CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application Numbers 63/267,190, 63/268,351, and 63/368,751, filed on January 26, 2022, February 22, 2022, and July 18, 2022, respectively. The disclosure of each application is incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] This invention is made with government support under Grant No. ARO W911NF-18-1-0032 awarded by the Army Research Office. This invention is also made with government support under Grant No. EFMA-1935252 from the National Science Foundation, Air Force Office of Scientific Research under Grant No. MURI: FA9550-16-1- 0031. The government has certain rights in the invention.

TECHNICAL FIELD

[0003] This patent document relates to an electrochemical actuator.

BACKGROUND

[0004] While ciliary pumping is one of the most important and ubiquitous fluidic transport methods in the microscopic world, it has been challenging to engineer artificial cilia platforms that can be widely adopted. While several pioneering studies have demonstrated methods for fabricating artificial cilia whose actuation is based on light, electrostatic, and magnetic interactions, these systems have limitations.

SUMMARY

[0005] Embodiments disclosed herein may be implemented to provide a metasurface that actively manipulates fluid flow near the surface and yield desired fluid flows.

[0006] In a first aspect, an artificial cilium device includes a substrate and a voltage- actuated cilia-shaped structure attached at a proximal end to the substrate. The voltage- actuated cilia-shaped structure has a first layer of a first material and a second layer of a second material. The second layer of the second material includes an exposed surface that causes the cilia-shaped structure to, in a working medium, (a) change shape from a first shape to a second shape responsive to application of a first voltage and (b) change shape from the second shape to the first shape responsive to application of a second voltage different than the first voltage.

[0007] In a second aspect, an artificial cilium includes a first actuator, a second actuator, a proximal panel, a middle panel, a distal panel, and wire. The first actuator includes a first passive layer on a first active layer. The second actuator includes a second passive layer on a second active layer. The middle panel is between the proximal panel and the distal panel, and has a length less than a distance between the proximal panel and the distal panel when the proximal panel and the distal panel are coplanar. The wire is [i] electrically connected to the second actuator and (ii) on each of the proximal panel and the distal panel. The first actuator is on each of, and spanning a proximal gap between, the proximal panel and the middle panel. The second actuator is on each of, spanning a distal gap between, the middle panel and the distal panel.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 shows an embodiment of electrically-actuated artificial cilia.

[0009] FIG. 2 shows an example of SEM image of released artificial cilia arrays with each row connected by a single busbar.

[0010] FIG. 3 shows experimental results for pumping velocity versus frequency for an embodiment of a cilia array.

[0011] FIG. 4 shows an example of nonreciprocal motion of one 50-pm long cilium driven at 40 Hz.

[0012] FIG. 5 shows an example of an extensional flow generated by an embodiment of a programmable cilia unit.

[0013] FIG. 6 shows an example of 3D flow generated by surface-driven extensional flow.

[0014] FIG. 7 shows an embodiment of a tiled cilia array that can produce arbitrary flow patterns.

[0015] FIGs. 8, 9, 10, and 11 show, respectively, [i] two independent flow trajectories, (ii) a local rotation, (hi) a localized transport, and (iv) trajectories that split and merge, each generated by the tiled cilia array of FIG. 7.

[0016] FIG. 12 shows (a) circuit layout indicating circuit components, and (b) an optical image of the CMOS circuit integrated with four artificial cilia arrays, in an embodiment. [0017] FIG. 13 shows measurements of four example voltage outputs from the CMOS circuit of FIG. 12.

[0018] FIG. 14 is a graph of pumping velocity as a function of different phase delays applied to the cilia arrays of the CMOS circuit of FIG. 12.

[0019] FIG. 15 shows an example fabrication process of an artificial cilium.

[0020] FIG. 16 is a graph illustrating cyclic voltammetry of artificial cilia, in an embodiment.

[0021] FIG. 17 is a graph illustrating durability of artificial cilia, in an embodiment.

[0022] FIG. 18 shows an example of a microscopic device for measuring the trajectory of one cilium.

[0023] FIG. 19 is a graph illustrating Sperm number as a function of actuation frequency for cilia with different lengths.

[0024] FIG. 20 shows an example of a control system for artificial cilia that produces arbitrary flow patterns.

[0025] FIG. 21 shows an example a fabrication process for untethered artificial cilia integrated with a CMOS circuit.

[0026] FIG. 22 shows an example a CMOS circuit, its block diagram, and example output current.

[0027] FIG. 23 shows an example of a two-hinge cilium, its actuation sequences, positions of particles moved by the cilium, and example pumping distance.

[0028] FIG. 24 shows simulated and measured pumping efficiency of an embodiment of an artificial cilium.

[0029] FIG. 25 shows the symmetry-breaking of an example cilium.

[0030] FIG. 26 shows a comparison of the streamlines for various cilia activation patterns open channels without a top wall and closed channels with a top wall included.

[0031] FIGs. 27 - 29 show respective views of an embodiment of an artificial cilium.

[0032] FIG. 30 is a schematic of a cilia array that includes artificial cilia of FIGs. 27 - 29, in embodiments.

[0033] FIG. 31 is a schematic of a cilia device, which includes two cilia arrays of FIG.

30, in embodiments. DETAILED DESCRIPTION

[0034] Cilial pumping is a powerful strategy used by biological organisms to control and manipulate fluids at the microscale. Despite numerous recent advances in optically, magnetically, and electrically driven actuation, however, development of an engineered cilial platform with comparable capabilities has remained elusive. Embodiments disclosed herein may be implemented to provide active metasurfaces of electronically actuated artificial cilia that can create arbitrary flow patterns in liquids near a surface. For example, embodiments, of voltage-actuated cilia generate non-reciprocal motions to drive surface flows at tens of microns per second at actuation voltages of IV. A cilia unit cell implemented based on some embodiments can locally create a range of elemental flow geometries. In some embodiments, an active cilia metasurface includes a plurality of cilia unit cells that generate and switch between any desired surface flow pattern. In some embodiments, a light-powered complementary metal-oxide-semiconductor (CMOS) clock circuit enables wireless operation of the cilia. In one example, the light-powered clock circuit outputs voltage pulses with various phase delays to demonstrate improved pumping efficiency using metachronal waves. The results obtained using some embodiments illustrate a new pathway to fine scale microfluidic manipulations, with applications from microfluidic pumping to microrobotic locomotion.

[0035] There have been many attempts to manipulate fluids at a microscale using artificial cilia platforms. Despite numerous recent advances in optically, magnetically, and electrically driven artificial cilia platforms, none of them is efficient and feasible to be applied to a microfluid system.

[0036] Embodiments disclosed herein may be implemented to provide a metasurface that actively manipulates fluid flow near the fluid surface and yield desired flows. In some implementations, a surface electrochemical microactuator can be used in microfluidic pumping. In one example, the microactuator can be used to implement artificial cilia in tens of micrometers, which is smaller than most other artificial cilia. The artificial cilia implemented in some implementations can operate in an aqueous solution.

[0037] Embodiments disclosed herein may be implemented to provide a method for creating and reprogramming arbitrary micro scale flow patterns. In some implementations, cilia patterns include periodic cellular structures that can be used to generate arbitrary flow near the surface. [0038] Embodiments disclosed herein may be implemented to provide wireless cilia integrated with control circuits. In some implementations, the control circuit is used to remotely control the artificial cilia to generate metachronal wave. In one example, the control circuit includes a photovoltaic unit, a clock unit, and a phase shifter unit.

[0039] In embodiments, a fabrication process of an artificial cilia device includes a photolithography process that is performed in a cleanroom. At first, a release layer that includes aluminum and aluminum oxide is grown and patterned. Thicknesses of the aluminum and aluminum oxide may be in the following respective ranges: 160 nm - 200 nm and 15 nm - 25 nm. Then, a thin titanium layer and a platinum layer are grown and patterned. Thicknesses of the titanium layer and platinum layer may be in the following respective ranges: 2 nm - 4 nm and 5 nm - 10 nm, respectively.

[0040] Electrodes with 10 nm Ti and 60 nm Pt are then patterned. Polymer panels are patterned on the top to regulate the actuation. The device is then cut into pieces, e.g., having dimensions of approximately 1 cm by 1 cm. These pieces are then wire bonded into the chip carrier. The chip carrier is then connected to a computer and controlled by a system design platform such as LabView. The device may be placed in an etchant to etch away the release layer, after which the aqueous solution is applied to the device. The actuation of artificial cilia is controlled to get the desired flow patterns.

Integrated microfluidic chip with artificial cilia

Fabrication of artificial cilia

[0041] A fabrication process of artificial cilia includes growing layers of Pt and Ti, etching these layers, fabricating polymeric panels, and finally releasing the cilia structures. The fabrication process may include at least one of the following enumerated steps. (1) A release layer of 180 nm aluminum is deposited on glass, e.g., Borofloat® glass, using a thermal evaporator (e.g., CVC SC4500). To protect this release layer during the fabrication process, an additional 20 nm A1 ₂ O ₃ is grown at 110 °C using atomic layer deposition (ALD). To pattern these release layers, a positive photoresist (e.g., Microposit S1813) is spin-coated and exposed using an ABM contact aligner; the wafer is then developed in a developer (e.g., MicroChemicals AZ 726 M1F). The exposed releasing layers are etched by an aluminum etchant. Then, the photoresist is stripped by an organic remover (e.g., Microposit Remover 1165) with sonication, followed by oxygen plasma clean for 3 min (e.g., Oxford PlasmaLab 80+) . (2) To fabricate the cilia, 3 nm of Ti is sputtered onto the sample at 3 mTorr and 400 W (e.g., AJA sputter tool). (3) Then, a 7.5 nm Pt layer is grown using ALD at 250 °C. (4) A positive photoresist S1813 is spin-coated, and the cilia pattern is defined by photolithography. (5) The Ti and Pt layers are then etched by an ion mill tool at 600 V (e.g., AJA ion mill). Then the photoresist is stripped in the organic remover. (6) A negative photoresist (e.g., MicroChemicals NLOF 2020) is spin-coated and patterned as the rigid panels to regulate the deformation of artificial cilia. 7) To balance the prestress in Pt/Ti layers, the top surface of Pt layer is oxidized by 1-min oxygen plasma. 8) Finally, the sample is baked at 170 °C for 30 minutes to strengthen the adhesion between the Pt layer and polymer panels.

Fabrication of cilia metasurface

[0042] Between the aforementioned steps (5) and (6), metal electrodes (e.g., 10 nm Ti and 60 nm Pt) are patterned to interconnect the cilia to the soldering pads. The chip is then packaged into a chip carrier with Dual In-line Package (DIP) and Ceramic Pin Grid Array (CPGA) using aluminum wires via wire bonding (e.g., Westbond 7400A Ultrasonic Wire Bounder) after the fabrication of artificial cilia. Finally, the aluminum wires are protected by epoxy glue (e.g., NOA 60 from Norland Products Inc.).

Artificial cilia with internal degrees of freedom

[0043] The cilia can be designed to have internal degrees of freedom that can vastly increase its swept area, and hence its pumping efficiency. We demonstrate this concept using a multi-hinge cilia that include two hinges that may be actuated independently with a phase delay. The fabrication of these cilia is very similar to the fabrication steps for the single hinge cilia. A multi-hinge cilium may include a secondary wire that passes through the first hinge and activates the second hinge. Its operation can be characterized by the two hinge angles. We fabricated and implemented the stroke of an example two-hinge cilium; its mean pumping distance per cycle is about 4.9 ± 0.5 pm. Moreover, the two-hinge cilia can be made much larger and operated at much lower frequencies than their one hinge counterparts. These results highlight the versatility of our system for creating cilia with internal degrees of freedom.

Wireless microfluidic chip with artificial cilia

Design of the control circuit

[0044] The control circuit of the wireless microfluidic chip with artificial cilia may include optically powered CMOS circuits that drive the actuators. In some implementations, the circuit includes two sets of silicon photovoltaics (PVs), one to power the surface electrochemical actuators (SEAs) and one to power the circuit. The electronics may include a Proportional to Absolute Temperature (PTAT) current source, a relaxation oscillator, a frequency divider consisting of D-type flip-flops that reduces the frequency of the relaxation oscillator to a useable range (approximately 2 Hz to 256 Hz, which can be set by hardwiring the circuit in post processing), a phase shifter that produces square waves with a phase offset, and a driver that uses the phase-shifted waves from the circuit to control the voltage applied to the artificial cilia.

Fabrication of CMOS integrated artificial cilia

[0045] Embodiments of an artificial cilia device may be built on a silicon on insulator (SOI) substrate with CMOS circuit. A process for building such a device includes at least one of the following enumerated steps. (1) The SiO ₂ layer on top of the CMOS circuit is first thinned by inductively coupled plasma etching (e.g., Oxford PlasmaLab 80+) . (2) A 180-nm aluminum (doped with 1% silicon) layers and a 30-nm ALD A1 ₂ O ₃ layer are deposited and patterned as release layers. (3) The electrical contacts are made by selectively etching the top SiO ₂ layer. (4) Metal wires (e.g., 10 nm Ti and 60 nm Pt) are patterned to interconnect the CMOS circuit and artificial cilia. (5) A 300-nm silica insulation layer is then patterned on top of the CMOS circuit, preventing short circuits among the circuit, the subsequent layers and the electrolyte. (6) Chrome is deposited and patterned as the light shielding layer on top of the CMOS circuit, leaving only the photovoltaics exposed to light. Finally, the artificial cilia are fabricated as discussed above.

[0046] FIG. 1 shows a plurality of electrically-actuated artificial cilia 100. Each cilium 100 includes a thin surface electrochemical actuator 140 made of a platinum strip (Pt) capped on one side by a titanium film (Ti). Each cilium 100 is attached to a substrate 120 (or a busbar 130 arranged on substrate 120) at one end and actuated by raising and lowering the potential of the film relative to the reference electrode to drive oxidation (at 1 V, for example) and reduction (at -0.2 V, for example) processes that expand and contract the platinum surface. In addition, one or more (e.g., three) panels 150 are fabricated to set the bending direction. Panel 150 may be formed of a dielectric, such as polymer or an oxide, e.g., silicon dioxide.

[0047] FIG. 2 shows an example of SEM image of released artificial cilia arrays with each row connected by a single busbar. A STEM image of a cilium cross section showing the platinum (white), titanium (black) is presented in the bottom right inset.

[0048] FIG. 3 shows experimental results for pumping velocity versus frequency for a single cilia array such as the one shown in the top left inset. The data points show the mean pumping velocity over five different measurements at different actuation frequencies; the shaded regions indicate the standard deviation. The optimal frequency for achieving the highest pumping velocities at first increases then decreases with the cilia length.

[0049] At lower actuation frequencies, the viscous force is not large enough to break the symmetry. At higher frequency, the viscous drag is too large, diminishing the motion of the cilia. To extract the local velocity values, we focused on tracer particles in the vicinity of the cilia tips where the most efficient pumping occurred. The focal depth of the objective (20x, NA=0.4) is about 5 pm according to the resolution equation along the axial direction f = 1.4nA /NA ² , where f, n, , and NA are the focal depth, refractive index, wavelength, and numerical aperture, respectively. In the lateral dimension, the particles in a 20 pm by 20 pm area surrounding the cilia tips were chosen to calculate the velocity. The velocities were obtained for tracer particles in a 20 pm by 20 pm by 5 pm region surrounding the cilia tips.

[0050] FIG. 4 shows an example of nonreciprocal motion of one 50-pm long cilium driven at 40 Hz. Zoom-in trajectories of the tip are shown at the top right for each of four instants in time. T is the period of actuation cycle. The filled black circles indicate the positions of the cilium tip at times t corresponding to different moments in the stroke cycle. The trajectory traced out by the tip is elliptical, which indicates that the cilium is executing a non-reciprocal stroke capable of driving flows even at low Reynolds numbers.

[0051] FIG. 5 shows an example of an extensional flow generated by a programmable cilia unit. Each unit includes eight cilia arrays, with each array includes eight cilia spaced laterally by a distance 514, which in this example equals 25 pm. Each cilium has a length 512, which in this example equals 50 pm. The white tracks indicate the trajectories of florescent particles in the fluid.

[0052] FIG. 6 shows an example of 3D flow generated by surface-driven extensional flow. Image 651 is a composite experimental and simulation image showing the extensional flow measured in the experiments from FIG. 5. Projection 652 illustrates simulated 3D flow geometry projected onto the surface of a cuboid with a quadrant removed. Simulated flow 653 is averaged over the entire depth. Gray-level bar 602 indicates the logarithm of the flow magnitude. The upper left schematic of a cilia unit 680 highlights active cilia arrays 600A and resulting flow directions (red arrows) for this elementary flow geometry. Each cilia array 600A includes a plurality of cilia 600. [0053] FIG. 7 shows an example of a cilia chip 790 that can generate arbitrary flow patterns. Cilia chip 790 includes a plurality of cilia units , which are tiled to form a cilia metasurface 780A. Each cilia unit 780 includes four cilia arrays 700A, each of which includes an artificial cilia 700. FIG. 7 illustrates a four-by-four section of the array, which in this example includes sixty-four individual cilia arrays, which are wire bonded to a chip carrier of cilia chip 790. FIG. 7 denotes a scale that denotes a fifty-micrometer length for this particular embodiment. The spatial dimension of this scale may differ from fifty micrometers without departing from the scope hereof.

[0054] In the example of FIG. 7, cilia unit 780 includes four cilia arrays 700A arranged as a rectangle. In embodiments, cilia unit 700A may include a different number of cilia arrays 780. For example, cilia unit 780 may include a total of three cilia arrays arranged as an equilateral triangle, or a total of six cilia arrays arranged as a hexagon.

[0055] Cilia unit 780 includes two cilia arrays 700A(l) and two cilia arrays 700A(2), which are horizontally oriented and vertically oriented, respectively, and are on adjacent sides of a rectangle. Cilia arrays 700A(l) and 700A(2) have respective lengths 702 and 704, which may be either equal or unequal. Each cilium 700 has a length 707. Cilia unit 780 has respective lengths 782 and 784 along the horizontal and vertical axes, respectively. Length 782 may be greater than or equal to L™ ⁱⁿ , which is length 702 plus two times length 707. Length 782 may be less than L ^m plus M times a spacing between adjacent cilia of cilia array 700A, where M is greater than or equal to one.

Length 784 may be greater than or equal to Ly ⁱⁿ , which length 704 plus two times length 707. Length 784 may be less than L™ ⁱⁿ plus M times a spacing between adjacent cilia of cilia array 700A, where M is greater than or equal to one.

[0056] FIG. 8 shows two independent flow trajectories generated by cilia metasurface 780A, including the experimentally measured particle velocimetry data (left) a schematic of the activated cilia arrays (upper right), and the simulated flow pattern (lower right). For clarity, an individual particle track for each flow trajectory is indicated. FIG. 9 shows a local rotation generated by cilia metasurface 780A. FIG. 10 shows a localized transport generated by the cilia metasurface 780A. FIG. 11 shows trajectories that split and merge generated by cilia metasurface 780A.

[0057] FIG. 12 shows circuit 1210 indicating circuit components, and an image of a CMOS circuit 1220 that includes four CMOS integrated artificial cilia arrays 1200A(l-4). CMOS circuit 1220 includes circuit 1210. Circuit 1210 includes four photovoltaic cells, an oscillator, a frequency divider, and a phase shifter. In this example of CMOS circuit 1220, a shielding layer 1222 obscures all but the photovoltaic cells of circuit 1210. Artificial cilia array 1200A is an example of artificial cilia array 700A. Untethered control of artificial cilia arrays 1200A generates metachronal waves. FIG. 13 shows measurements of voltage outputs 1310(1-4) of CMOS circuit 1220, which control respective cilia arrays 1200A(l- 4). Relative to voltage outputs 1310(1), voltage outputs 1310(2), 1310(3), and 1310(4) are phase-delayed by phases equal to 0, 20, and 30 respectively. In the example of FIG. 13, 0 = TT/2.

[0058] FIG. 14 is a graph of pumping velocity versus phase delay for artificial cilia arrays 1200 driven at 16 Hz averaged over five separate measurements. The error bars indicate the standard deviation. In this example, a TT/2 phase delay between the arrays produces a pumping velocity that is ~ 370% higher than that obtained without phase delays, and ~ 84% higher than that obtained for phase delay of n.

[0059] FIG. 15 shows an example fabrication process of an artificial cilia array 700A. 180 nm Al and 20 nm A1 ₂ O ₃ are first grown and patterned as the release layer. 3 nm Ti and 7.5 nm Pt are then grown and patterned as the actuator. Finally, several polymer panels are patterned on the actuator to prevent twisting of the cilium.

[0060] FIG. 16 is a cyclic voltammetry curve for an artificial cilium actuated between -0.2 V to 1 V at a sweep rate of 1 V/s. The peak current density is about 1 mA/cm ² , which means a 1-cm by 1-cm device fully covered by artificial cilia would only consume about 1 mW of power.

[0061] FIG. 17 shows the durability of artificial cilia expressed as the relative velocity as a function of the number of actuation cycles. The relative velocity is scaled by the initial pumping velocity. The linear fit to the data indicates the relative velocity will decrease by 50% after 20,000 actuation cycles.

[0062] FIG. 18 shows an example of a microscopic device for measuring the trajectory of one cilium. At first, a fixed voltage is applied to the hinge through electrode 1 to make the hinge bend up to about 90°, then another oscillating voltage is applied through electrode 2 to actuate the cilium.

[0063] FIG. 19 is a plot cilia Sperm number as a function of cilia actuation frequency for cilia with different lengths. The shaded region of FIG. 19 indicates the range of Sperm numbers corresponding to the maximum measured pumping velocities. The shaded region roughly indicates the maximal pumping velocities measured in the experiments.

[0064] FIG. 20 shows an example of the control system of the artificial cilia for arbitrary flow patterns. In an example, a Lab VIEW program may be used to generate voltage signals and send these signals to a data acquisition device. The output of the data acquisition device is connected to the micro fluidic chip through a breadboard.

[0065] FIG. 21 shows a process 2100 for fabricating untethered artificial cilia integrated with a CMOS circuit. Process 2100 includes steps 2110, 2120, 2130, 2140, 2150, 2160, and 2170. 180-nm thick Al and 20 nm thick A1 ₂ O ₃ are first grown and patterned (step 2110) as the release layer. The metal contacts are then etched and exposed (step 2120). Ti/Pt interconnects are patterned to wire the contacts (step 2130). A protective SiO ₂ layer is grown and patterned to prevent electrical shorts and current leaks (step 2140). A Cr shielding layer is fabricated to protect the circuit from the light (step 2150). Actuator layers that consist of Ti and Pt are grown and patterned (step 2160). Finally, polymer panels are patterned on the actuator (step 2170).

[0066] FIG. 22 shows an example CMOS circuit. Specifically, FIG. 22(a) shows an optical image of integrated circuit 2210. The circuit outputs up to eight square waves with phase delays to drive the actuators. In one example, the frequency is set by hard wiring, and the available driving frequencies range from 2 Hz to 256 Hz. FIG. 22(b) shows a block diagram of circuit 2210. FIG. 22(c) shows current versus time outputs from circuit 2210 under different light intensities. The output current ranges from 140 nA under a light intensity of 1 kW/m ² equivalent to 1 sun, to about 880 nA at a light intensity of 5 suns.

[0067] FIG. 23(a) shows an optical image of a fabricated two-hinge cilium 2301, which is an example of cilium 700, FIG. 7. FIG. 23(b) is a schematic of a two-hinge cilium 2300, of which two-hinge cilium 2301 is an example. Cilium 2300 includes a first panel 2310 and a second panel 2320, which have respective panel lengths l-^ and Z ₂ and respective hinge angles 6 _hl and 0 _h2 - Cilium 2300 also includes electrodes 2360(1) and 2360(2).

[0068] FIG. 23(c) shows actuation sequences that maximize a swept area (shaded region) for two-hinge cilium 2301. FIG. 23(d) shows the positions of representative particles 2391, 2392, and 2393 after zero, one and two cycles of actuations (from left to right). FIG. 23(e) shows the pumping distance per cycle for fabricated two-hinge cilium 2301 operating at 0.5 Hz and a one-hinge cilium operating at 10 Hz. [0069] Fabrication of cilia 2300 may be similar to fabrication steps for a singlehinge cilia, e.g., as in FIG. 15. Here, however, the fabrication includes a secondary wire that passes through the first hinge and activates the second hinge.

[0070] Cilium 2300 has internal degrees of freedom, which can vastly increase its swept area and hence its pumping efficiency. Operation of cilium 2300 can be characterized by two hinge angles, 6 _hl and 0 _h2 . To maximize the pumping efficiency, a geometric calculation may be used to tune the initial and final angles for each hinge so that the swept area over one cycle, which includes four actuation steps, is maximized (FIG. 23 (c)). Assuming equal length panels (/ _x = Z ₂ )> the hinge angles at the start of the stroke that maximize the swept area are 6 _hl = 2.02°, 0 _h2 = 2.23°. This stroke can be implemented in fabricated two-hinge cilium 2301. The mean pumping distance per cycle is about 4.9 ± 0.5 pm (FIG. 23 (d)J. This result is larger compared to the pumping distance, which is about 2.9 pm per cycle (FIG. 23 (e)J. Moreover, two-hinge cilia 2300 may be made much larger and operated at much lower frequencies than their one hinge counterparts. These results highlight the versatility of our system for creating cilia with internal degrees of freedom.

[0071] The disclosed technology may be implemented in some embodiments to control the local chemical environment and the chemical reactions by controlling the local flows. Devices based on some embodiments may be integrated with sensors to measure the chemical, optical, and thermal state of the surrounding fluid to determine an appropriate microfluidic manipulation. The cilia based on some embodiments can be used to replace the natural cilia to help the organisms function properly. The cilia based on some embodiments can be used to drive the microrobot in aqueous solution.

[0072] The disclosed technology can be implemented in some embodiments to provide artificial cilia including the surface electrochemical actuator. In some implementations, each of the artificial cilia includes an electrochemically active layer (EAL), an electrically passive layer (EPL) and several panels. In some implementations, the exposed surface of EAL is expanded when the hydrogen or oxygen atoms adsorb onto or intercalate into the EAL materials and is shrunk when the hydrogen or oxygen atoms escape from the EAL materials. Applying periodic voltages causes the actuator to bend and flatten. This actuation is then interacted with the fluid around the cilia.

[0073] By designing the thickness of cilia at about 10 nm, width 5 gm and length

50 gm, the elastic force of cilia and the fluid force roughly in one order (the ratio of these two forces is called Sperm number) can get non-reciprocate motions to pump fluid in Low Reynold’s number. The cilium can either be actuated using one actuation with Sperm number of order 1 or using multiply actuations with Sperm number smaller than 1 to enable transport at low frequency (see FIG. 23). Cross panels can be used to stabilize bending.

[0074] FIG. 24 shows pumping efficiency in simulation and experiment, (a) A cilium beating at around 1 Hz, corresponding to a Sperm number of 1. At these low Sperm numbers, the viscous force is not large enough to break the actuation symmetry, (b) A cilium beating at around 230 Hz, corresponding to a Sperm number of 7. At these high Sperm numbers viscous drag is too large, diminishing the motion of the cilia, (c) The relationship between swept area, displaced volume, and Sperm number. Displaced volume per period and the swept area as a function the Sperm number. Results are obtained by numerical simulations of the single cilium model. The area is defined as the ratio between the area covered by the cilium tip and the square of the length of the cilium. This range of Sperm numbers reflects the conditions under which the area swept by a cilium is largest, and is consistent with classical work on artificial microswimmers and biological cilia, (d) The relationship between Sperm number and the actuation frequency for cilia with different lengths. The blue shaded region roughly indicates the maximal pumping velocities measured in the experiments.

[0075] In some implementations, the fluid velocity can be experimentally shown and numerically validated to scale with the “swept area.” To address this in some embodiments of the disclosed technology, additional numerical computations can be performed based on the theoretical model of a single cilium. FIG. 24 (c) shows a plot for the total fluid volume displaced per period of actuation (i.e., the integrated fluid flux, in blue) and the “swept area” (in red) as a function of the dimensionless Sperm number (essentially, varying the frequency of actuation). FIG. 24 (c) shows qualitative agreement between the two curves, verifying that the velocity scale does indeed scale with the swept area in some embodiments of the disclosed technology.

[0076] FIG. 25 shows an illustrative representation of the symmetry-breaking of an example cilium. In this representation, the example cilium comprises a fixed proximal end at the example origin (0, 0) and a distal end (i.e., the tip of the cilium) that is free. Responsive to an example driving function, locations of the cilium tip over a full stroke of an example driving function (e.g., applied voltage at 40 Hz), such as is shown by way of example in FIG. 4, sweep out an elliptical trajectory indicating non-reciprocal motion resulting from interplay between viscous forces and the elasticity of the cilium. Forced chemical reactions induce internal elastic stress and relaxation of the elastic stresses starts from the distal end and propagates toward the proximal end on a timescale controlled by the viscous forces (e.g., the elasto hydrodynamic timescale). In at least some examples of the present concepts, the period of the driving voltage is set to be comparable with the elastohydrodynamic timescale of the cilium or cilia resulting in a continuous lag between the distal end (tip or free end) of the cilium or cilia and the proximal end (root or fixed end) of the cilium or cilia, which gives rise to non-reciprocal motion.

[0077] FIG. 26 shows comparison of the streamlines for various cilia activation patterns for open channels without a top wall and closed channels with a top wall included. All the figures are obtained through numerical simulations. The qualitative features of the streamlines are preserved when the top wall is added. The parts of the streamlines that deviate from the single wall case the most are located exactly where the regularized singularities are located, and therefore where the simulation error is largest. The biggest change occurs for the expansion flows, which are inherently 3D. These simulation results suggest thus that the tessellation idea will work in a channel geometry as well.

[0078] As shown in FIG. 26, similar patterns are generated when an additional upper boundary is included. The disclosed technology can also be implemented in some embodiments to determine whether such elementary flows can be generated when there is an additional boundary parallel to the substrate. The flow due to a point force can be approximated in this case. The leading order of the flow, averaged over the wall-to-wall distance, is parallel to the walls and has the same streamline structure for any value of the channel height. However, this leading order flow is singular near the horizontal locations of the active cilia, so we regularize the singularities by an algebraic blob of size 0.45 cilia lengths.

[0079] The experiments discussed herein may be performed in neutral PBS solution, which is compatible with biological environments. Since the redox reaction of Pt only requires a conductive aqueous solution with trace electrolyte (Na ⁺ , K ⁺ , Mg ²⁺ , etc.), artificial cilia implemented based on some embodiments of the disclosed technology may be operated in environments ideal for biological/biomedical applications. There is a pH dependence to the electrochemical operation of the cilia, but it is slight. According to the Nernst equation, the voltage driving the electrochemical reaction changes by about 59 mV per pH unit at room temperature. As such, this actuator work over a broad range of pH from acidic to basic solutions. In one example, the Pt/Ti microactuator works in 0.5M sulfuric acid (pH=0.3) and 0.25M sodium hydroxide (pH = 13.4).

[0080] In some implementations, the deformation of artificial cilia implemented based on some embodiments of the disclosed technology is not sensitive to the oxidation of the Pt layer in the fabrication process. In some implementations, the cilia are oxidized so that they initially lay flat and are less susceptible to damage during the various fluid transfer processes. Once the cilia are operated, the oxidized layer reduces and re-oxidizes based on the applied voltage. Overall, the fabrication process based on some embodiments of the disclosed technology is robust consistently yielding over 95% operational cilia per fabrication run. To balance the prestress in Pt/Ti layers, the top surface of Pt layer can be oxidized by 1-min oxygen plasma. This step can control the shape of the cilia upon release so that they do not get damaged during the various fluid exchange processes.

[0081] In some implementations, natural cilia are characterized by a large, enclosed area that the cilium tip makes during a full stroke. This swept area is directly linked to the fluid driving performance of the cilia at low Reynolds numbers. The limited size of the presented swept area is a direct consequence of using the viscous forces to break symmetry, a 4 ^th -order effect. For natural cilia and recent magnetic and fluidic cilia, symmetry breaking is present in the actuator itself and does not rely on fluidic interactions.

[0082] In some embodiments, the cilia can be designed to have internal degrees of freedom. While more complicated, such cilia can break time reversal symmetry without the need for elastic deformations due to hydrodynamic forces.

Theory and Simulations

[0083] Model of a single cilium. To elucidate the physical mechanism behind the motion of the cilia, we develop a simple theoretical model that captures all the important dynamical features that are experimentally observed. We model a single artificial cilium as a slender, inextensible elastic rod with a centerline x(s, t), at time t, parameterized by its arc-length s. In the experiments, the motion is driven by expansion/contraction of one side of the cilium caused by chemical reactions due to an applied oscillating electrical potential. We model this forcing as a periodic variation of the natural curvature of the centerline and assume it is uniform along its length. K ₀ (t) = K + Asinoit, (1) where A and K are constants and a) is the actuation (angular) frequency.

[0084] The rest of the model is based on a standard approach for microsized slender, elastic filaments immersed in a viscous fluid, at low Reynolds number . The elastic forces are computed using a classical Kirchhoff rod model (linear elasticity) with prescribed natural curvature while the hydrodynamic forces are based on the standard resistive force theory of slender filaments that assumes that the drag force density is local and anisotropic and can be found as where n and t are a local unit normal and a tangent to the centreline while = 2^| are the drag coefficients in the said directions.

[0085] For the boundary conditions, we assume that the rod is clamped at one end (s = 0) and there is no force or torque applied at the other (s = L). For simplicity, we non- dimensionalize the governing equations by scaling length by the length of a cilium L, time by the elasto-hydrodynamic timescale where B is the elastic bending modulus of the effective cross-section that we assume is constant in time and uniform along the length. Also, as we assume the shape remains two-dimensional, it is most convenient to use the tangential angle 0(s, t), which is the angle between a local tangent to the center- line and the clamping direction at the fixed end.

[0086] Finally, the model is then described by the following set of equations with boundary conditions where 4(s, t) is a Lagrange multiplier that ensures the inextensibility of the centerline and letters in subscript denote a partial derivative with respect to the variable written in the subscript. [0087] The governing equations (Eqs. 3 and 4) represent the local balance between the viscous drag and the internal elastic forces, algebraically manipulated to be most suitable for numerical simulations. The boundary conditions shown in Eq. 5 are those imposed by the assumptions that the root (s = 0) is clamped in a fixed direction and the tip (s = 1) is free of any external forces and moments and thus, as we are in the inertialess limit, free of any internal forces and moments. The remaining boundary conditions (Eqs. 6 and 7) represent the vanishing elastic force density at the root. The elastic force vanishes because it is balanced by the viscous drag which vanishes since the root is not moving.

[0088] Besides the initial shape of the centerline and the dimensionless mean and amplitude of the natural curvature (/< and A in Eq. 1), the evolution of the model centerline depends on the dimensionless Sperm number Sp that was mentioned above. In terms of the equations, the Sperm number comes in through the natural curvature forcing as its dimensionless frequency.

[0089] The equations are evolved in time by a backward time-stepping scheme as described in Quennouz, etal. (doi:10.1017/jfm.2015.115). Results of an example simulation are shown in FIGs. 24(a) and 24(b). The relationship between pumping efficiency and Sperm number is shown in FIG. 24(c).

[0090] In some implementations, the coupling may decrease with cilia spacing. For example, the coupling may decrease as the spacing goes to about 5 cilia lengths. In some embodiments of the disclosed technology, the spacing is about 1.4 cilia lengths, creating even more coupling. Moreover, the results on metachronal pumping demonstrate that there is indeed a significant effect due to coupling between cilia in different arrays. Given a separation of about 1.4 cilia lengths between the arrays, significant coupling between the induced flows is expected. In one example, pumping is optimal when adjacent cilia arrays have a phase delay of about TT/2 (see FIG. 14).

[0091] The cilia implemented based on some embodiments of the disclosed technology can exhibit non-reciprocal motions. When arranged in specific layouts (e.g., metasurfaces) and actuated in a particular sequence and/or in spatial patterns, various controlled (e.g., programmable) microfluidic flow patterns can be generated. In some implementations, the cilia and other CMOS electronics can be incorporated into a single device.

[0092] Some embodiments of the disclosed technology can be applied to a wide variety of applications that utilize complex surface driven manipulations. In some implementations, cilia metasurfaces may enable numerous fluidic applications in lightweight devices under simple exposure to the sun.

[0093] In some implementations, the EAL may include, but not limited to, platinum, ruthenium, rhodium, palladium, osmium, iridium, gold, and silver. In some implementations, The EPL may include, but not limited to, inorganic materials (titanium, TiO ₂ , SiO ₂ , SiN _x , HfO ₂ , etc.), organic materials (polymers, gels, biomaterials, etc.) or other electrochemically inert materials. In some implementations, the panels may include, but not limited to, inorganic materials (titanium, TiO ₂ , SiO ₂ , SiN _x , HfO ₂ , etc.), organic materials (polymers, gels, biomaterials, etc.) or other electrochemically inert materials.

[0094] The disclosed technology can be implemented in some embodiments to provide an integrated microfluid chip with programmable flow patterns. In some implementations, arrays of cilia are used to make a matrix and selectively actuate the desired arrays to get the desired flow patterns, the flow patterns can be changed if needed. The arrays are patterns parallelly and perpendicularly oriented. By wiring out each array and connecting it to chip carrier, a computer can be used to send voltage signals to the cilia to get flow patterns. In some implementations, the number of cilia in one array can be changed. For example, 8 cilia can be used, and it can also be from 1 to more than 1000 cilia. In some implementations, the dimension of the cilia arrays can be changed, currently, the chip has 64 independently controlled cilia arrays, this number can be changed to other numbers from 1 to more than 1000. In some implementations, the control method can be changed. In one example, voltage signals are generated (e.g., using LabView or MATLAB) and sent to a data acquisition device and the data acquisition device is connected to the chip carrier to do actuation. Instead of data acquisition device, a micro controller unit may be used.

[0095] The disclosed technology can be implemented in some embodiments to provide a wirelessly controllable artificial cilia using an onboard CMOS circuit. In this configuration, the artificial cilia can be controlled using a light-powered CMOS circuit, which includes photovoltaics and a timing circuit. In some implementations, the artificial cilia can be integrated with this circuit. After fabrication, the artificial cilia can be actuated by shining light on the circuit. Distinct from the integrated microfluidic chip in the previous case, this is a completely untethered system that can get several oscillating voltage signals with phase delays. By making more complex circuit and integrating more parts such as sensors, the artificial cilia will be able to make its own decision of actuation based on the environment. In some implementations, the output frequency can be changed from 0.01 Hz to 1000Hz, it allows us to change the pumping velocity. In some implementations, the output current of the photovoltaics may vary from InA to 1A based on the applications. In some implementations, the number and the pattern of cilia can be changed based on the design. In some implementations, the circuit design can be changed. For examples, we have 8 phased in the current circuit, we can design more phases (e.g., 1000) if needed. Also, in the future, we can integrate sensors on the circuit to let the cilia change the actuation mode based on the environment.

[0096] The artificial cilia implemented based on some embodiments of the disclosed technology have advantages over traditional microfluidic devices in many aspects. The traditional microfluidic devices need external bulky pumps to get flow while the device implemented based on some embodiments of the disclosed technology is a fully integrated microfluidic system which does not need external pumps. The traditional microfluidic devices cannot change the flow pattern once fabricated, the device implemented based on some embodiments of the disclosed technology can generate programmable/arbitrary flow patterns as wish. The device implemented based on some embodiments of the disclosed technology can achieve wirelessly control of the cilia in the environment where the tethered control is not possible, while the traditional microfluidic devices need setups attached to the devices.

[0097] In some implementations of the disclosed technology, an electrochemically actuated artificial cilia can be formed by thin film fabrication processes and can exhibit, by applying voltage, non-reciprocal motions. When arranged in specific layouts (e.g., metasurfaces) and actuated in a particular sequence and/or in spatial patterns, various controlled (e.g., programmable) microfluidic flow patterns can be generated. The artificial cilia work at low voltage (< 1 V) which makes them in principle suitable for aqueous environments. Moreover, when integrated with a light-powered CMOS clock circuits, the artificial can be driven wirelessly.

[0098] Some example artificial cilia, whose actuation is based on pressure, light, electrostatic, and magnetic interactions, may have severe limitations. For example, cilia that are pressure driven or optically driven can be locally actuated, but it is difficult to implement such cilia at the microscale. However, the disclosed technology can be implemented in some embodiments to manipulate fluids at a microscale using artificial cilia platforms. [0099] In some implementations, the cilia are comprised of surface electrochemical actuators (SEAs). The cilia can exhibit non-reciprocal motions, be arranged in metasurfaces and actuated in controlled spatial patterns and integrated with CMOS electronics. In one example, the untethered cilia implemented based on some embodiments of the disclosed technology are powered by photovoltaics and can incorporate CMOS electronics. Different from another example implementation where the user has to switch between shining a laser on the front or back photovoltaic to activate the robot legs, the cilia implemented based on some embodiments of the disclosed technology can be activated by simply exposing the entire chip to ambient light. In some implementations, photovoltaics in conjunction with a user guided laser can be used to control actuation.

[0100] In some implementations, each cilia array only provides unidirectional pumping, and thus two arrays, which provide bidirectional pumping, can be used to generate arbitrary flow patterns. In one example, two arrays on each side can be implemented to enable bidirectional pumping.

[0101] FIG. 27 is a plan view, and FIGs. 28 and 29 are respective cross-sectional views, of an artificial cilium 2700. Examples of artificial cilium 2700 include artificial cilia 100, 600, 700, and 2300. FIGs. 27 - 29 are best viewed together in the following description. Figures herein depict orthogonal axes Al, A2, and A3, also referred to as the x axis, y axis, and z axis, respectively. Herein, the x-y plane is formed by orthogonal axes Al and A2, and planes parallel to the x-y plane are referred to as transverse planes. Unless otherwise specified, thicknesses of objects herein refer to the object’s extent along axis A3. Also, herein, a horizontal plane is parallel to the x-y plane, a width refers to an object’s extent along the x or y axis respectively, and a vertical direction is along the z axis.

[0102] Artificial cilium 2700 includes actuators 2710(1) and 2710(2), a wire 2722, proximal panel 2740(1), middle panel 2740(2), and distal panel 2740(3). Actuators 2710(1,2) include respective passive layers 2710(1, 2) and respective active layers 2720(1,2). Passive layers 2710(1, 2) are on respective active layers 2720(1,2). Wire 2722 is (i) electrically connected to actuator 2710(2) and (ii) located on each of panel 2740(1) and panel 2740(3).

[0103] Middle panel 2740(2) is between proximal panel 2740(1) and distal panel 2740(3), e.g., when panels 2740 are coplanar. When panels 2740(1) and 2740(3) are coplanar, panels 2740(1) and 2740(3) are separated by a distance 2748. Middle panel 2740(2) has a length 2746, which is less than distance 2748, such that (i) panels 2740(1) and 2740(2) are separated by gap width 2742 and (ii) panels 2740(2) and 2740(3) are separated by gap width 2744. When panels 2740(1 - 3) are coplanar, the sum of length 2746 and gap widths 2742 and 2744 equals distance 2748. When panels 2740(1 - 3) are coplanar in a horizontal plane, each of panels 2740 intersects a vertical plane that is perpendicular to the horizontal plane. Each of length 2746, distance 2748, and widths 2742 and 2744 is along axis A2.

[0104] Actuator 2710(1) is on each of, and spans a proximal gap between, proximal panel 2740(1) and middle panel 2740(2). Actuator 2710(2) is on each of, and spans a distal gap between, middle panel 2740(2) and distal panel 2740(3). The proximal gap and the distal gap have gap widths equal to gap widths 2742 and 2744, respectively. Gap widths 2742 and 2744 may be between 0.1 micrometer and 10 micrometers.

[0105] FIGs. 27 - 29 denote a hinge 2701 between panels 2740(1) and 2740(2), and a hinge 2702 between panels 2740(2) and 2740(3). Actuators 2710(1) and 2710(2) enable artificial cilium 2700 to bend at each of hinges 2701 and 2702. Passive layer 2710(1) and active layer 2720(1) may have different respective surface stresses, which results in a nonzero resting bend angle of hinge 2701, such that despite an absence of oxidation or reduction at active layer 2720(1), panels 2740(1) and 2740(2) are not coplanar. Similarly, passive layer 2710(2) and active layer 2720(2) may have different respective surface stresses, which results in a non-zero resting bend angle of hinge 2701, such that despite an absence of oxidation or reduction at active layer 2720(2), panels 2740(2) and 2740(3) are not coplanar. FIGs. 28 and 29 denote bend directions 2703(1) and 2703(2) attainable by hinges 2701 and 2702, respectively.

[0106] Each of passive layers 2710 may include an inorganic material or a combination of inorganic materials. Examples of such materials include titanium, titanium dioxide, silicon dioxide, a nitride of silicon, and hafnium dioxide. Each of active layers 2710 may include at least one of a metal, a transition metal, or a combination thereof. The metal may be one of gold, silver, and platinum, or a combination thereof. The transition layer may be one of ruthenium, rhodium, palladium, osmium, iridium, or a combination thereof.

[0107] FIGs. 28 and 29 illustrate passive layers 2710 as between panels 2740 and active layers 2720. In such embodiments, passive layer 2710(1) includes two regions respectively located (i) between the first active layer 2720(1) and proximal panel 2740(1), and (ii) between active layer 2720(1) and middle panel 2740(2). Also in such embodiments, passive layer 2710(2) includes three regions located between active layer 2720(1) and (i) panel 2740(1), (ii) panel 2740(2), and (iii) panel 2740(3), respectively.

[0108] In embodiments, actuators 2710 may be oriented such that active layers 2720 are between panels 2740 and passive layers 2710. In such embodiments, active layer 2720(1) includes two regions respectively located (i) between passive layer 2710(1) and panel 2740(1), and (ii) between passive layer 2710(1) and panel 2740(2). Also in such embodiments, active layer 2720(2) includes three regions located between passive layer 2710(1) and (i) panel 2740(1), (ii) panel 2740(2), and (iii) panel 2740(3), respectively.

[0109] Wire 2722 and active layer 2720(2) may be monolithic. For example, wire 2722 and active layer 2720(2) may be formed of the same material and be integrally formed.

[0110] Wire 2722, actuator 2710(1), and actuator 2710(2) have respective widths 2723, 2714, and 2716 along axis Al. Width 2723 may less than one-tenth of width 2716, and width 2714 may be at least four-fifths that of width 2716.

[0111] Artificial cilium 2700 has cilium width 2706 and a cilium length 2707. Cilium width 2706 may equal the maximum of the following widths: width 2716 and respective widths of panels 2740. Each panel 2740 may have an equal width along axis Al. Width 2716 may be less than width 2706, e.g., when cilium width 2716 equals a width of panel 2740(3). Length 2707 may equal the sum of the lengths of panels 2740 plus widths 2742 and 2744, as shown in FIG. 27.

[0112] Along axis A3, actuators 2710(1) and 2710(2) have respective thicknesses 2713(1) and 2713(2), which may exceed five nanometers to ensure uniformity of thicknesses 2713. Thicknesses 2713 may be less than fifteen nanometers, such that desired bending radii of curvature is achievable. Active layers 2720(1,2) have respective thicknesses 2723(1,2). Since oxidation of active layers 2720 drives bending of actuators 2710, and an approximate oxidation depth is one nanometers, each of thicknesses 2723 may be at least one nanometer. Panels 2740(1-3) have respective thicknesses 2743(1-3), each of which may be 0.3 micrometers and 0.6 micrometers. FIG. 28 denotes a horizontal distance 2717 between actuator 2710(1) and wire 2722, and a vertical distance 2718 between actuator 2710(1) and actuator 2710(2). Each of distances 2717 and 2718 may exceed five micrometers for ease of fabrication, and yet may be less than five micrometers, e.g., less than one micrometer. [0113] In some implementations, for Sperm number * 1 for example, spatial dimensions of cilia may be changed in a reasonable range: cilium width 2706 may be between 50 nm and 1 mm, and the cilium length 2707 may be between 100 nm and 10 mm. In one example, the thickness of active layers 2720 may be between 1 nm and 100 pm. In another example, the thickness of passive layers 2710 may be between 0.1 nm and 100 pm. In another example, panel thickness 2743 may be between 1 nm and 1 mm. In another example, the working frequency may be between 0.1 Hz and 1000 Hz.

[0114] In some implementations, for Sperm number less than one, the dimension of cilia can be changed in a reasonable range, for example, cilium width 2706 be between 50 nm and 1mm, the cilium length 2707 may be between 100 nm and 10mm. In an example, the thickness of active layers 2720 may be between 1 nm and 100 pm. In another example, the thickness of passive layers 2710 may be between 0.1 nm and 100 pm. In another example, panel thickness 2743 may be between 100 nm and 1 mm. In another example, the working frequency may be between 0.01 Hz to 1000 Hz. In some implementations, the control voltage may be between -50 V and 50 V based on the used EAL materials. In some implementations, the working medium may be, or include, aqueous solution, organic solvent, ionic liquid, etc., or any combination thereof. In some implementations, the number of panels may increase with increasing cilia length. In embodiments, the number of panels is between two and ten. The number of panels may exceed ten.

[0115] Artificial cilium 2700 may include a substrate 2792, which includes electrodes 2761 and 2762 thereon. Electrodes 2761 and 2762 are electrically connected to active layer 2720(1) and active layer 2720(2), respectively.

[0116] FIG. 30 is a schematic of a cilia array 3000, which includes a N electrode pairs 3060(1 - N and N artificial cilia 2700(1 - N arranged as a linear array along an array-axis 3098. That is, when all cilia 2700(1 - N are flat and coplanar, respective centers of artificial cilia 2700(1 - IV) are colinear along a line parallel to array-axis 3098. In the example of FIG. 30, axis 3098 is parallel to axis Al. Integer N may be greater than two. For example, in cilia arrays 600A and 700A, N = 8. Each of cilia arrays 600A and 700A is an example of cilia array 3000.

[0117] Each electrode pair 3060 includes one electrode 2761 and one electrode 2762, and is on a substrate 3092, which is an example of substrate 2792, FIG. 27. Electrode pairs 3060 may be collinear on substrate 3092, and hence be a linear array of electrode pairs, which may be parallel to the array formed by artificial cilia 2700(1 - N . Cilia array 3000 may also include substrate 3092.

[0118] Each artificial cilium 2700(fc) is electrically connected to a respective electrode pair 3060(fc), where index k is a positive integer less than or equal to N. Specifically, active layers 2720(1) and 2720(2) of artificial cilium 2700(fc) are electrically connected to respective electrodes 2761 and 2762 of electrode pair 3060(fc).

[0119] Cilia array 3000 has a length 3006, herein also L _A . Each artificial cilium 2700(fc) has a respective width 2706(fc). Denoting the sum of N widths 2706(fc) at 1 t _ot , a fill factor Vft _ot /L of cilia array 3000 may be between 0.1 and one. In embodiments, the fill factor is between s and %. When the fill factor is less than 0.1, cilia array 3000 may not generate uniform flow.

[0120] FIG. 31 is a schematic of a cilia device 3100, which includes two cilia arrays 3000, denoted as 3000(1) and 3000(2), on a substrate 3192. Cilia device may also include substrate 3192. Cilia arrays 3000(1,2) have respective axes 3098(1) and 3098(2), which are oriented in different respective directions. FIG. 30 denotes an angle 3198 between axes 3098(1) and 3098(2). Example values of angle 3198 include 60°, 90°, and 120°, which correspond to when cilia arrays 3000 are respective sides of a triangular cilia unit, a rectangular cilia unit (e.g., cilia unit 780), and a hexagonal cilia unit. Cilia arrays 3000(1,2) are part of a cilia unit 3180, which may be tiled on substrate 3192 to yield a cilia metasurface, such as cilia metasurface 780A.

[0121] Cilia unit 3180 may include one or more additional cilia arrays 3000, for example, cilia array 3000(3), which is oriented at angle 3198 with respect to cilia array 3000A(2). Cilia unit 3180 may include a total of three, four, or six cilia arrays 3000, in which case angle 3198 equals 60°, 90°, and 120°, respectively, and cilia unit 3180 is triangular, rectangular, and hexagonal, respectively.

Combinations of Features

[0122] Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following enumerated examples illustrate some possible, non-limiting combinations:

[0123] (Al) An artificial cilium device includes: a substrate; and a voltage-actuated cilia-shaped structure attached ata proximal end to the substrate, the voltage-actuated cilia-shaped structure has a first layer of a first material and a second layer of a second material, the second layer of the second material includes an exposed surface that causes the cilia-shaped structure to, in a working medium, (a) change shape from a first shape to a second shape responsive to application of a first voltage and (b) change shape from the second shape to the first shape responsive to application of a second voltage different than the first voltage.

[0124] (A2) The embodiment (Al) further includes a plurality of voltage-actuated cilia-shaped structures includes the first layer of the first material and the second layer of the second material, the second layer of the second material includes an exposed surface configured to cause the cilia-shaped structure to, in a working medium, change shape from the first shape to the second shape responsive to application of the first voltage and configured to change shape from the second shape to the first shape responsive to application of the second voltage.

[0125] (A3) Either of embodiments (Al) or (A2) further include a controller to regulate application of voltage to the plurality of voltage-actuated cilia-shaped structures.

[0126] (A4) In any of embodiments (Al) - (A3), the plurality of voltage-actuated cilia-shaped structures are individually addressable by the controller.

[0127] (A5) In any of embodiments (Al) - (A4), the plurality of voltage-actuated cilia-shaped structures are arranged in an array.

[0128] (A6) In any of embodiments (Al) - (A5), the plurality of voltage-actuated cilia-shaped structures are arranged to influence surface flow of an aqueous media along the substrate responsive to selective application of the first voltage and/or the second voltage to selected ones of the plurality of voltage-actuated cilia-shaped structures and actuation of the selected ones of the plurality of voltage-actuated cilia-shaped structures to cause the selected ones of the plurality of voltage-actuated cilia-shaped structures to change shape from the first shape to the second shape and/or from the second shape to the first shape.

[0129] (A7) In any of embodiments (Al) - (A6), the first material comprises titanium and the second material comprises platinum.

[0130] (A8) In any of embodiments (Al) - (A7), the first layer of the first material is thinner than the second layer of the second material.

[0131] (Bl) An artificial cilium includes a first actuator, a second actuator, a proximal panel, a middle panel, a distal panel, and wire. The first actuator includes a first passive layer on a first active layer. The second actuator includes a second passive layer on a second active layer. The middle panel is between the proximal panel and the distal panel, and has a length less than a distance between the proximal panel and the distal panel when the proximal panel and the distal panel are coplanar. The wire is (i) electrically connected to the second actuator and (ii) on each of the proximal panel and the distal panel. The first actuator is on each of, and spanning a proximal gap between, the proximal panel and the middle panel. The second actuator is on each of, spanning a distal gap between, the middle panel and the distal panel.

[0132] (B2) In embodiments of (Bl), (i) the first passive layer and the first active layer have different respective surface stresses; and (ii) the second passive layer and the second active layer have different respective surface stresses.

[0133] (B 3 ) In either of embodiments (Bl) or (B2), each of the first passive layer and the second passive layer includes an inorganic material.

[0134] (B4) In any of embodiments (Bl) - (B3), the inorganic material includes at least one of titanium, titanium dioxide, silicon dioxide, a nitride of silicon, and hafnium dioxide, or a combination thereof.

[0135] (B5) In any of embodiments (Bl) - (B4), the first active layer and the second active layer includes at least one of a metal, a transition metal, or a combination thereof.

[0136] (B6) In any of embodiments (Bl) - (B5), the metal is one of gold, silver, and platinum, or a combination thereof.

[0137] (B7) In any of embodiments (Bl) - (B6), the transition metal is one of ruthenium, rhodium, palladium, osmium, iridium, or a combination thereof.

[0138] (B8) In any of embodiments (Bl) - (B7), the first passive layer includes two regions respectively located (i) between the first active layer and the proximal panel, and (ii) between the first active layer and the middle panel; the second passive layer includes three regions located between the first active layer and (i) the proximal panel, (ii) the middle panel, and (hi) the distal panel, respectively.

[0139] (B9) In any of embodiments (Bl) - (B8), the first active layer includes two regions respectively located (i) between the first passive layer and the proximal panel, and (ii) between the first passive layer and the middle panel; the second active layer includes three regions located between the first passive layer and (i) the proximal panel, (ii) the middle panel, and (hi) the distal panel, respectively.

[0140] (BIO) In any of embodiments (Bl) - (B9), the wire and the first active layer are monolithic. [0141] (Bll) In any of embodiments (Bl) - (BIO), when the proximal, the middle, and the distal panels are coplanar in a horizontal plane, each of the proximal, the middle, and the distal panel also intersects a vertical plane that is perpendicular to the horizontal plane.

[0142] (B12) In any of embodiments (Bl) - (Bll), the distance is along a length direction of the artificial cilium, and in a width direction perpendicular to the length direction, a width of the wire is at most one-tenth of a width of the second actuator.

[0143] (B13) In any of embodiments (Bl) - (B12), the distance is along a length direction of the artificial cilium, and in a width direction perpendicular to the length direction, a width of the first actuator is at least four-fifths that of the second actuator.

[0144] (B14) In any of embodiments (Bl) - (B13), the distance is along a length direction of the artificial cilium, each of the proximal gap and the distal gap is between 0.1 micrometer and ten micrometers.

[0145] (B15) In any of embodiments (Bl) - (B14), the distance is along a length direction of the artificial cilium, each of the first actuator and the second actuator has a respective thickness, perpendicular to the length direction, between five nanometers and fifteen nanometers.

[0146] (B16) In any of embodiments (Bl) - (B15), the distance is along a length direction of the artificial cilium, each of the first active layer and the second active layer has a respective thickness, perpendicular to the length direction, that is at least one nanometer.

[0147] (B17) In any of embodiments (Bl) - (B16), the distance is along a length direction of the artificial cilium, each of the proximal panel, the middle panel, and the distal panel has a respective thickness, perpendicular to the length direction, between 0.3 micrometers and 0.6 micrometers.

[0148] (B18) Any of embodiments (Bl) - (B17) further includes a substrate; further includes a first electrode and a second electrode on the substrate, and electrically connected to the first active layer and the second active layer, respectively.

[0149] (Cl) A cilia array includes: a substrate that includes a plurality of electrode pairs thereon; and a linear array of artificial cilia of any one of embodiments (Bl) - (B18). Each artificial cilium of the linear array is electrically connected to a respective electrode pair of the plurality of electrode pairs. [0150] (C2) In embodiments of (Cl), for each artificial cilium of the linear array, the first active layer and the second active layer are electrically connected to a first electrode and a second electrode, respectively, of the electrode pair of the plurality of electrode pair electrically connected thereto.

[0151] (C3) In either of embodiments (Cl) or (C2), the artificial cilia of the linear array is arrayed in an array direction and has a total width i _tot along the array direction. The linear array has a length L _A along the array direction. A fill factor ft _ot /L of the linear array is between s and %.

[0152] (C4) In any of embodiments (Cl) - (C3), the plurality of electrode pairs is a one-dimensional array oriented parallel to the linear array of artificial cilia.

[0153] (C5) Any of embodiments (Cl) - (C4) the linear array is oriented in a horizontal direction, and an additional linear array of artificial cilia of any one of embodiments (Bl) - (B18), each electrically connected to a respective electrode pair of the plurality of electrode pairs, the additional linear array is oriented in a second direction that differs from the horizontal direction.

[0154] (C6) Any of embodiments (Cl) - (C5) a third linear array of artificial cilia of any one of embodiments (Bl) - (B18), each electrically connected to a respective electrode pair of the plurality of electrode pairs.

[0155] (C7) Any of embodiments (Cl) - (C6) the second direction is parallel to the horizontal direction, the third linear array is oriented in a vertical direction that is perpendicular to the horizontal direction and the second direction, and a fourth linear array of artificial cilia of any one of embodiments (Bl) - (B18), each electrically connected to a respective electrode pair of the plurality of electrode pairs, the fourth linear array is oriented in the vertical direction, further includes the linear array, the additional linear array, the third linear array, and the fourth linear array forming a rectangular cilia-unit on the substrate.

[0156] (C8) Any of embodiments (Cl) - (C7) further includes a plurality of additional rectangular cilia-units that, with the rectangular cilia-unit, form an array of rectangular cilia-units on the substrate.

[0157] Changes may be made in the above methods and systems without departing from the scope of the present embodiments. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. Herein, and unless otherwise indicated, the phrase “in embodiments” is equivalent to the phrase “in certain embodiments,” and does not refer to all embodiments. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.