PDMS film, operation wavelength, and microfiber diameter, the sensitivity and working range of an optical microfiber flow rate sensor can be optimized in a wide range for different flow rate measurements.
Fig. 5. (a-c) Deflection of a flow rate sensor packaged in an 8-mm-diameter pipeline under an entrance flow rate of 3.0 L/min with a PDMS film of 4-mm length, 4-mm width, and 0.75-mm (a), 1-mm (b), 1.25-mm (c) thickness, respectively; (d) Flow-rate-dependent transmittance of flow rate sensors using microfibers with the same diameter (1.7 µm) while different thicknesses of PDMS films (0.75, 1 and 1.25 mm, respectively) at 700-nm wavelength; (e) Flow-rate-dependent transmittance of flow rate sensors using PDMS films with the same thickness (1 mm) while different microfiber diameters (1.2 and 1.7 µm, respectively) at 700-nm wavelength; Inset: Electric field intensity distributions of the embedded microfiber in PDMS under a bending angle of 20 degrees with a diameter of 1.2 and 1.7 µm at 700-nm wavelength.
4. Conclusion
In this work, we have demonstrated a bio-inspired optical microfiber flow rate sensor by embedding a U-shaped silica microfiber in a thin PDMS film. The PDMS film does not only protect the microfiber from surface contamination, but also work as a bending transducer for enabling the microfiber-based flow rate sensing. By optimizing the thickness of the PDMS film, the microfiber diameter, and/or the working wavelength, an optical flow rate sensor with low detection limit (<0.05 L/min), high resolution (0.005 L/min) and fast response (12 ms) is realized, which is suitable and attractive for the flow rate sensing in millimeter-scale pipelines. Finally, the initial results shown here may pave a way towards a category of packaged microfiber structures for compact and sensitive photonic sensing with high flexibility.
Funding
National Key Research and Development Program of China (2016YFB1001300); National Natural Science Foundation of China (No. 61975173); Major Scientific Research Project of Zhejiang Lab (No. 2019MC0AD01); Fundamental Research Funds for the Central Universities.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. S. Garimella, Heat Transfer and Fluid Flow in Minichannels and Microchannels, (Elsevier Science Ltd, 2006), Chap. 6.
2. J. Huang, H. Ji, Z. Huang, B. Wang, and H. Li, “A New Contactless Method for Velocity Measurement of Bubble and Slug in Millimeter-Scale Pipelines,” IEEE Access 5, 12168–12175 (2017). [CrossRef]
3. F. E. Jones, Techniques and Topics in flow Measurement (CRC, 1995).
4. Y. Z. Wen, X. P. Wang, P. J. Cai, and B. Zhang, “Tungsten oxide electrode for measurement of ultralow liquid flow velocity,” Sens. Actuators, B 215, 459–463 (2015). [CrossRef]
5. B. Tian, H. F. Li, H. Yang, D. L. Song, X. W. Bai, and Y. L. Zhao, “A MEMS SOI-based piezoresistive fluid flow sensor,” Rev. Sci. Instrum. 89(2), 025001 (2018). [CrossRef]
6. W. Peng, G. R. Pickrell, Z. Y. Huang, J. C. Xu, D. W. Kim, B. Qi, and A. B. Wang, “Self-compensating fiber optic flow sensor system and its field applications,” Appl. Opt. 43(8), 1752–1760 (2004). [CrossRef]
7. V. Lien and F. Vollmer, “Microfluidic flow rate detection based on integrated optical fiber cantilever,” Lab Chip 7(10), 1352–1356 (2007). [CrossRef]
8. P. Lu and Q. Y. Chen, “Fiber Bragg grating sensor for simultaneous measurement of flow rate and direction,” Meas. Sci. Technol. 19(12), 125302 (2008). [CrossRef]
9. L. Yuan, J. Yang, and Z. Liu, “A Compact Fiber-Optic Flow Velocity Sensor Based on a Twin-Core Fiber Michelson Interferometer,” IEEE Sens. J. 8(7), 1114–1117 (2008). [CrossRef]
10. Z. Liu, M. L. Tse, A. P. Zhang, and H. Y. Tam, “Integrated microfluidic flowmeter based on a micro-FBG inscribed in Co2+-doped optical fiber,” Opt. Lett. 39(20), 5877–5880 (2014). [CrossRef]
11. M. S. Cheri, H. Latifi, J. Sadeghi, M. S. Moghaddam, H. Shahraki, and H. Hajghassem, “Real-time measurement of flow rate in microfluidic devices using a cantilever-based optofluidic sensor,” Analyst 139(2), 431–438 (2014). [CrossRef]
12. Y. Li, G. Yan, L. Zhang, and S. He, “Microfluidic flowmeter based on micro “hot-wire” sandwiched Fabry-Perot interferometer,” Opt. Express 23(7), 9483–9493 (2015). [CrossRef]
13. Y. Gong, Q. F. Liu, C. L. Zhang, Y. Wu, Y. J. Rao, and G. D. Peng, “Microfluidic Flow Rate Detection with a Large Dynamic Range by Optical Manipulation,” IEEE Photonics Technol. Lett. 27(23), 2508–2511 (2015). [CrossRef]
14. C. R. Zamarreno, C. Martelli, V. H. V. Baroncini, E. N. dos Santos, M. J. da Silva, R. E. M. Morales, P. Zubiate, F. J. Arregui, and I. R. Matias, “Single and Multiphase Flow Characterization by Means of an Optical Fiber Bragg Grating Grid,” J. Lightwave Technol. 33(9), 1857–1862 (2015). [CrossRef]
15. P. P. Kirwan, D. Creighton, C. Costello, T. P. O’Brien, and K. W. Moloney, “Momentum Change Flow Meter with Pressure Compensation Using FBGs,” IEEE Sens. J. 16(19), 7061–7064 (2016). [CrossRef]
16. S. C. Yan, Z. Y. Liu, C. Li, S. J. Ge, F. Xu, and Y. Q. Lu, ““Hot-wire” microfluidic flowmeter based on a microfiber coupler,” Opt. Lett. 41(24), 5680–5683 (2016). [CrossRef]
17. B. Zhou, H. Jiang, C. Lu, and S. He, “Hot Cavity Optical Fiber Fabry-Perot Interferometer as a Flow Sensor with Temperature Self-Calibrated,” J. Lightwave Technol. 34(21), 5044–5048 (2016). [CrossRef]
18. Y. Gong, L. M. Qiu, C. L. Zhang, Y. Wu, Y. J. Rao, and G. D. Peng, “Dual-Mode Fiber Optofluidic Flowmeter with a Large Dynamic Range,” J. Lightwave Technol. 35(11), 2156–2160 (2017). [CrossRef]
19. R. Gao, D. Lu, J. Cheng, and Z.-m. Qi, “Simultaneous measurement of refractive index and flow rate using graphene-coated optofluidic anti-resonant reflecting guidance,” Opt. Express 25(23), 28731–28742 (2017). [CrossRef]
20. Z. Liu, L. Htein, L.-K. Cheng, Q. Martina, R. Jansen, and H.-Y. Tam, “Highly sensitive miniature fluidic flowmeter based on an FBG heated by Co2+-doped fiber,” Opt. Express 25(4), 4393–4402 (2017). [CrossRef]
21. Y. Zhao, Y. F. Gu, R. Q. Lv, and Y. Yang, “A Small Probe-Type Flowmeter Based on the Differential Fiber Bragg Grating Measurement Method,” IEEE Trans. Instrum. Meas. 66(3), 502–507 (2017). [CrossRef]
22. C. Shen, X. Lian, V. Kavungal, C. Zhong, D. Liu, Y. Semenova, G. Farrell, J. Albert, and J. F. Donegan, “Optical spectral sweep comb liquid flow rate sensor,” Opt. Lett. 43(4), 751–754 (2018). [CrossRef]
23. C. Yanez, F. J. Azcona, and S. Roy, “Confocal flowmeter based on self-mixing interferometry for real-time velocity profiling of turbid liquids flowing in microcapillaries,” Opt. Express 27(17), 24340–24352 (2019). [CrossRef]
24. L. Tong, “Micro/Nanofibre Optical Sensors: Challenges and Prospects,” Sensors 18(3), 903 (2018). [CrossRef]
25. L. Zhang, Y. Tang, and L. Tong, “Micro-/Nanofiber Optics: Merging Photonics and Material Science on Nanoscale for Advanced Sensing Technology,” iScience 23(1), 100810 (2020). [CrossRef]
26. Y. Gong, M. Zhang, C. Gong, Y. Wu, Y. Rao, and X. Fan, “Optofluidic microring flowmeter based on heat transfer effect,” in 2017 25th Optical Fiber Sensors Conference(OFS), (IEEE, 2017), pp. 1–4.
27. J. Montgomery, G. Carton, R. Voigt, C. Baker, and C. Diebel, “Sensory processing of water currents by fishes,” Philos. Trans. R. Soc., B 355(1401), 1325–1327 (2000). [CrossRef]
28. M. J. McHenry and S. M. van Netten, “The flexural stiffness of superficial neuromasts in the zebrafish (Danio rerio) lateral line,” J. Exp. Biol. 210(23), 4244–4253 (2007). [CrossRef]
29. F. Xu and G. Brambilla, “Preservation of Micro-Optical Fibers by Embedding,” Jpn. J. Appl. Phys. 47(8), 6675–6677 (2008). [CrossRef]
30. Y. Xu, W. Fang, and L. Tong, “Real-time control of micro/nanofiber waist diameter with ultrahigh accuracy and precision,” Opt. Express 25(9), 10434–10440 (2017). [CrossRef]
31. H. Yu, S. Wang, J. Fu, M. Qiu, Y. Li, F. Gu, and L. Tong, “Modeling bending losses of optical nanofibers or nanowires,” Appl. Opt. 48(22), 4365–4369 (2009). [CrossRef]
32. L. Zhang, J. Pan, Z. Zhang, H. Wu, N. Yao, D. Cai, Y. Xu, J. Zhang, G. Sun, L. Wang, W. Geng, W. Jin, W. Fang, D. Di, and L. Tong, “Ultrasensitive skin-like wearable optical sensors based on glass micro/nanofibers,” Opto-Electron. Adv. 3(3), 190022 (2020). [CrossRef]
33. R. D. Blevins, Applied Fluid Dynamics Handbook (Krieger Publishing Company, 2003).
34. J. Gere, Mechanics of Materials (Cengage Learning, 2003).
35. R. P. Hu and X. G. Huang, “A Simple Fiber-Optic Flowmeter Based on Bending Loss,” IEEE Sens. J. 9(12), 1952–1955 (2009). [CrossRef]
36. P. Caldas, P. A. Jorge, G. Rego, O. Frazao, J. L. Santos, L. A. Ferreira, and F. Araujo, “Fiber optic hot-wire flowmeter based on a metallic coated hybrid long period grating/fiber Bragg grating structure,” Appl. Opt. 50(17), 2738–2743 (2011). [CrossRef]
37. M. Asadnia, A. G. P. Kottapalli, Z. Shen, J. Miao, and M. Triantafyllou, “Flexible and Surface-Mountable Piezoelectric Sensor Arrays for Underwater Sensing in Marine Vehicles,” IEEE Sens. J. 13(10), 3918–3925 (2013). [CrossRef]
