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All issues Volume 4 / No 2 (2025) Natl Sci Open, 4 2 (2025) 20240046 Full HTML
Issue
Natl Sci Open
Volume 4, Number 2, 2025
Special Topic: Flexible Electronics and Micro/Nanomanufacturing
Article Number 20240046
Number of page(s) 28
Section Engineering
DOI https://doi.org/10.1360/nso/20240046
Published online 18 December 2024

© The Author(s) 2024. Published by Science Press and EDP Sciences.

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

INTRODUCTION

Flow, manifesting as airflow, blood flow, breath, or water flow, is ubiquitous both in nature and within living bodies, providing vital information for numerous natural creatures to escape from threats and seek sustenance. For instance, spiders utilize their trichobothria to sense air currents, which alert them to nearby prey or predators [1]. Similarly, relying on the lateral line system, a unique sensory organ composed of mechanoreceptors, fish can navigate and evade obstacles in intricate aquatic environments by feeling subtle variations in vibration waves, flow acceleration, and pressure gradients [2]. Moreover, bats employ an echolocation method where they emit and receive high-frequency ultrasonic waves to determine surroundings in the dark [3].

Inspired by these biological organisms, the study of flow dynamics has boosted the development of a wide range of flow sensors over the last few decades, aiming at perceiving the intensity and direction of flow [4–8]. For example, an electromagnetic catheter flow sensor is developed to measure the flow rate using two parallel bundles of wires in opposite directions [9]. Besides, in industrial environments, flow sensors are often installed invasively, involving mechanical structures like grooves and holes [10–12]. As a counterpart of catheter flow sensors that require fixed installations and bulky structures, flexible flow sensors based on flexible substrates are introduced [13–15]. Such substrates can deform in response to the movement and applied force, allowing these flow sensors to be attached freely and installed without causing any damage. Furthermore, as such sensors can be designed more delicately and ingeniously, accessory structures such as compensation circuits and thermal insulators can be incorporated to enhance sensor sensitivity and reduce noise interference [16,17].

As flow interacts with a range of physical phenomena including heat, sound, force, light, and magnetism, flexible flow sensors are designed based on various principles, such as thermal calorimetry [18], Doppler effect [19], triboelectricity [20], and piezoresistive effect [21]. In addition, a variety of manufacturing techniques such as laser processing [22], printing [23], and photolithography [24], facilitate the fabrication of sensitive materials in response to flow, such as copper [25], nickel [26], and laser-induced graphene (LIG) [27] on flexible substrates like polyimide (PI) [28] and polydimethylsiloxane (PDMS) films [29]. Notably, benefiting from the adjustable and precise steps in these state-of-the-art techniques, microstructures that mimic natural creatures can be realized, such as fluffy fabric flow sensors [30], artificial lateral line flow sensors [31], and whisker flow sensors [32], all of which substantially enhance sensor performance.

These high-performance, fast-responding, sensitive flexible flow sensors are applied in diverse scenarios. To be specific, visually impaired individuals wearing fluffy fabric flow sensors can receive alerts when quick-moving objects approach [30]. Additionally, the velocity of dolphins and turtles can be noninvasively measured with artificial lateral line flow sensors [33]. Furthermore, an array of flexible flow sensor units allows for the remapping of flow fields using interpolation algorithms [34]. By integrating flexible flow sensors with wireless transmission patches and machine learning algorithms, several crucial clinical indicators, such as seismocardiograms (SCGs), electrocardiograms (ECGs), and photoplethysmograms (PPGs) can be continuously captured at home, potentially saving patients suffering from obstructive sleep apnea [35].

Herein, this review presents a comprehensive overview of recent advances in flexible flow sensors, especially focusing on the working mechanisms and diverse applications (Figure 1). First, such sensors are designed based on various working mechanisms, among which thermal, acoustic, piezoresistive and piezoelectric flow sensors are primarily analyzed. Subsequently, the applications of flexible flow sensors are categorized into four aspects according to the type of flow including airflow, blood flow, breath, and water flow applications. Finally, the future trends of flexible flow sensors are explored.

thumbnail Figure 1

Overview of bioinspired flexible flow sensors comprising major working mechanisms including thermal, piezoresistive, piezoelectric and acoustic flow sensors. Four main applications including airflow, blood flow, breath, and water flow applications [50,59,71,81,82,85,92,98].

WORKING PRINCIPLES OF VARIOUS FLOW SENSORS

Thermal flow sensors

Thermal flow sensors utilize the heat transfer between the flow field and thermal field to detect flow intensity and direction [36–39]. According to the Law of Conservation of Energy, the heat transfer can be expressed as [40]

∂ T ∂ τ + v x ∂ T ∂ x + v y ∂ T ∂ y = K t ( ∂ 2 T ∂ x 2 + ∂ 2 T ∂ y 2 ) , (1) where T refers to temperature, τ refers to time, the x direction belongs to the flow direction, and y is perpendicular to the flow direction. Parameters vx and vy represent the velocity components in the x and y directions, respectively. Kt is the thermal diffusivity of the flow. Specifically, thermal flow sensors can be subclassified into thermal anemometer, thermal calorimetric, and thermal time-of-flight flow sensors. Thermal anemometer flow sensors typically have one heater, while thermal calorimeter sensors have one heater and a pair of temperature sensors. Both types perceive flow dynamics through the heat exchange between flow and the sensors. Additionally, the thermal time-of-flight flow sensor evaluates flow intensity by quantifying the transit time of a short heat pulse as it travels across a predetermined spatial interval [41].

Thermal anemometer

In terms of hot-wire, the heater is usually detached from the substrate and supported by stands, whereas in hot-film, the heater is located in a film. Thermal anemometer usually operates in two modes: the constant temperature approach [42] and the constant power approach [43]. The former adjusts power to keep the heater temperature constant under varying flow intensities, while the latter maintains power fixed and measures the temperature variance versus flow intensity. King’s Law can be used to describe a hot anemometer’s behavior [44]:

h = A v f C + B , (2)

where h is the heat transfer coefficient related to the temperature of the heater and vf refers to the flow rate. Parameters A, B, and C are related to the type of flow, properties of substrate, etc. For example, Ma et al. [26] achieved a typical hot-film flow sensor by fabricating nickel thin-film resistors on a PI film substrate (Figure 2b). Afterwards, a polymer compatible micromachining technology was developed to realize a waterproof coating, and eventually they successfully detected dynamic wave flow at a sampling frequency of 40 Hz (Figure 2c).

thumbnail Figure 2

Thermal flow sensors. (a) Conceptual illustrations of thermal anemometer flow sensors: hot-wire and hot-film. (b) Fully flexible thermal anemometer sensor array on PI film substrate, with enlarged images showing sensor array and copper leads [26]. (c) Fully flexible thermal anemometer sensor’s output in wave flow [26]. (d) Conceptual illustration of thermal calorimeter flow sensors. (e) Top view of flexible thermal calorimeter flow sensors integrated on a printed circuit board (PCB) (left) and schematic of the membrane (right) [47]. (f) Exploded view illustration of a platform that incorporates a central thermal actuator surrounded by 100 precision temperature sensors, placed over the skin with an underlying shunt catheter, with enlarged images showing optical micrograph of the device (surrounded by black dashed line), serpentine interconnects (blue dashed line) and individual resistive temperature sensors (red dashed line) [49]. (g) IR thermographs with color and contrast enhancement highlight the spatial isotropy of the distribution of temperature in the absence of flow (left) and the anisotropy in the presence of flow (right). Flow is to the right (arrow) [49]. (h) Conceptual illustrations of thermal anemometer + thermal calorimeter flow sensors. (i) Photo images of the LIG-based flexible thermal anemometer + thermal calorimeter flow sensor on curved surfaces [50]. (j) Resistance variation measured from the two temperature sensors as a function of flow rate [50]. (k) Resistance variation measured from the heater as a function of flow rate [50]. (l) Principal component analysis of collected data from the eight temperature sensors under the four flow directions [50]. (m) Cubic convolution interpolation of the eight temperature sensors after normalization when the flow is incident at 45° [50].

Thermal calorimeter

Although thermal anemometer flow sensors are able to measure a wide range of flow velocity, it is difficult to determine flow direction through a single heater. The second type, thermal calorimeter flow sensors, is capable of perceiving both flow intensity and direction simultaneously.

Typically, this type includes at least a pair of thermoresistive temperature sensors alongside one heater with a constant power approach (Figure 2d). Initially, there should be no temperature difference between the pairs of temperature sensors when the flow velocity is zero. When applying flow, the heat generated by the heater transfers downstream, resulting in the downstream temperature sensor being at a higher temperature than the upstream one. However, the flow itself cools the entire field as well, so the temperature difference of the temperature pairs decreases when the flow velocity exceeds the saturated velocity. The whole calorimetric mechanism can be expressed as [45,46]

∆ T   = T 0   ( e γ d l d − e γ u l u ) , (3)

where T0 represents the temperature of the heater, γ is associated with the flow rate, flow thermal diffusivity, and the thickness of the thermal and fluid boundary layer, and l refers to the distance between the heater and temperature sensors. The subscripts u and d indicate the upstream and downstream. Using high temperature deposition, Hannes Sturm and Walter Lang presented a silicone membrane-based thermal flow sensor with one heater and a pair of temperature sensors (Figure 2e), which had a sensitivity of 30.4 mV/(m/s) [47].

To broaden the capacity to perceive flow direction, Murakami et al. [48] developed a MEMS subsonic flow sensor with one microheater and three pairs of temperature sensors. In addition to measuring flow velocity ranging from 30 to 170 m/s in a wind tunnel, this sensor was also capable of distinguishing the flow angle by the sinusoidal variation in temperature difference between two opposing temperature sensors. Furthermore, Krishnan et al. [49] proposed a thermal calorimeter flow sensor with 50 temperature sensor pairs and one heater to drastically improve the resolution of flow direction detection (Figure 2f). Through infrared (IR) thermographs, the spatial isotropy of the distribution of temperature in the absence of flow and the anisotropy in the presence of flow were illustrated (Figure 2g), indicating that this type of sensor with high resolution could be applied for precise skin thermography.

Combined thermal anemometer and calorimeter

To combine the advantages of the thermal anemometer which can perceive a wide range of flow rates and the thermal calorimeter which can determine flow direction, Xu et al. [50] designed a flow sensor featuring one thermal resistive heater and eight thermal resistive temperature sensors (Figure 2h). This work optimized the characterization of laser-induced graphene by tailoring laser factors and design patterns during the fabrication process (Figure 2i). Consequently, this combined flow sensor exhibited high sensitivity (~162 K s/m) (Figure 2j) at small flows with an extended flow detection range (~25 m/s) (Figure 2k), and was able to distinguish flow direction using principal component analysis (PCA) and interpolation algorithms, as shown in Figure 2l and m.

Typically, all thermal flow sensors face a problem: heat loss occurring between the heater and the substrate degrades sensitivity and increases energy consumption. Hence, Xu et al. [16] proposed thermal insulators to enhance the accuracy of temperature sensors by approximately 50-fold. Besides, Arakane et al. [51] applied four layer-by-layer laminations of two-dimensional (2D) micropatterns to thermally isolate microheaters from substrates.

On the other hand, ambient temperature and the temperature of the flow itself may influence the output of flow sensors. Sosna et al. [17] reported a temperature compensation circuit, reducing errors to less than 1% when ambient temperature increased from 25 to 65 °C. In terms of the temperature of the flow itself, Ferreira et al. [52] minimized errors to approximately 3% when the flow temperature rose from 28.5 to 32.75 °C.

Piezoresistive and piezoelectric flow sensors

Flow generates a force termed drag force when disturbed by an object. Piezoresistive and piezoelectric flow sensors utilize this effect, which can be expressed as [53]

F D   = 1 2 A F C D ρ v 2 , (4)

where FD is the drag force applied to the object, ρ is the mass density of the flow, v is the flow velocity, AF is the object area perpendicular to the flow, and CD is the drag coefficient, which generally depends on the Reynolds number. The direction of the drag force FD is in that of the flow velocity v. Usually, such sensors are fabricated into a cantilever beam structure perpendicular to the direction of flow velocity. Its deflection can be calculated according to the effect balance equation [54]:

E I d 4 w d x 4   = q ( x ) , (5)

where E is the Young’s modulus of the material, I is the moment of inertia of the cross-section, w is the deflection of the object, and q(x) is the transverse load per unit length. To simplify the model, q(x) is usually calculated as q(x)≡FDL (Figure 3a) [55].

thumbnail Figure 3

Piezoresistive and piezoelectric flow sensors. (a) Conceptual illustration of piezoresistive flow sensors [55]. (b) Schematic diagram of the flexible piezoresistive flow sensor using VGNs [57]. (c) Sensor output as a function of flow velocity (calibration plot) [57]. (d) Working mechanism of three LIG airflow sensors with equivalent circuit diagram and schematic illustration of PLIG, VLIGF, and SLIGF [59]. (e) Digital photos of cotton, caterpillar, and Lepidoptera insect-butterfly, with SEM images of PLIG, VLIGF, and SLIGF from top view. The scale bars are 250, 250 and 500 μm, respectively [59]. (f) Relative current variation within the airflow range of 0.0023–2.35 m/s [59]. (g) Conceptual illustration of piezoelectric flow sensors [60]. (h) Optical image of the hydrodynamic artificial velocity sensor [60]. Distribution of stress in the x direction when pressure is at 0° (i) and at 90° (j) [60]. (k) Results of the directivity detection [60]. (l) Relationship between charge output and velocity [60].

Piezoresistive effect

Piezoresistive flow sensors are composed of materials that exhibit a measurable alteration in electrical resistivity when deflected under external stress, which can be expressed by [56]

∆ R R 0 = K θ max , (6)

where R0 is the static reference resistance under initial conditions, ∆R is the resistance difference when an external load is applied, K is the deflection coefficient, and θmax is the maximum deflection angle of all the points in the sensor, which is related to the deflection w of the object. One typical piezoresistive flow sensor, reported by Abolpour Moshizi et al. [57], was made of 4.5 mm-high vertical graphene nanosheets (VGNs) (Figure 3b), exhibiting a high sensitivity of 103.91 mV/(mm/s) and a low velocity detection threshold of 1.127 mm/s (Figure 3c). Such features allowed this sensor to mimic sensory hair cells in the vestibular system and hearing system.

To shorten the sensor size, thereby reducing its influence on the original field distribution and decreasing the response time, some researchers drew inspiration from natural creatures [58]. For example, Wang et al. [30] proposed a flexible all-textile flow sensor with in-situ grown carbon nanotubes (CNTs), by mimicking spider’s fluff. They changed the single pillar into numerous fibers and leveraged the variation in contact resistance among fibers to detect flow intensity. Consequently, the all-textile flow sensor reached an ultra-low detection limit of approximately 0.05 m/s, a fast response time of 1.3 s and a wide airflow velocity range up to 7.0 m/s. Furthermore, Huang et al. [59] employed LIG with poststructural biomimicry to further enhance the performance of sensors. Inspired by cotton, caterpillar fluff, and Lepidoptera, the structures of cotton-like porous LIG (PLIG), vertical LIG fiber (VLIGF) and suspended LIG fiber (SLIGF) were analyzed, respectively (Figure 3d). They found that despite the intrinsic bulk resistance, the compression resistance of PLIG changed when applying flow. In terms of VLIGF, the top vertical fibers connected or separated with each other when subjected to flow, causing changes in contact and separation resistivity. Conversely, SLIGF was free of separation resistance because the suspended fibers and wing scales leaned unidirectionally. Figure 3e presents the morphologies of these three structures. Among these three LIG-based flow sensors, SLIGF exhibited the best sensor performance with a sensitivity of 0.11 s/m, an average response time of 0.5 s, and a detection threshold of 0.0023 m/s, as shown in Figure 3f.

Piezoelectric effect

The other type, the piezoelectric flow sensor, is made of dielectric materials that generate surface distributions of electric charges when subjected to mechanical loads (direct piezoelectric effect). Hence, due to the mechanical connection between the film and the substrate, the deflection of the film transfers the bending moment to the bottom substrate, causing the piezoelectric output (Figure 3g) [60].

One typical piezoelectric flow sensor, reported by Hu et al. [60], featured a 40 μm-thick polarized poly (vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)]/barium titanate (BTO) electrospinning nanofiber mat as the sensing layer, a 50 μm-thick PI film with arrays of circular cavities as the substrate, and a 5 mm-high poly(methyl methacrylate) (PMMA) pillar as the cilium (Figure 3h). After simulating the piezoelectric output when pressure was at 0° (Figure 3i) and 90° (Figure 3j), the authors demonstrated that the two semicircular electrodes could obtain the piezoelectric signals on both sides of the pillar. Subsequently, they used a dipole vibration to characterize the sensor’s performance. Owing to the semicircular electrode, the direction could be detected from 0° to 360°. However, when the flow direction was perpendicular to the electrode, such as 90° and 270°, the charge was partially neutralized, leading to a reduced output (Figure 3k). In the velocity response section, the sensor exhibited a high sensitivity of 0.08 pC/(m/s) and a significant enhancement in velocity detection threshold to 0.23 mm/s (Figure 3l), probably attributed to the enhanced piezoelectricity of the P(VDF-TrFE)/BTO nanofiber mat after polarization.

Acoustic flow sensors

Acoustic flow sensors, which utilize ultrasound or sound waves to interact with the flow, can be categorized based on two principles: Doppler effect and acoustic time-of-flight. Both types rely on ultrasound transducers as their most crucial components, which affect the quality of ultrasound waves and ultimately determine sensor performance. However, the major difference between these two types is that flow sensors based on the Doppler effect analyze signals in the frequency domain using Fourier transform (FT), while the latter determines flow rates in the time domain.

Doppler effect

The former type features a Doppler device that emits an incident ultrasound beam and simultaneously receives the corresponding reflected ultrasound beam. Scattered by the flow, the frequency of the reflected beam deviates from that of the incident beam (Figure 4a), which is known as the Doppler effect [19]:

thumbnail Figure 4

Acoustic flow sensors. (a) Conceptual illustration of Doppler flow sensors. (b) Schematic diagram and optical image (inset) of the flexible acoustic wave device [61]. (c) Frequency responses of the acoustic wave device when the flow rate increases from 0 to 0.8 LPM and then decreases from 0.8 to 0 LPM in step of 0.2 LPM [61]. (d) Schematics (left) and exploded view (right) of the device structure. ACF, anisotropic conductive film [62]. (e) Schematic of the DBUD method [62]. (f) Measured PFV versus true PFV curves. Error bars represent ±SD (N = 5) [62]. (g) Typical carotid blood flow spectra during a cardiac cycle (left) and several cycles (right). Feature points are marked in the left image. Inset: an image showing the device mounted on the neck [62]. (h) Conceptual illustration of time-of-flight flow sensors. (i) Ultrasonic air-coupling time-of-flight configuration [66]. (j) Experimental DC steps linearity test [66].

∆ f   = 2 v f cos γ v s f 0 , (7)

where f0 is the incident beam frequency, vf is the flow velocity, vs is the ultrasound velocity and γ is the angle between the axis of the beam and the direction of the flow. By depositing a patterned layer of Cr/Au as interdigital transducers (IDTs) on a composite film consisting of ZnO and aluminum foil, Zhang et al. [61] achieved a total thickness of approximately 55 μm (Figure 4b). Attached to the inner wall of a pipe, this device exhibited a response time of ~2 s, a sensitivity of 2176.8 ppm for 0.8 liters per minute (LPM) and a nearly negligible hysteresis (Figure 4c).

However, in real application scenarios, it is troublesome to accurately measure the angle γ between the flow direction and the ultrasound beam. To resolve this problem, Wang et al. [62] reported a 1 mm-thick wearable Doppler device with a 3 by 3 array of 1–3 composite piezoelectric transducers (Figure 4d) and a dual-beam ultrasound Doppler (DUBD) method to calculate θ automatically (Figure 4e). To be specific, two beams with different angles of incidence, θ1 and θ2, emitted by two transducers are governed by the following equations:

∆ f D i = 2 v f cos γ i v s f 0 ,    i = 1 , 2 , (8)

and the relationship between θ and γ can be derived from geometric conditions:

arcsin ( sin θ 1 η ) − arcsin ( sin θ 2 η ) = γ 1 − γ 2 , (9)

where η is related to the refractive index. This method demonstrated a relative error of less than 8.69% between the true peak flow velocity (PFV) and the measured PFV (Figure 4f). Such a convenient method ensures that this device can consistently monitor pulsatile carotid blood flow and identify significant feature points for carotid artery stenosis analysis, such as peak velocity (S1), systolic velocity (S2), peak diastolic velocity (D), and end-diastolic velocity (d) (Figure 4g).

Acoustic time-of-flight

Another acoustic type, time-of-flight, typically separates the sensor into one transmitter and one receiver at a constant distance. Then the time spent by the ultrasound to travel the defined distance is related to ultrasound velocity and flow velocity, which can be expressed as [63]

t = D v s + v f cos γ , (10)

where D is the defined constant distance, vs is ultrasound velocity, vf is flow velocity and γ is the angle between ultrasound and flow direction (Figure 4h). Notably, ultrasound velocity is affected by temperature, humidity and pressure, with temperature being the most critical factor [64,65]. To address this deviation, Begin et al. [66] developed a bidirectional transmit/receive prototype made from piezo-crystals to measure the phase differences (TOF1 and TOF2) in coupled directions sequentially (Figure 4i). To evaluate its performance, the authors compared the sensor with a calibrated commercial reference pneumotach, demonstrating that it offered a resolution of 0.03 L/s and a linearity of 95% (Figure 4j).

Other categories of flow sensors

In addition to thermal, piezoresistive, piezoelectric, and acoustic flow sensors, there are several other categories of flow sensors. One instance was the magnet flow sensor based on the longitudinal spin Seebeck effect, which utilized a magnetic Ni0.2Zn0.3Fe2.5O4 film that generated a spin current when a heated flow passed through this film [67]. This type could be attached to variously shaped heat sources without obstructing original heat flux, allowing it to be seamlessly integrated into versatile systems for heat measurements and management. Another category was the optical time-of-flight flow sensor, which involved three short sections of optical fibers: one for heating flow and the other two for observing temperature variations downstream based on the Bragg gratings principle [68]. This type could perceive flow rates ranging from 1 to 1200 mL/h, providing a broad dynamic range. Besides, it was insensitive to deviations in heat loss in optical fibers, fluctuations in optical heat source power, and variations in the thermal properties of the liquid. Moreover, triboelectric flow sensors were designed to detect the repetitive flows such as vortices [69]. By modeling the interaction mechanism between the vortex and this sensor in both simulation and experimental sections, the authors optimized the cylinder diameter to generate vortices, as well as key sensor parameters such as membrane length, width, thickness, and electrode gap. Finally, an energy transducing performance at approximately 0.6 m/s was achieved. The advantages and disadvantages of each principle are compared in Table 1.

Table 1

Comparison among different mechanisms

These diverse types of flow sensors highlight the wide range of physical principles utilized to measure the intensity and direction of flow. Furthermore, flexible flow sensors, with their excellent performance and flexible conformability, offer a broader range of application scenarios compared with rigid flow sensors. They can be utilized for aerodynamics detection for airflow [70], hemodynamics identification for blood flow [71], disease diagnosis for breath [72], and hydrodynamics characterization for water flow [73].

APPLICATIONS OF FLEXIBLE FLOW SENSORS

Applications in monitoring airflow

Airflow is commonly present and utilized in daily life, providing numerous indicators that are crucial for warning potential danger and operating autonomous aircraft intelligently [74–76]. In addition, the distribution of airflow field can help researchers investigate flow behaviors comprehensively.

Stall detection

Generally, modern airplanes gain lift force from airflow, which can be expressed by Bernoulli’s equation [77]:

P + 1 2 ρ v 2 + ρ g h = constant , (11)

where P is pressure, ρ is the density of flow, v is flow velocity, g is gravitational acceleration and h is the relative height. Hence, the pressure on the upper surface of the airfoil is less than that on the lower surface, contributing to the lift force that keeps airplanes flying safely in the sky. Specifically, the lift force can be expressed as [78]

F = 1 2 ρ v 2 S C l , (12)

where S is the area of the airfoil and Cl is a coefficient related to the angle of attack (AOA). The lift force dramatically decreases when AOA increases to a certain level that disrupts the airflow over the airfoil, resulting in a stall (Figure 5a) [79].

thumbnail Figure 5

Applications in airflow monitoring: stall detection. (a) Conceptual illustration of stall, with red region representing positive pressure while the blue region representing negative pressure [80]. (b) Schematic of the airfoil integrated with the iFlexSense skin (P: piezoelectric sensor; H: hot-film sensor; C: capacitive pressure sensor; T & S: temperature & strain sensors) [80]. (c) The electronic skin mounted on a standard NACA 0012 airfoil under varying AOA from 25° to +25° (an incremental step of 1°) [80]. (d) Time-averaged pressure of the suction peak under different free stream velocities from 4 m/s up to 11.16 m/s [80]. (e) Principle and structure diagram of digital-visualization array for turbulence stall sensing (DATSS) [81]. (f) DATSS system stall sensing T-signal after STD processing [81]. (g) DATSS system stall sensing raw P-signal [81]. (h) The photograph of fixed-wing remote control Cessna 182 aircraft with a wing length of 1420 mm for flight test, equipped with two DATSS units [81]. (i) The wireless flight signal of the arrayed DATSS system [81].

Various indicators highlight the abnormal conditions when stall occurs, such as shear stress, pressure and flutter. For example, Xiong et al. [80] presented a bio-inspired multifunctional skin (iFlexSense skin) consisting of 21 capacitive sensors for wind pressure, 30 piezoelectric sensors for impact locating, 12 hot-film sensors for wall shear stress, 4 resistive temperature detectors for surface temperature, and 4 strain gauges for structural strain (Figure 5b). This multimodal system was tested in a wind tunnel for a sequential series of AOA (Figure 5c), and the results from pressure sensors, hot-film sensors and piezoelectric sensors cooperatively indicated that airflow separation began at 14° when the lift force reached maximum and full stall occurred after 20° (Figure 5d).

Likewise, Xu et al. [81] developed a real-time stall sensing system based on triboelectric and piezoelectric effects, which could sense and warn the pre-stall and during stall of aircraft in intermediate Reynolds numbers (Figure 5e). In a wind tunnel test, the triboelectric signal (T-Signal) fluctuated obviously before stall while its amplitude and frequency dropped significantly when the aircraft was close to stall, causing the airflow separation effect to have a much greater impact on the sheet than the flutter effect (Figure 5f). Conversely, during the stall, as the reverse airflow curled, the piezoelectric signal (P-Signal) dominated the system (Figure 5g). Furthermore, the authors mounted this sensor on a small fixed-wing aircraft for field test (Figure 5h). The results demonstrated that before stall occurred, the triboelectric signals started to weaken and the piezoelectric signals were enhanced. The signal amplitude for DATSS-2 was higher than that for DATSS-1 during stall, because the actual stall depth varied across the wings, depending on the location and other intricate environmental factors (Figure 5i).

Aircraft monitoring

Another airflow application is to monitor typical indicators such as velocity, angle, and displacement when the aircraft is in continuous operation. To achieve this, extraordinary resolution in velocity and angle detection, conformal deformation capacity, fast response and high sensitivity should be balanced simultaneously. For example, Gong et al. [82] proposed a flexible calorimetric flow (FCF) sensor consisting of three pairs of vanadium oxide (VOx) thermistors and one spiral Cr/Au heater (Figure 6a). To decrease heat loss, the authors designed a suspended structure between VOx thermistors and the PI film, contributing to a high temperature coefficient of resistance (TCR) of −2% K−1 with low pink noise. Additionally, by optimizing the distance between thermistors and the heater, a velocity resolution of 0.11 mm/s and angular resolution of 0.1° were realized. Such superior performance ensured that it could accurately identify the flight velocity components along a certain axis in the body coordinate system when attached to a fly-wing micro-air-vehicle (MAV). The results from flow sensors corresponded well with the calculated flight velocity using an extended Kalman filter (EKF) algorithm (Figure 6b). Furthermore, in addition to estimating the relative velocity and angle during flight, it could also indicate the vibration of the wing due to its fast response time of approximately 20 ms. The signal that was analyzed using the short-time Fourier transform (STFT) revealed characteristic frequencies of 10 and 20 Hz, corresponding to wing vibrations (Figure 6c). These results aligned closely with data obtained from a commercial inertial measurement unit (IMU).

thumbnail Figure 6

Applications in airflow monitoring: aircraft monitoring and flow field mapping. (a) MAV equipped with two FCF sensors and an external IMU module, with an exploded view of the FCF sensor [82]. (b) Comparison of the flight velocity calculated by the EKF method with the relative velocity estimated by the FCF sensor when the MAV performs forward flight, backward flight, and hovering outdoors [82]. (c) Comparison of the spectra of signals from IMU and P1 of FCF sensor #2, illustrating the wing vibration with 10 and 20 Hz as the characteristic frequencies. IMU inertial measurement unit, EKF extended Kalman filter [82]. (d) Photo of a flexible 3 × 2 thermal flow sensor array attached onto a pipe with a 7.5 cm diameter, with a photo showing the flow sensor is comprised of eight temperature sensors surrounding a heater [16]. (e) Thermal mapping image under air flow corresponding to the flow direction monitoring [16]. (f) 2D cross-sectional FEM simulation of the air flow distribution affected by a circular obstruction [16]. (g) Schematic map of a device, with indication of the tube position (blue shading), and the temperatures at upstream (Tu) and downstream (Td) locations. i, j, and k represent coordinates for sensor identification (j and k for Tu and Td, respectively) [49]. (h) Thermographs from IR imaging (top) and epidermal sensing array (ESA)-generated temperature maps (bottom) in the absence (left) and presence (right) of flow (0.02 mL/min; flow from right to left) with actuation at 1.8 mW/mm2. All data were collected on a skin phantom [49]. (i) Photo of the sensor system attached onto the robotic arm [50]. (j) Cubic convolution interpolation of the eight temperature sensors as the robotic arm runs for one cycle [50].

Flow field mapping

Generally, a flow field is not as simple as one-dimensional (1D), while it can extend across a 2D plane or within a three-dimensional (3D) space, offering comprehensive information for simulation and analysis [83]. To visualize the distribution of flow field, Xu et al. [16] attached a 3 × 2 large-scale thermal flow sensor array onto a 7.5 cm diameter tube, with each flow sensor pixel consisting of one heater and eight temperature sensors (Figure 6d). Figure 6e shows the corresponding flow mapping image, indicating that turbulence occurred on the side of the pipe where the flow entered. With finite element method (FEM) simulation, the authors concluded that the 3D pipe structure acted as an obstruction (Figure 6f).

However, relying on just a few temperature sensors limits the resolution when mapping the original flow field. An ultra-resolution thermal flow sensor with 100 temperature sensors was achieved by Krishnan et al. [49], by placing clusters around a central thermal actuator (Figure 6g). To organize the complex structure, a method that connects unique combinations of rows (to supply a sensing voltage) and columns (to measure a resulting current) was developed to individually access each temperature sensor. Furthermore, PCA and meshed bicubic interpolation algorithms were applied to remap the flow field (Figure 6h).

Generally, data collected from sensors are analyzed and visualized offline, confining the flexibility and real-time applicability of sensors. For example, Xu et al. [50] equipped their thermal flow sensor with a high-performance acquisition board, which had a sampling rate of 197 Hz, 24-bit depth, and 16 channels (Figure 6i). This board wirelessly transmitted data to a 2D graphical user interface (GUI), displaying the flow field extracted from eight temperature sensors through a cubic spline interpolation algorithm, at a real-time refresh rate of 50 Hz. Figure 6j illustrates the periodic normalized images when the robotic arm operated in a loop along an elliptically rectangular path, indicating that this system could remotely and dynamically monitor motion.

Applications in tracking blood flow

Blood flow is another type of flow, containing numerous invaluable indicators such as blood pressure and blood flow rate, which are helpful in assessing health conditions and precisely locating hematoma and thrombosis [84]. Furthermore, continuous monitoring of blood flow through a wearable flow sensor is vital for individuals who lack access to professional clinical equipment in their daily lives.

Blood pressure measurement

In terms of blood pressure, Boutry et al. [85] reported a wireless and battery-free blood pressure sensor based on the fringe-field capacitor technology, primarily consisting of a capacitive sensor whose capacitance changed with vessel diameter due to the pulsatile nature of blood pressure (Figure 7a). With a poly(lactic acid) (PLLA) insulation layer, the bilayers of Mg wires functioned as an inductor coil which collaborated with the capacitive sensor to form an inductor-capacitor-resistor (LCR) circuit. The resonant frequency of LCR circuit shifted in response to changes in capacitance and was detected contactlessly through an external vector network analyzer (VNA) in a battery-free method. Notably, the authors selected biocompatible materials to ensure that this sensor could be used both in vitro and in vivo environments. Figure 7b shows the set of the in vivo experiment. The blood pressure sensor was implanted into the femoral artery below the skin of a rat and was coupled with an external reader coil to transmit data wirelessly. The results showed that the measured resonant frequency shifted, corresponding to the artery expansion with pulsation, and the pulse rate was calculated to be 3.47 beats per second (b.p.s), close to 3.52 b.p.s., obtained via a commercial Doppler ultrasound device (Figure 7c).

thumbnail Figure 7

Applications in blood flow monitoring. (a) Illustration of the sensor with an exposed view of the bilayer coil structure for wireless data transmission, the cuff-type pulse sensor wrapped around the artery, a close-up view of the pressure-sensitive region of the sensor with the two variable capacitors C1 and C2 before they are wrapped around the artery, and its equivalent electrical circuit [85]. (b) Image of an implant site where the sensor is implanted and the skin stitched; the reader antenna is placed in close proximity to the antenna of the implant for Δf0 recordings [85]. (c) Plot of measured Δf0 versus time; the pulse rate is calculated to be 3.47 b.p.s [85]. (d) Schematics of the stretchable ultrasonic device, with key components labelled [86]. (e) A typical pulse waveform measured from the carotid artery, directly correlated to the left atrial and ventricular events [86]. (f) A typical pulse waveform from the internal jugular vein, directly correlated to the right atrial and ventricular activities. Different phases and characteristic morphologies are marked [86]. (g) Schematic illustration of the device layout, with a photograph and an infrared image of a device on the skin over a vein, during application of power to the actuator [34]. (h) (I) Changes in blood flow as measured by a laser speckle contrast imager (LSCI, black) and our device (blue). (II and III) Fourier transform spectrogram determined from (II) LSCI data (FFT length = 128 s, five samples per second; the color bar is the amplitude of the LSCI spectrogram) and (III) presented device (FFT length = 128 s, two samples per second; the color bar is the amplitude of the thermal anisotropy spectrogram) [34]. (i) Illustration of the position of the vein relative to the device and flow field map. The red arrows show the relative magnitudes of the thermal distribution at peak flow [34]. (j) Full thermal distribution map during peak flow as measured by the presented device [34]. (k) and (l) Similar analyses as (i) and (j), except during occluded flow [34]. (m) Illustration of the wireless design and sensing scheme to simultaneously monitor pressure, heart rate (HR), and flow [87]. (n) Summary of wireless flow monitoring comparing the pressure gradients monitored by the wireless sensor and commercial sensors [87].

To overcome the problems in non-invasive approaches that only allow access to superficial peripheral vasculature, Wang et al. [86] described a conformal ultrasonic device that extended the detectable depth up to 4 cm (Figure 7d). Additionally, featuring similar mechanical properties to the skin, an ultrathin (240 μm) and stretchable (with strains up to 60%) profile, this sensor realized conformal intimate contact with skin continuously. Figure 7e shows a typical period of the carotid artery blood pressure, indicating a clear systolic peak and a dicrotic notch, which corresponded to the results from a commercial tonometer. Besides, this device measured a typical jugular venous pressure waveform, comprising three characteristic peaks (A: atrial contraction, C: tricuspid bulging and ventricular contraction, V: systolic filling of the atrium) and two descents (X: atrial relaxation, Y: early ventricular filling) that were crucial for predicting right-side heart failure (Figure 7f). Another approach to continuously monitoring blood pressure based on electrical bioimpedance was introduced by Kireev et al. [71]. The atomically thin, self-adhesive, and lightweight graphene tattoos were able to monitor arterial blood pressure non-invasively for over 300 min, with an accuracy of (0.2 ± 4.5) mmHg for diastolic pressures and (0.2 ± 5.8) mmHg for systolic pressures.

Blood flow rate measurement

Blood flow rate is another prominent indicator to reflect vessel conditions. For example, Webb et al. [34] introduced an ultrathin, soft, conformable blood flow sensor based on calorimetric principles (Figure 7g). Fifteen Cr/Au temperature sensors in total and one Cr/Au central actuator enabled quantitative monitoring of both the speed and direction of near-surface blood flow up to 2 mm in depth. Attached to the skin conformally, this sensor could measure changes in intensities and directions of local venous blood flow by occlusion and reperfusion of the forearm. As shown in Figure 7h, the changes in blood flow were measured by the presented sensor, with the frequency-time spectrograms exhibiting similar levels of agreement. Additionally, the snapshots in time during peak flow (Figure 7i, j) and occluded flow (Figure 7k, l) indicated the strength and disappearance of the flow signal, corresponding to unoccluded and occluded flow, respectively.

In contrast to non-invasive methods, Zavanelli et al. [35] reported an implantable vascular electronic sensor, consisting of an inductive stent and printed soft capacitive sensors. Notably, this multimaterial stent applied conductive loops and non-conductive connectors to create a conductive pathway and serve as an inductive antenna (Figure 7m). Benefiting from the reliable mechanical properties offered by the stent, fast-response and highly durable capacitive sensors were successfully printed, enabling this system to monitor flow rate through an inductor-capacitor (LC) circuit without batteries and extra circuits. To be specific, the capacitive sensors detected a pressure gradient corresponding to the blood flow rate across the length of stent, as shown in Figure 7n. The difference in linearity between data from this sensor and the commercial sensor was attributed to wireless resolution and minor pressure changes within the stent.

Applications in monitoring breath

Continuously detecting the frequency and intensity of breath is crucial for alerting about abnormal respiratory conditions such as apnea, hypopnea, polypnea, and the asymmetry between the right and left nostrils [88]. To achieve this, Jiang et al. [89] demonstrated a wearable breath sensing system, composed of a hot-film sensor in the center and two calorimetric sensors on the sides (Figure 8a). Notably, the authors limited the power to 60 mW, allowing this system to be attached to the upper lip. Figure 8b depicts the breath velocity measured by this system, clearly indicating the normal exhaling and inhaling processes. In terms of abnormal breath conditions, each featured a unique frequency and magnitude, which could be calculated through continuous wavelet transform (Figure 8c). Specifically, apnea with interruptions in both frequency and magnitude, hypopnea was characterized by low magnitude, and polypnea was identified by high-frequency signals.

thumbnail Figure 8

Applications in breath monitoring. (a) The presented device is composed of two PI films to encapsulate the gold patterns and a medical tape is used to attach the device to human skin. Sensor-2 and Sensor-3 locate at two sides of the Heater/Sensor-1 (Hot-Film type), which is the only device to be heated up by the external power [89]. (b) The breath velocity vs. time, measured by using Heater/Sensor-1 during the continuous exhaling and inhaling process [89]. (c) The continuous wavelet transforming results, to show the frequency and magnitude parameters of apnea, hypopnea, and polypnea [89]. (d) Schematic of Morse code [59]. (e) Schematic diagram of a quadriplegic aphasia to communicate with the help of the presented sensor [59].

To further utilize the on-off keying property of breath signals, Huang et al. [59] used their flow sensor for information encryption according to Morse code, as shown in Figure 8d. This was helpful for those suffering from quadriplegic aphasia and enabled them to regain the ability to communicate with others (Figure 8e).

Applications in monitoring water flow

With the advancement of robotics and autonomous vehicles, there is growing interest in exploring underwater environments. Notably, Li et al. [90] developed an untethered soft robot for deep-sea exploration, targeting challenging areas like the Mariana Trench. In such settings, the physical properties of water flow significantly affect sensor design and functionality [91]. For instance, water flow’s higher thermal conductivity, 0.6 W/(m K), compared to airflow’s 0.024 W/(m K), enables more efficient heat transfer, necessitating highly sensitive thermal flow sensors. Additionally, since water flow is electrically conductive, an insulation layer is essential to protect sensors from short circuits [92].

Underwater vehicles monitoring

By mimicking fish lateralis neuromasts (FLN), Shu et al. [93] introduced an artificial FLN (AFLN) flow sensor to detect precise water flow changes (Figure 9a). This sensor comprised a 110 μm-thick 3D poly(vinylidene fluoride) (PVDF) film to generate a potential difference when subjected to mechanical disturbances, and a 20 μm-thick waterproof package made of parylene (Figure 9b). After integrating this sensor with a microcontroller unit (MCU) and a motor control board, the autonomous underwater vehicle (AUV) used FT to discriminate between ocean-wave-induced noise and various stimuli, including water flow, acoustic signals and electric fields. Figure 9c shows the complete process of the navigation obstacle avoidance.

thumbnail Figure 9

Applications in water flow monitoring. (a) Schematics of biological fish sensing weak water pressure changes, acoustic waves, and underwater electric fields with the help of the FLN system, and an underwater robot recognizing water waves, water sounds, and underwater electric fields with the help of different responses of the AFLN system [93]. (b) The AFLN system structure and sensing method. The inset shows its potential application in underwater robotics. Scale bar: 2 mm [93]. (c) Illustration of the AUV’s obstacle avoidance application. The inset showcases the real-time signal acquired from the system [93]. (d) Schematic of a target perceived through the effect of the vortex on the whiskers [94]. (e) Structural diagram of UBWS [94]. (f) Three states during the movement of the robotic fish, with corresponding voltage signal of the UBWS [94]. (g) Schematic of an individual microfabricated, out-of-plane HWA sensor used to build artificial neuromasts. The hot wire is elevated above the substrate surface by a prescribed distance [99]. (h) Analytical model of pressure contours (blue lines) and a linear array of lateral line canal neuromasts (in orange) [99]. (i) Time-elapsed spatial profiles of displacement amplitude with step-by-step translation of the dipole source along the artificial lateral line following path 1 [99]. (j) Displacement profiles under step-by-step translation following path 2 [99]. (k) Schematic showing experimental set-up [99]. (l) The pattern of RMS water velocity in the wake of a cylinder [99]. (m) The pattern of peak water velocity at vortex shedding frequency in the wake of a cylinder. Both RMS and peak water velocities were normalized by free-stream inflow velocity [99].

Likewise, Wang et al. [94] proposed an underwater bionic whisker sensor (UBWS) based on the triboelectric nanogenerator (TENG), by mimicking seal whiskers (Figure 9d). This sensor consisted of an inner TENG perceiving unit to detect the vortex and a packaging layer made of aluminum-coated polyethylene glycol terephthalate/cast polypropylene (A-PET/CPP). Notably, the authors incorporated the Faraday cage effect to achieve electrostatic shielding, which confined the sensor’s performance loss to 10% underwater compared to air (Figure 9e). The whisker design allowed the sensor to sense a pressure difference when a vortex passed nearby. When connected to an Arduino control module, this system successfully captured and tracked the vortex generated by an underwater target. As the distance decreased, the voltage signal from the sensor reached a preset threshold, eventually triggering the system to cease tracking (Figure 9f).

Hydrodynamic characterization

In addition to monitoring underwater vehicles, water flow characterizes various features such as turbulence [95], interfacial phenomena [96], and Kármán vortex street [97]. Leveraging the fluorescent tracer technique, which is particularly suited to water flow, some researchers designed underwater flow sensors to conduct experiments in complex hydrodynamic characterization [98].

Based on the hot-wire anemometry (HWA) principle, Yang et al. [99] demonstrated a system by mimicking the fish lateral line. This system consisted of a monolithically integrated array of individual sensors, with each size of approximately 50 μm (Figure 9g). The nickel filament hot-wire was sandwiched by two layers of PI for passivation and structural support, and exhibited a temperature coefficient of resistance of 4100 ppm/K. In the application section, a vibrating sphere was used to function as a dipole source (Figure 9h), and the system with 16 individual sensors showed that the spatial distribution of the pressure gradient amplitude resembled a “Mexican hat” (Figure 9i and j). Moreover, based on maximum-likelihood analysis, the location of the dipole could be predicted. Additionally, this system could also identify the Kármán vortex street, as shown in Figure 9k. The distributions of root mean square (RMS) velocity (Figure 9l) and peak velocity (Figure 9m) could both be captured, with two clearly defined peaks occurring along the entire field of view.

In response to the complexities of the marine environment, Wang et al. [100] proposed an optical flow sensor. As flow interacted with the sensor, it induced a mechanical deformation in the embedded S-tapered optical structure, leading to a variation in the optical spectrum of the fiber. The core fiber was encapsulated by a 3D-printed structure that served as an artificial supporting cell, enhancing the sensor’s resistance to corrosion. Overall, the characteristics of flexible flow sensors, including their materials, principles, applications and performance, are summarized in Table 2.

Table 2

Summary of characteristics of flexible flow sensors a

CONCLUSIONS

In conclusion, flexible flow sensors offer various advantages, particularly notable for their compact structure, flexible nature, rapid response, and exceptional sensitivity. To further enhance the performance of these sensors, features inspired by natural creatures like spiders and fish are investigated to develop biomimetic flow sensors, such as fabric-based and artificial lateral line flow sensors. This comprehensive review categorizes the principal types of flow sensors into thermal, piezoresistive, piezoelectric, and acoustic flow sensors, considering their working mechanisms, designs, and characterization. Among them, thermal flow sensors are the most extensively studied and applied due to their minimal material requirements and flexible design approaches. However, the generation and transmission of heat in these sensors require a considerable amount of energy. Piezoresistive and piezoelectric sensors offer the most feasible modeling and simulation but may introduce disturbances into the flow field due to their pillar-like structures, which detect flow through direct mechanical interaction. Acoustic flow sensors, while more complex to fabricate and sensitive to the environmental temperature and humidity, have the advantage of remote sensing capabilities, making them ideal for vessel monitoring.

Four typical applications are then introduced, including the monitoring of airflow, blood flow, breath, and water flow. Sensors used for airflow and water flow typically require the larger sizes or arrays to cover vehicles or aircraft with a skin-like layer. In contrast, sensors for health monitoring are designed to be minimally invasive and compact, as they primarily measure signals from the body and must be comfortable to wear for extended periods. Moreover, biocompatibility is a critical factor that should be taken into account in such a sophisticated physiological environment. Wearable and implantable flow sensors may need to accurately measure physiological signals on a microscopic scale, where a high sensitivity and precision design strategy is required.

Despite the promising advancements, several hurdles still need to be overcome to further improve the performance of flexible flow sensors. Issues such as heat loss, humidity levels, and ambient temperature significantly affect sensor sensitivity and precision. Moreover, the development of wireless transmission systems with higher sampling frequencies and the formulation of stable, fully biocompatible materials are imperative for advancing more sophisticated applications. Currently, flexible flow sensors have achieved the remapping of flow fields. However, to accurately monitor flow fields over more extensive areas, proposing a multi-array with ultra-high-resolution flow sensor units remains essential. Additionally, while the obstacle avoidance of underwater vehicles has been realized with water flow sensors, future enhancements could include the integration of more complex control models, such as the model predictive controller, to facilitate intelligent operations of underwater vehicles in real marine environments. Furthermore, there have been accomplishments where flow sensors are integrated with other types of sensors into a skin-like system design, yet the full potential of comprehensive systemic bionics with balanced precision and recall algorithms requires further development (Figure 10).

thumbnail Figure 10

Typical challenges and future trends in flexible flow sensors.

It can be predicted that in the near future, flexible flow sensors will be one of the vital flexible devices. The applications include marine environment monitoring, vessel condition assessment, and remote robot manipulation. Notably, in health monitoring, flexible flow sensors are able to determine the absolute velocity of blood flow with the greater detection depth, compared with pressure, strain, and other sensors. Similarly, in marine sensing, these sensors have the potential to enable researchers to directly measure the flow field surrounding the underwater vehicles.

Funding

This work was supported by the National Natural Science Foundation of China (52105593, 52475610), and the “Pioneer” and “Leading Goose” R&D Program of Zhejiang (2023C03007).

Author contributions

Q.L. wrote the manuscript. Y.L. assisted in commenting the manuscript. K.X. conceived the idea, supervised the project and revised the manuscript.

Conflict of interest

The authors declare no conflict of interest.

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All Tables

Table 1

Comparison among different mechanisms

In the text
Table 2

Summary of characteristics of flexible flow sensors a

In the text

All Figures

thumbnail Figure 1

Overview of bioinspired flexible flow sensors comprising major working mechanisms including thermal, piezoresistive, piezoelectric and acoustic flow sensors. Four main applications including airflow, blood flow, breath, and water flow applications [50,59,71,81,82,85,92,98].
In the text
thumbnail Figure 2

Thermal flow sensors. (a) Conceptual illustrations of thermal anemometer flow sensors: hot-wire and hot-film. (b) Fully flexible thermal anemometer sensor array on PI film substrate, with enlarged images showing sensor array and copper leads [26]. (c) Fully flexible thermal anemometer sensor’s output in wave flow [26]. (d) Conceptual illustration of thermal calorimeter flow sensors. (e) Top view of flexible thermal calorimeter flow sensors integrated on a printed circuit board (PCB) (left) and schematic of the membrane (right) [47]. (f) Exploded view illustration of a platform that incorporates a central thermal actuator surrounded by 100 precision temperature sensors, placed over the skin with an underlying shunt catheter, with enlarged images showing optical micrograph of the device (surrounded by black dashed line), serpentine interconnects (blue dashed line) and individual resistive temperature sensors (red dashed line) [49]. (g) IR thermographs with color and contrast enhancement highlight the spatial isotropy of the distribution of temperature in the absence of flow (left) and the anisotropy in the presence of flow (right). Flow is to the right (arrow) [49]. (h) Conceptual illustrations of thermal anemometer + thermal calorimeter flow sensors. (i) Photo images of the LIG-based flexible thermal anemometer + thermal calorimeter flow sensor on curved surfaces [50]. (j) Resistance variation measured from the two temperature sensors as a function of flow rate [50]. (k) Resistance variation measured from the heater as a function of flow rate [50]. (l) Principal component analysis of collected data from the eight temperature sensors under the four flow directions [50]. (m) Cubic convolution interpolation of the eight temperature sensors after normalization when the flow is incident at 45° [50].
In the text
thumbnail Figure 3

Piezoresistive and piezoelectric flow sensors. (a) Conceptual illustration of piezoresistive flow sensors [55]. (b) Schematic diagram of the flexible piezoresistive flow sensor using VGNs [57]. (c) Sensor output as a function of flow velocity (calibration plot) [57]. (d) Working mechanism of three LIG airflow sensors with equivalent circuit diagram and schematic illustration of PLIG, VLIGF, and SLIGF [59]. (e) Digital photos of cotton, caterpillar, and Lepidoptera insect-butterfly, with SEM images of PLIG, VLIGF, and SLIGF from top view. The scale bars are 250, 250 and 500 μm, respectively [59]. (f) Relative current variation within the airflow range of 0.0023–2.35 m/s [59]. (g) Conceptual illustration of piezoelectric flow sensors [60]. (h) Optical image of the hydrodynamic artificial velocity sensor [60]. Distribution of stress in the x direction when pressure is at 0° (i) and at 90° (j) [60]. (k) Results of the directivity detection [60]. (l) Relationship between charge output and velocity [60].
In the text
thumbnail Figure 4

Acoustic flow sensors. (a) Conceptual illustration of Doppler flow sensors. (b) Schematic diagram and optical image (inset) of the flexible acoustic wave device [61]. (c) Frequency responses of the acoustic wave device when the flow rate increases from 0 to 0.8 LPM and then decreases from 0.8 to 0 LPM in step of 0.2 LPM [61]. (d) Schematics (left) and exploded view (right) of the device structure. ACF, anisotropic conductive film [62]. (e) Schematic of the DBUD method [62]. (f) Measured PFV versus true PFV curves. Error bars represent ±SD (N = 5) [62]. (g) Typical carotid blood flow spectra during a cardiac cycle (left) and several cycles (right). Feature points are marked in the left image. Inset: an image showing the device mounted on the neck [62]. (h) Conceptual illustration of time-of-flight flow sensors. (i) Ultrasonic air-coupling time-of-flight configuration [66]. (j) Experimental DC steps linearity test [66].
In the text
thumbnail Figure 5

Applications in airflow monitoring: stall detection. (a) Conceptual illustration of stall, with red region representing positive pressure while the blue region representing negative pressure [80]. (b) Schematic of the airfoil integrated with the iFlexSense skin (P: piezoelectric sensor; H: hot-film sensor; C: capacitive pressure sensor; T & S: temperature & strain sensors) [80]. (c) The electronic skin mounted on a standard NACA 0012 airfoil under varying AOA from 25° to +25° (an incremental step of 1°) [80]. (d) Time-averaged pressure of the suction peak under different free stream velocities from 4 m/s up to 11.16 m/s [80]. (e) Principle and structure diagram of digital-visualization array for turbulence stall sensing (DATSS) [81]. (f) DATSS system stall sensing T-signal after STD processing [81]. (g) DATSS system stall sensing raw P-signal [81]. (h) The photograph of fixed-wing remote control Cessna 182 aircraft with a wing length of 1420 mm for flight test, equipped with two DATSS units [81]. (i) The wireless flight signal of the arrayed DATSS system [81].
In the text
thumbnail Figure 6

Applications in airflow monitoring: aircraft monitoring and flow field mapping. (a) MAV equipped with two FCF sensors and an external IMU module, with an exploded view of the FCF sensor [82]. (b) Comparison of the flight velocity calculated by the EKF method with the relative velocity estimated by the FCF sensor when the MAV performs forward flight, backward flight, and hovering outdoors [82]. (c) Comparison of the spectra of signals from IMU and P1 of FCF sensor #2, illustrating the wing vibration with 10 and 20 Hz as the characteristic frequencies. IMU inertial measurement unit, EKF extended Kalman filter [82]. (d) Photo of a flexible 3 × 2 thermal flow sensor array attached onto a pipe with a 7.5 cm diameter, with a photo showing the flow sensor is comprised of eight temperature sensors surrounding a heater [16]. (e) Thermal mapping image under air flow corresponding to the flow direction monitoring [16]. (f) 2D cross-sectional FEM simulation of the air flow distribution affected by a circular obstruction [16]. (g) Schematic map of a device, with indication of the tube position (blue shading), and the temperatures at upstream (Tu) and downstream (Td) locations. i, j, and k represent coordinates for sensor identification (j and k for Tu and Td, respectively) [49]. (h) Thermographs from IR imaging (top) and epidermal sensing array (ESA)-generated temperature maps (bottom) in the absence (left) and presence (right) of flow (0.02 mL/min; flow from right to left) with actuation at 1.8 mW/mm2. All data were collected on a skin phantom [49]. (i) Photo of the sensor system attached onto the robotic arm [50]. (j) Cubic convolution interpolation of the eight temperature sensors as the robotic arm runs for one cycle [50].
In the text
thumbnail Figure 7

Applications in blood flow monitoring. (a) Illustration of the sensor with an exposed view of the bilayer coil structure for wireless data transmission, the cuff-type pulse sensor wrapped around the artery, a close-up view of the pressure-sensitive region of the sensor with the two variable capacitors C1 and C2 before they are wrapped around the artery, and its equivalent electrical circuit [85]. (b) Image of an implant site where the sensor is implanted and the skin stitched; the reader antenna is placed in close proximity to the antenna of the implant for Δf0 recordings [85]. (c) Plot of measured Δf0 versus time; the pulse rate is calculated to be 3.47 b.p.s [85]. (d) Schematics of the stretchable ultrasonic device, with key components labelled [86]. (e) A typical pulse waveform measured from the carotid artery, directly correlated to the left atrial and ventricular events [86]. (f) A typical pulse waveform from the internal jugular vein, directly correlated to the right atrial and ventricular activities. Different phases and characteristic morphologies are marked [86]. (g) Schematic illustration of the device layout, with a photograph and an infrared image of a device on the skin over a vein, during application of power to the actuator [34]. (h) (I) Changes in blood flow as measured by a laser speckle contrast imager (LSCI, black) and our device (blue). (II and III) Fourier transform spectrogram determined from (II) LSCI data (FFT length = 128 s, five samples per second; the color bar is the amplitude of the LSCI spectrogram) and (III) presented device (FFT length = 128 s, two samples per second; the color bar is the amplitude of the thermal anisotropy spectrogram) [34]. (i) Illustration of the position of the vein relative to the device and flow field map. The red arrows show the relative magnitudes of the thermal distribution at peak flow [34]. (j) Full thermal distribution map during peak flow as measured by the presented device [34]. (k) and (l) Similar analyses as (i) and (j), except during occluded flow [34]. (m) Illustration of the wireless design and sensing scheme to simultaneously monitor pressure, heart rate (HR), and flow [87]. (n) Summary of wireless flow monitoring comparing the pressure gradients monitored by the wireless sensor and commercial sensors [87].
In the text
thumbnail Figure 8

Applications in breath monitoring. (a) The presented device is composed of two PI films to encapsulate the gold patterns and a medical tape is used to attach the device to human skin. Sensor-2 and Sensor-3 locate at two sides of the Heater/Sensor-1 (Hot-Film type), which is the only device to be heated up by the external power [89]. (b) The breath velocity vs. time, measured by using Heater/Sensor-1 during the continuous exhaling and inhaling process [89]. (c) The continuous wavelet transforming results, to show the frequency and magnitude parameters of apnea, hypopnea, and polypnea [89]. (d) Schematic of Morse code [59]. (e) Schematic diagram of a quadriplegic aphasia to communicate with the help of the presented sensor [59].
In the text
thumbnail Figure 9

Applications in water flow monitoring. (a) Schematics of biological fish sensing weak water pressure changes, acoustic waves, and underwater electric fields with the help of the FLN system, and an underwater robot recognizing water waves, water sounds, and underwater electric fields with the help of different responses of the AFLN system [93]. (b) The AFLN system structure and sensing method. The inset shows its potential application in underwater robotics. Scale bar: 2 mm [93]. (c) Illustration of the AUV’s obstacle avoidance application. The inset showcases the real-time signal acquired from the system [93]. (d) Schematic of a target perceived through the effect of the vortex on the whiskers [94]. (e) Structural diagram of UBWS [94]. (f) Three states during the movement of the robotic fish, with corresponding voltage signal of the UBWS [94]. (g) Schematic of an individual microfabricated, out-of-plane HWA sensor used to build artificial neuromasts. The hot wire is elevated above the substrate surface by a prescribed distance [99]. (h) Analytical model of pressure contours (blue lines) and a linear array of lateral line canal neuromasts (in orange) [99]. (i) Time-elapsed spatial profiles of displacement amplitude with step-by-step translation of the dipole source along the artificial lateral line following path 1 [99]. (j) Displacement profiles under step-by-step translation following path 2 [99]. (k) Schematic showing experimental set-up [99]. (l) The pattern of RMS water velocity in the wake of a cylinder [99]. (m) The pattern of peak water velocity at vortex shedding frequency in the wake of a cylinder. Both RMS and peak water velocities were normalized by free-stream inflow velocity [99].
In the text
thumbnail Figure 10

Typical challenges and future trends in flexible flow sensors.
In the text

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