Concurrent Actuation and Sensing in Fluid by Cilia-Like Transducers

Motile cilia are miniature, hair‐like organelles whose beating moves fluid in various organisms and the human body. Motile cilia are also able to sense many mechanical or fluidic cues. Inspired by the motile cilia in nature, a type of artificial cilia that can both actuate and sense is investigated. These artificial cilia can operate their sensing and actuation individually to sense the flow speed and collaboratively transport objects. More importantly, they can also sense the viscosity of the fluid and the distance from the wall by beating and feeling their own motion. In the latter function, two different sensing modes (modes 1 and 2) are proposed for low and high Reynolds numbers. They are investigated through both computational fluid dynamics and experiments. It is found that mode 1 can sense a wall distance up to 3 times the body length of the cilium, while mode 2 can sense up to 2 times. Such sensing of distance can be further converted into the ability to compute the morphology of the boundary inside the fluid. This work can be useful for small‐scale soft robots that work inside fluid and other flow control applications.


Introduction
Cilia are tiny hair-shaped organelles that exist widely in various organisms [1][2][3] and the human body. [4][5][6] Nonmotile cilia, also called primary cilia or sensory cilia, have inspired various artificial sensing devices. [7][8][9][10][11] Meanwhile, motile cilia, which can actively deform, have recently inspired many artificial actuator arrays. These actuator arrays could be driven by magnetic field, [12][13][14] light, [15] pH change, [16] acoustic wave, [17,18] mechanical excitation, [19] and pneumatic actuation. [20] They have demonstrated their ability to drive miniature robots [21] and manipulate fluid and micro-objects. [12,22,23] These works have been well summarized and discussed in the recent critical review. [24] While cilia-like artificial devices on either sensing or actuation have gained fast developments, it is found that motile biological cilia, in fact, also carry out critical sensing functions. This combination can enable functions that cannot be achieved by mere sensing or actuation. For example, Ref. [25] showed that the motile cilia of the airway epithelial cells can adjust the mechanics according to the viscosity around them to maintain a ciliary beat frequency, which is essential for maintaining the transport of mucus. Ref. [26] demonstrated that the quiescent abfrontal cilia on the gills of the mollusk mytilus edulis can react to direct bending forces by generating a cycle of recovery and active stroke. The motile cilia on a paramecium can transiently reverse the direction of beating when they strike on an object. [27] This sequence is repeated until the organism is able to avoid the obstacle. Note that each of the examples listed above actually involves two steps, a sensing step, in which the cilia gather information from the environment, and an execution step, in which they respond to sensory input. In the present study, we refer to the first step only as the sensory function, that is, the ability to detect the influence of the surrounding environment.
Despite the numerous reports on the sensory function of motile cilia, research on the concurrent actuating and sensing of artificial cilia is missing. Given the potential here, we conducted research on the functions of the artificial cilia that can both actuate and sense in this report. These artificial cilia can operate their sensing and actuation individually to sense the flow speed and collaboratively transport objects. More importantly, they can also sense the viscosity of the fluid and the distance from the wall by beating and feeling their own motion. For the distance sensing function, two different sensing modes (modes 1 and 2) were proposed for low and high Reynolds numbers (Re). They were investigated through both computational fluid dynamics (CFD) simulations and experiments. It was found that mode 1 can sense a wall distance up to 3 times the body length of the cilia, while mode 2 can sense up to 2 times. Such sensing of distance can be further converted into an ability to compute the morphology of the boundary inside fluids. Such research could be useful for small-scale soft robots that work inside fluids and other fluid control applications.

Numerical Methods
For the numerical simulation of the interaction between the cilia-like transducer and fluids, we used the hybrid finite difference/ finite-element immersed boundary (IB) method, [28] which was implemented in the open source software IBAMR, a widely tested Cþþ framework for the IB method. The immersed boundary formulation of the problem describes the momentum, velocity of the couple fluid-structure system in Eulerian form, and the deformation and elastic response of the immersed structure in Lagrangian form. In the current work, we mainly used 2D simulation as it served well enough to present the physics behind the sensing mechanism of our transducers. Let x ¼ ðx 1 , x 2 Þ ∈ Ω ⊂ ℝ 2 denote Cartesian physical coordinates, with Ω denoting the physical region that is occupied by the coupled fluid-structure system; let X ¼ ðX 1 , X 2 Þ ∈ W ⊂ ℝ 2 denote the Lagrangian material coordinates that were attached to the structure, with W denoting the Lagrangian domain; and let χðX, tÞ ∈ Ω denote the physical position of the material point X at time t. The strong form of the equation of motions is where ρ is the mass density, uðx, tÞ is the Eulerian velocity field, μ is the dynamic viscosity, f e ðx, tÞ is the Eulerian elastic force density, ℙ e ðX, tÞ is the first Piola-Kirchhoff elastic stress tensor, δðxÞ is the 2D delta function, and NðXÞ is the normal vector along the fluid-solid interface. In the computations of the current study, the physical domain is Ω ¼ ½À6L, 6L Â ½0, H þ L, where L is the length of the transducer and H is the distance between the transducer tip and the top wall. No-slip boundary condition was applied on the upper and bottom boundaries, and periodic boundary condition was applied on the left and right boundaries. We used a staggered-grid finite difference scheme to discretize the incompressible Navier-Stokes equations in space. The spatial resolution was Δx ¼ L=64, and the total number of the Cartesian grid was Oð10 5 Þ. The rectangular shape structure was discretized into a mesh of bilinear quadrilateral elements with a node spacing of ΔX ¼ L=64. The time stepping was performed using an implicit scheme proposed by Ref. [29]. The time step size was adjusted so that Courant-Friedrichs-Lewy (CFL) number was %0.1.

Experimental Methods
For experimental verification, the cilia-like transducer we used was composed of both an actuator and a sensor (Figure 1a). The actuator was made of a ferromagnetic-elastic sheet, which could be driven with magnetic fields. It was made of composite materials of silicone rubber, Ecoflex 00-30 (Smooth-On Inc.), and NdFeB hard magnetic microparticles. All the fabrication steps were similar to that of our previous work. [12] Its length, width, and thickness were made to be 15 mm, 5 mm, and 400 μm, respectively. The crack-based sensor used in Ref. [30] was composed of three layers. A 50 nm Cr layer and a 10 nm Au layer were sequentially sputtered on a 13 μm polyester film (ES30-FM-000230, Goodfellow). The sensors were then stretched 2% (5940 series, Instron GmbH). The sensors were then laser machined into designed geometry (Figure 1a). The crack-based sensor was then glued to the magnetic-sheet with silicone rubber. The sensor part was then coated with a thin layer of Ecoflex 00-30 for protection. This sensor was connected in series with a resistor and powered by a 2.0V supply. The voltage of the sensor changed as the resistance of the sensor changed, which was recorded with an analog acquisition module (NI-9239, National Instruments Corp.).

Flow Pumping, Velocity Sensing, Viscosity Sensing
As a start, we demonstrate several basic functions of the transducer. First, like other cilia-like actuators, [12,23] the current transducer is capable of manipulating flow fields to transport objects. Figure 1b illustrates the transport of a plastic bead through the collective beating of a four-transducer array (see Movie S1, Supporting Information). We further demonstrate in movie S2, Supporting Information that the transport function in glycerin can be achieved by programming the transducers' magnetization profile (see supplementary note 1, Supporting Information). Additionally, the transducer can sense flow velocity. In Figure 1c(i), a transducer was placed at the outlet of a syringe. The jet flow impinged on the transducer and imposed friction drag on it, which bent the transducer away from the flow direction. Figure 1c(ii) shows that the transducer voltage increases accordingly as the jet velocity increases from 0.06 to 0.23m s À1 . At last, Figure 1d(i) shows how the transducer can sense fluid viscosity, which cannot be done only by a sensor.
To enable sensing, the transducer was oscillated back and forth by a rotating magnetic field. During this process, the deformation of the transducer depends on the friction drag related to the viscosity of the fluid. The higher the viscosity, the more friction drag the transducer experiences, and consequently the deformation is smaller. This is illustrated by the time sequence of the voltage of the transducer in Figure 1d(ii). The magnitude of the deformation is captured by the amplitude of the voltage signal. Figure 1d(iii) shows that the standard deviation of the voltage of the transducer σ U decreases monotonously as the viscosity of the fluid increases. With this relation, it is possible to detect viscosity by measuring σ U . In Movie S3, Supporting Information, we demonstrate a feedback control system of the transducer beating frequency based on the viscosity-sensing function. The transducer automatically switches beating frequency when the viscosity of the surrounding fluid is changed (see supplementary note 2, Supporting Information for a detailed description).

Wall Distance Sensing
The remainder of the manuscript is devoted to the transducer's distance sensing function. Distance sensing inside fluids could be very useful for robotic locomotion, localization, and object manipulation. Conventionally, this is achieved by sonar, [31] laser, [32] or IR sensors, [33] which could be very bulky for smallscale robot applications. In nature, cilia could sense the presence of an object when they beat in proximity to it. [27] This inspires us to use the transducer with both actuation and sensing for distance sensing.

Mode 1 for Low Re
To detect the distance from the wall, it is necessary to understand the influence of the wall on the flow. The no-slip boundary condition of the wall asserts that the flow velocity is zero at a fixed wall boundary. This suggests that the fluid closer to the wall is more difficult to accelerate. When a moving object enters the near-wall region, the difference in velocity between the object and the near-wall fluid causes additional friction drag. Thus, the kinematics of the object will be affected. Based on this phenomenon, we design the first wall distance sensing configuration, namely, mode 1, which is shown in Figure 2. In this mode, the transducer beats periodically to establish a relative speed between the wall and itself. We conducted both numerical simulations and experiments to quantify the influence of the wall on the transducer.

CFD Investigation and Modeling
In the simulation, the transducer is modeled as a beam discretized by finite elements. The transducer is attached to the bottom wall and is upright in its initial state. The driving force f and torque τ in the beam mimic those of a magnetized beam under the effect of a rotating magnetic field. This is consistent with the experiment to be introduced later. The dimension of the beam is also consistent with that of the transducer in SI units, so that they can be directly compared. The modeled force and torque are defined as f ðs, tÞ ¼ ðA cross ½R z ðθðs, tÞÞM ⋅ ∇ÞBðχ ðsÞ, 0Þ τðs, tÞ ¼ A cross ½R z ðθðs, tÞÞM Â Bðχ ðsÞ, 0Þ where , e x is the unit vector in x direction, B is the magnetic field, A cross is the cross area of the beam, R z is the rotation matrix in x-y plane, and θðs, tÞ is the rotational angle at time t.
In current study, B is modeled as the magnetic field adjacent to a dipole m, which is where μ 0 ¼ 4π Â 10 À7 T ⋅ m ⋅ A À1 , r is the location vector at the coordinate of the dipole m, and⋅ indicates unit vectors. The dipole vector m is modeled as where θ m ðtÞ ¼ π=3sinð2πf tÞ controls the rotation angle of dipole evolving periodically in the range ðÀπ=3, π=3Þ with a frequency f, and m mag is the magnitude of the dipole. For the mode 1 configuration, we choose a magnitude of m mag ¼ 250 A ⋅ m 2 . The imaginary dipole is placed 10 mm below the bottom of the transducer. In this way, the B field at the bottom of the transducer is around 25 mT, which is the same as that of the magnet used in the experiment. Furthermore, we set the frequency f ¼ 1 Hz for all cases.
In immersed boundary methods, the equation of angular momentum is not involved. Therefore, the magnetic torque τ along the center line of the transducer is first converted to equivalent force couples, whose distance is the thickness of the transducer and the force directions are tangent to the local surface. The force couples, together with the magnetic forces f on the Lagrangian nodes, are interpolated from the Lagrangian mesh to the Eulerian grid with a force-prolongation operator [28] and added to the Eulerian elastic force density f e in Equation (1).
We studied the performance of mode 1 in four fluids of different viscosities, that is, water and 70%, 90%, and 99.7% glycerin. The basic parameters of the studied cases are listed in Table 1. The Reynolds number is defined as Re ¼ u max L=ν, where u max is the maximum velocity in the flow field, L is the length of the transducer, and ν is the kinematic viscosity. The Strouhal number is defined as St ¼ f L=u max , where f is the oscillating frequency of the transducer. The Sperm number describes the ratio between the viscous forces and the elasticity of the cilium, [34,35] which is defined as Sp ¼ Lðωξ=KÞ 1=4 . ω is the angular frequency, which is about 4π=3 rad s À1 for current cases. Variable ξ ¼ 4πμ=lnðL=aÞ, a being the thickness of the transducer. K is the bending stiffness of the transducer.
The quiver plots in Figure 2 illustrate the increase of the velocity gradient at the tip of the beam as the top wall approaches. Consequently, the bending amplitude (illustrated by the displacement between the gray and black lines) decreases due to the  To quantify the bending of the beam, we introduce a variable CðtÞ to describe the overall curvature change of the transducer, that is where s is the Lagrangian position along the beam centerline; χ 1 is the horizontal position in Cartesian coordination. Function sgn is the sign function. The absolute value of this nondimensional parameter represents the overall bending curvature of the beam, while the sign of it indicates the bending direction. Figure 3a shows the time sequence CðtÞ of the transducer in 99.7% glycerol at different wall distances. As observed earlier in Figure 2, the beam bends less as the wall distance decreases. This trend is quantitatively described in Figure 3b (the scatter plot), where the magnitude of CðtÞ is evaluated by the standard deviation σ C . It is shown that σ C and the wall distance H have a strong monotonous relation in high-viscosity fluids, that is, 90% and 99% glycerin, where the Reynolds number Re is in the range of Oð0.1Þ À Oð1Þ. However, the influence of the wall becomes marginal as Re increases above Oð10Þ in 70% glycerin and Oð10 2 Þ in water.
The profiles of σ C at different Re in Figure 3b exhibit similar shapes, suggesting that the beam bending shares a similar physical mechanism despite the different viscosities. To look into it more in detail, we consider a structure element at the tip of the transducer. When the wall is close enough, the drag force experienced by the structure element consists of two main sources. The first part is from the hydrodynamics drag force due to the flow attached to the beam, which can be estimated based on the theory of slender filaments [36] and the second source of drag is the friction due to the shearing layer between the tip and the wall. The total drag can then be expressed as where ξ is the coefficient determined by the shape of the element, μ is the dynamic viscosity of the fluid, u is the streamwise velocity of the element, l is the size of the element, and A cross is again the cross area of the beam. We simply assume that the structure element is moving at a constant speed u, so the drag is constant D and hence where a ¼ ξl=D and b ¼ A cross =D are constants related to the geometry of the structure element. According to this relation, the tip velocity u is monotonously related to the wall distance H. As H approaches zero, the friction drag from the shearing layer of the wall becomes dominant, and u approximates zero.
As H grows large, the influence of the wall decreases, and u approximates a constant where the driving force balances with Stokes drag. This matches the scenario illustrated by the flow field in Figure 2. When H is small (Figure 2c), a strong shear layer forms between the tip of the transducer and the wall, indicating considerable shear friction. As H increases (Figure 2b), the velocity gradient in the shear layer decreases, suggesting a lower friction drag. Further raising the wall (Figure 2a), the velocity gradient at the tip does not change much, so the friction drag from the wall reaches a constant value. However, there is a weak backward flow at the wall, indicating the formation of a vortex. The vortex and backward flow at the wall are clearly outside the scope of the model in Equation (11). However, since they are quite weak, we can still assume that this model is approximately correct.
For a fixed beating frequency as in the current study, the tip velocity u is related to the maximum displacement of the beam and hence the curvature of the transducer, which is reflected by the variable σ C . In Figure 3b, we fit the σ C profiles with an empirical model similar to Equation (11) where C 1 and C 2 are coefficients to be determined. It shows that the model works well in the three fluids of higher viscosity because Re is low, but does not match the profile in water due to the unaccounted flow structures and drag sources in higher Re flow. www.advancedsciencenews.com www.advintellsyst.com

Experiment Verification
The configuration of mode 1 was verified by experiments. The transducer is fixed to the bottom wall of a tank with a movable wall above (Figure 4a, see also Movie S5, Supporting Information). The transducer is then actuated by a magnet rotating periodically in the angle range ðÀπ=3, π=3Þ at 1 Hz. The magnetization of the transducer is M ¼ 4 Â 10 3 A ⋅ m À1 and the magnetic flux density measured at the bottom of the transducer is jBj ¼ 25 mT, which is consistent with the strength of magnetic field in the numerical simulation. Figure 4b shows excerpts of the voltage (U ) signals from the transducer in 99.7% glycerin, which reflects the time variation of its resistance. It is obvious that the peak of the signal (see the zoomed-in panel in Figure 4b) is more damped when the wall distance is smaller, leading to a smaller standard deviation σ U . The change of σ U with wall distance is shown in Figure 4c. The damping effect of the wall is more obvious in high-viscosity fluids (90% and 99.7% glycerin). In the low-viscosity fluids, the influence of the wall is almost in the same order as the statistical error, which is hardly detectable.
To further demonstrate the function of mode 1, we used the transducers to detect the distance from walls of complex shapes and reconstructed their morphology from the collected data. Figure 5a illustrates the two target walls above the transducers, which we named as the 'Π-shape' and 'U-shape', respectively. We used the same setup as shown in Figure 1b, where four transducers are arranged in streamwise with an interval of 2L.
Each transducer is individually controlled. In this experiment, we turned on only one transducer each time to minimize the interference between them. As the first step, we calibrated each transducer to find their corresponding σ U ðHÞ profiles (see Figure 5b). The profiles are fit with a model similar to that in Equation (12) to enhance their resolution, that is Note that an additional constant C 3 is added in the model. There are several factors that contribute to this additional offset. First, the model in Equation (11) assumes that the flow velocity is parallel in streamwise and neglects the effect of vortices and flow separation, while in the experiment the flow structure is 3D and can be rather complicated. In addition, there are also influences from the sensor during the conversion of deformation into voltage signals. Therefore, we include an additional constant for a better fit of σ U profiles.
This model works well with all profiles with a coefficient of determination above 0.97. Then we collect the voltage signal from the four transducers and compute σ U . Combined with the calibration profile in Figure 5b, we can infer the local wall distances and therefore the shape of the walls. It can be seen in Figure 5c that the prediction is compatible with the ground truth. The maximum error of all positions is within AE15% of the true value. www.advancedsciencenews.com www.advintellsyst.com

Discussion
The results of both simulations and experiments demonstrate that the efficiency of mode 1 highly depends on the fluid viscosity. This can be roughly inferred from Equation (11). Suppose that there is a variation of the wall distance ΔH, the corresponding change of u in water would be on the order of Oð10 3 Þ of that in glycerin due to the coefficient of viscosity on the right-hand side. In other words, the beating velocity of the transducer in water has to be Oð10 3 Þ times faster than that of glycerin to detect this difference. This poses a strong challenge to the performance of the actuator on the transducer. Moreover, u cannot be raised without limit as the hypothesis of stokes flow would no longer apply at high Re. When Re is high, the emergence of turbulence and flow separation could introduce additional disturbances to Equation (11). Therefore, it is not ideal to use mode 1 in the higher Re regime. It is also noted that the decrease of σ U with H in the experiments is less significant than the σ H in the simulation. One of the main reasons is that we adopted 2D simulation, where the width of the transducer (in z-dimension) is presumed to be infinite. In contrast, the actual width of the transducer is quite small (0.33L). Therefore, the wall drag is more prominent in the 2D simulation. To clarify this problem, we performed a 3D simulation in two cases, H=L ¼ 0.33 and H=L ¼ 4.33, in 99.7% glycerin and compared the curvature C with the experiments (see Movie S6 and supplementary note 3, Supporting Information). It shows that the absolute value of C from the 3D simulation and experiment matches well.
The transducer's back and forth strokes are symmetrical, as the current magnetic sheet has a uniform magnetization profile. We also tested mode 1 with a transducer with nonuniform magnetization, which was also used for transport through asymmetrical beating in high-viscosity fluids (see Movie S7 and supplementary note 1, Supporting Information). The nonuniform magnetization sensor also performs distance sensing well in 99.7% glycerol.

Mode 2 for Moderate Re
Since mode 1 has limited sensing ability for Re ≫ 1, we designed a second sensing mode, as shown in Figure 6. It works for lowviscosity fluid where the shear layer between the wall and transducer can be neglected. In this sensing mode, we dedicated one or multiple transducers for actuating and one transducer for sensing. The actuating transducers were placed upstream, and they were the same as Figure 1a. The sensing transducer was placed downstream. Note that all transducers still have the same design shown in Figure 1a, and only their roles are different.
This configuration has its biological origin, as the sensory process of cilia could also be achieved through the coordination of motile and primary cilia. For example, one of the leading theories for how the left-right asymmetry of the body plan is established is that the motility of cilia on a population of nodal cells creates a leftward-directed flow in the embryo that bends a separate population of primary cilia, initiating a Ca 2þ -based signaling cascade in the cells, with which those primary cilia are associated. [37] In this case, the motile cilia cooperate with the primary cilia to regulate biological processes.
Since we use the magnetic actuation method, the sensing transducer is still inevitably influenced by the magnetic field used for the actuation of the actuating transducers. However, as shown later, this effect can be removed through posterior www.advancedsciencenews.com www.advintellsyst.com signal processing. Furthermore, the influence on the sensing transducer can also be resolved by replacing the magnetic actuators with electrical [23] or pneumatic actuators. [38] To totally remove the influence of the magnetic field on the sensing transducer and investigate mode 2 in a clean way, we also conducted experiments using only the sensor part marked by yellow in Figure 1a. To enhance its sensitivity to streamwise velocity, a 10 mm Â 10 mm polyester film is glued to the upper part of the sensor. In the current case, the distance between the actuation and sensing transducers is set to 2L. Suppose the actuating transducers are driven with a constant force, and the friction drag due to the shear layer is negligible in high Re regime; the volume of fluid pumped by the actuating transducer Q should be independent of the distance of the wall. The accelerated fluid will then convect downstream and impose hydrodynamics force on the sensing transducer. The mean flow velocity in the channel is related to the channel width by u % Q=H. Therefore, as the wall distance H decreases, the velocity around the sensing transducer will increase due to the inverse proportional relation. The drag will bend the sensing transducer to a higher curvature which can be detected.
One thing to note is that we design mode 2 based on the hypothesis that the shearing friction from the wall is marginal. However, this part of the drag can be considerably large when the wall distance is low enough, even in low-viscosity fluids (e.g., water). This can be observed in Figure 6 by comparing the beating amplitude of the actuating transducer at different wall distances (see Movie S8, Supporting Information). We will discuss this issue in detail in the following.

CFD Investigation
The simulation of mode 2 consists of two parts. In the first part, we designated the kinematics of the actuating transducer with the penalty force method. In this way, we can completely ignore the influence of the wall friction drag on the actuating transducer. Therefore, the kinematics of the actuating transducers was almost the same. In order to implement this in the simulation, the kinematics of the actuating transducer was fixated by applying a distributed penalty force f p on it, which is defined as f p ¼ Àk p ðχðs, tÞ À χ target ðs, tÞÞ where k p is the penalty coefficient, and χ target ðs, tÞ is the virtual target position for the material point at s. The force f p can be understood as a spring connecting the structure to the target position. With an extremely large k p , the structure moves along the designed trajectory χ target ðs, tÞ. For the current study, we defined χ target ðs, tÞ as the following.
θ target ðtÞ ¼ π=3sinð2πf tÞ The equations above describe the kinematics of rotating the beam back and forth with an angle range of 2π=3. We use frequency f ¼ 1 Hz to match the condition of experiment. We studied the performance of mode 2 in two fluids, that is, water and 99.7% glycerin. The basic parameters of the studied cases are www.advancedsciencenews.com www.advintellsyst.com listed in Table 2. Note that Re and St are independent of the wall distance in each fluid. Figure 7a shows the time variation of C of the sensing transducer in water at different wall distances. The H variation of standard deviation σ C for both the actuation and sensing transducers is summarized in Figure 7b. The curvature of the actuating transducer is generally consistent with a variation of less than 7% in the range tested H. In both water and glycerin, the profiles of σ C ðHÞ of the sensing transducer are close to a hyperbolic shape, consistent with our previous discussion about the inverse proportional relation u % Q=H.
In the second part, the actuating transducer was driven by modeled magnetic forces similar to the simulations of mode 1. The kinematics of the actuating transducer was closer to the experimental condition. To implement this in the simulation, we used the same magnetic force model as in Equation (5)- (8). The rotation angle of the magnetic field was also set to be ½Àπ=3, π=3, same as the rotation angle of the target point in the first part. The flow parameters of the cases are listed in Table 2. Figure 7c shows the time series of C of the sensor in water. The magnitude of C still decreases monotonically as H grows. However, it should be noted that the amplitude of C at the near wall position H=L ¼ 0.25 is significantly smaller than that with penalty-force-driven actuating transducer (Figure 7a). This is more clearly shown in Figure 7d where the change of σ C with H for both the actuating and sensing transducers is compared. In water, the σ C of the actuating transducer remains a constant until the wall distance drops below H=L ¼ 1, and the wall damping effect is not significant. Therefore, the hyperbolic profiles of σ C ðHÞ for the sensing transducer are largely unaffected. In glycerin, however, the scenario becomes more complicated. On one hand, the beating of the actuating transducer is significantly damped in the near wall. On the other hand, the fluid it pushes gains higher speed in a narrower channel, which bends downstream sensing transducer more. These two mechanisms compete against each other throughout the H range. The σ C profile of the sensing transducer shows that the wall damping effect dominates in the region near the wall H=L < 1, where σ C decreases as H becomes smaller. The second mechanism prevails in the range of H=L ¼ ð1; 3Þ, where σ C increases with a smaller H. As the distance rises beyond H=L ¼ 3, σ C only rises slightly with H, suggesting a quite weak influence from the wall. The coexistence of the two mechanisms above results in a peak and a valley in the range of H=L ¼ 1 À 4. Therefore, it is impractical to infer wall distance from this nonmonotonous function of σ C ðHÞ.  www.advancedsciencenews.com www.advintellsyst.com

Experiment Verification
Experiments were conducted to verify the result of the simulation. We installed five actuating transducers upstream and a sensing transducer 2L downstream. For the first part, all transducers are of the same design as in Figure 1a. The actuating transducers were driven by a magnet installed on a motor rotating at a speed of 240 RPM. We use a much faster actuating speed than the 2D simulation since in the experiment the transducers have only a limited width 0.33L, while the 2D simulation assumes an infinite width in z-dimension. Therefore the flow pumping of the actuating transducers is less efficient. Moreover, the limited width of the transducer also reduces the volume of fluid that impinges on the sensing transducer. Therefore, we have to use a much higher actuating frequency here to generate detectable flow. The experiment setup of the measurement is shown in Figure 8a(i). As mentioned earlier, the sensing transducer is also influenced by the magnetic field, which is different from the ideal case in the simulation. To remove this effect, we have to conduct an additional control experiment (Figure 8a(ii)), where the actuating transducers are clamped to the wall. In this way, the effects of the magnetic field and the upstream actuating transducer can be decoupled. Figure 8b compares the time series of the voltage signal from the sensing transducer with and without the influence of upstream actuating transducers. Note that all signals are low-pass filtered (f ≤ 10 Hz) and aligned at peaks. The amplitude of the voltage is smaller when the actuating transducers are released. This is due to the phase delay between the actuating and sensing transducers. The fluid pumping of the actuating transducer acts as a damper that diminishes the peaks of the sensing transducer. This is illustrated more clearly in Movie S9, Supporting Information. Comparing the signals at H=L ¼ 0.33 and H=L ¼ 4.33 (Figure 8a(i,ii)), it can be observed that the damping www.advancedsciencenews.com www.advintellsyst.com effect, which is reflected by the difference between the solid and dotted lines, is more significant at near wall position. Therefore, we use the voltage difference U 0 between the measurement and control experiments to represent the influence of the actuating transducer on the sensing transducer. The time series of the voltage signal U 0 at different wall distances are shown in Figure 8c, and the corresponding standard deviation σ U 0 is concluded in Figure 8d. σ U 0 of the sensing transducer decreases monotonously with H, which is consistent with the previous prediction. However, the standard deviation of σ U 0 is a bit high, which may be attributed to the external errors during the signal alignment process.
The experiment above demonstrates that mode 2 can be realized using the current transducer design. However, we have to conduct additional reference experiments and signal processing to remove the influence of the nonlocal magnetic field, which may introduce additional uncertainty to the result. Note that this additional work could be avoided by replacing the magnetic actuator with electrical [23] or pneumatic actuators. [38] To illustrate the mechanism of mode 2 in a cleaner way, we performed experiments using only the sensor part marked by yellow in Figure 1a to completely remove the influence of the magnetic field on the sensing transducer. The actuating transducers were driven by a magnet installed on a servomotor (Figure 9a, see also movie S10). The range of rotation angle is ½Àπ=3, π=3. The setup is the same as that in the experiment of mode 1. Figure 9b shows the time variation of C water at different wall distances. It should be noted that the time series is a bit noisy compared to the simulation data in Figure 7c. This can be attributed to several reasons. First, there were spaces between actuating transducers. The space is Δz=L ¼ 0.33, which may introduce turbulence in the accelerated flow. Second, the sensing transducer is also subject to the influence of 3D vortex shedding. However, the trend of σ U decreasing with H is preserved. Figure 9c shows the σ U sensor profiles in water and 99.7% glycerin. As observed in Figure 7d, the beating amplitude of the sensing transducer decreases monotonously with H. In glycerin, a valley appears on the σ U ðHÞ in the tested region, which is consistent with the simulation results. Note that here we only show the results of the sensing transducers as the actuating transducers follow the kinematics of mode 1.

Discussion
Based on the results above, it is concluded that sensing mode 2 may not be effective at low Re regime (e.g., in high-viscosity fluids). The design of sensing mode 2 is based on the hypothesis that the volume of fluid pumped by the actuating transducers does not change much for different wall distances. This is close being true in water as the Re is high and the boundary layer is very thin. In this case, the motion of the actuating transducers is almost independent of the wall distances. However, in highviscosity fluid (low Re), the actuating transducer is essentially following principles in mode 1, where the motion is highly influenced by the wall distance. In fact, the beating amplitude will decrease at a close wall distance, leading to a smaller volume of accelerated fluid. This will damage the monotonous relation between the bending amplitude of the sensing transducer and the wall distance. According to the simulation, this constraint can be solved using an extremely powerful actuator whose kinematics is independent of the drags from the viscosity.
Another thing to be noted is that the distance between the actuating transducers and the sensing transducer needs to be carefully adjusted. Although fixed at 2L in the current www.advancedsciencenews.com www.advintellsyst.com investigation, the interval could be an essential parameter for valid wall distance detection. When the sensing transducer is placed too far away from the actuating transducer, the flow pumped by the actuating transducer could be dispersed during the convection and becomes quite weak and undetectable when it reaches the sensing transducer. This is especially true when the actuating transducers are sparsely distributed. On the other hand, when the sensing transducer is placed too close to the actuating transducer, its motion will be strongly coupled with the motion of the latter due to the continuity constraint of the fluid.
In this case, both the actuation and sensing transducers will degrade into mode 1 motion.

Conclusion
In this manuscript, we proposed different functions of a cilia-like transducer with both actuation and sensing functions. Its sensing and actuation can be used individually and together for various functions. The current report used a combination of the magnetic soft actuator and the crack-based electrical sensor.
Other combinations can certainly be used and take advantage of the mechanisms we proposed, especially with respect to distance sensing. Although we only demonstrated the 1D distance sensing strategy, we see future possibilities for more advanced applications of the concurrent actuating and sensing on the cilia transducer, such as the sensing of a complicated shaped object during transport just like the motile cilia on a paramecium. [27] They can also be integrated into a sensing on soft carpet in microfluidic devices as in Ref. [23] to enable distributed sensing on soft robotics. This is particularly useful when there are local changes to the flow.
Another challenge may be when there are multiple variables changing simultaneously. For example, the effect of increasing viscosity can be misinterpreted as an approaching wall. This problem can also be solved by distributive sensing with transducers of different lengths. Short and long transducers have different sensitivities to wall drag. In fact, the wall effect can be neglected when the transducer is much shorter than the wall distance. Combining the signals from different transducers, one can decouple the influence of wall distance and viscosity. Other parameters of the transducer, such as its geometric shape, magnetization profile, and actuation method, can also be changed to adapt to the application requirements.
Furthermore, the combination of sensing and actuation can enable more intelligent functions through closed-loop control. With a feedback mechanism, it is possible to achieve selfadaptive motion regulation of the transducers, so that they can adjust their motions according to the change of environment, for example, the distance to the object, incoming flow, viscosity, etc., just like how the nature does. [24] Supporting Information Supporting Information is available from the Wiley Online Library or from the author.