Artificial carbon cilium using induced charge electro-osmosis

Artificial cilia are promising as a next generation microfluidic device. In this study, we experimentally report that fibrous carbon wires produced by the self-organization process show cilium motions due to induced charge electro-osmosis (ICEO) under AC electric fields in water. In particular, we experimentally demonstrate that the carbon ICEO cilium with a branching wire structure shows asymmetric beating motion. We believe that our findings will contribute to the research of artificial cilia having asymmetrical motions, which would provide net propulsion in a low Reynolds number regime.


I. INTRODUCTION
The use of fibers and high-aspect-ratio structures is essential for functional structures in biological creatures. 1 In particular, artificial cilia using a hair-like structure are promising as a next generation microfluidic device because of their multi-functionality, such as pumping, mixing, valving, sensing, etc. 2,3 For example, Hanasoge et al. 4 reported that a net flow can be generated in a circular channel by magnetic cilia. Chen et al. 5 reported mixed performance due to magnetic cilia. Alfadhel and Kosel 6 reported a tactile sensor using magnetic nanocomposite cilia with a giant magneto-impedance sensor. Here, one main strategy for cilium fabrication is a top-down approach using photolithography technology, e.g., Pokroy et al. 1 reported the soft-lithography replication method to allow the fabrication of a biomimic array of stable high-aspect-ratio features. The other main strategy is a bottom-up approach using self-organization phenomena, e.g., Vilfan et al. 7 demonstrated self-assembled artificial cilia using magnetic beads and suggested a self-repairing function of their cilia.
Although Vilfan's approach is highly challenging, it requires large magnetic equipment for fabrication, driving, and repairment, and thus, it may not be suitable for total miniaturization of systems. To realize total miniaturization of systems, electrostatic cilia driven by an electric field have an advantage, e.g., Toonder et al. 8 reported that electrostatic cilia with a curled beam structure can generate fluid velocities not in water but in silicone oil. In this context, we have proposed artificial cilia using induced charge electro-osmosis (ICEO) so far; a valve, 9 a pump, 10 and a catcher 11 were examined theoretically, and the basic beating motions were examined experimentally. 12,13 Note that the ICEO cilia work in water can be miniaturized in the future. Thus, ICEO cilia are promising for biomedical applications. However, ICEO cilia that use the self-organization process have not been explored yet.
Therefore, in this study, we experimentally report that fibrous carbon wires produced by the self-organization process 14 show cilium motions due to ICEO under AC electric fields in water. In particular, we experimentally demonstrate that the carbon ICEO cilium with a branching wire structure shows asymmetric beating motion. Furthermore, through the discussion of carbon ICEO cilia, we show the possibility of the metachronal motion due to the difference in the wire length for the carbon ICEO cilium with a simple wire structure. denotes the edge position, w 1 denotes the gap distance between XA and the right electrode, and θ denotes the tilt angle of the graphite rod, where l 0 ≡ |XA − X 0 |. Then, by applying a DC electric voltage V 0 between the electrodes during a time tDC (typically, 30-120 s; SW 2 on), we obtained a carbon wire through a self-wiring phenomenon at the position X 0 [=(X 0 , Y 0 )] on the right-side surface of the graphite rod. Here, we need not prepare any carbon suspension, and the carbon wire has a fibrous network structure microscopically, as shown in Fig. 1(b). In detail, the wire is considered to be an intercalational compound from the composition analysis by energy dispersive xray spectroscopy (EDS). 14 Second, to observe beating motions of the carbon wire, we turned off SW 2 . Then, by applying a rectangular AC voltage of peak value V 0 and frequency f between the right electrode and the graphite rod during a time tAC (SW 1 on), we observed that the tip position X 2 [=(X 2 , Y 2 )] of the carbon wire moved toward the right electrode. Here, we define the displacement h at t as h(t) ≡ |X 2 (t) − X 2 (0)|. Furthermore, we define the provisional wire lengths l 1 and l 2 as l 1 ≡ |X 1 − X 0 | and l 2 ≡ |X 2 (tAC) − X 1 |, where X 1 is a joint position that is considered not to move, and lt(=l 1 + l 2 ) denotes a total provisional wire length. Furthermore, we determined X 2 (t) and h(t) by using the recorded video data of size 1280 × 720 with a frame rate of 25-27 fps.

III. RESULTS
A. Beating motions of the carbon ICEO cilium with a simple structure returning motions at t = 2, 3, and 4 s without the AC electric field. As shown in Fig. 2 (Multimedia view), we observed a large deformation of the beam for the carbon cilia with a simple structure. Figure 3(a) shows the dependence of h on t under the AC electric field at V 0 = 20-40 V and at f = 100 Hz, whereas Fig. 3(b) shows the dependence without the AC electric field. As shown in these figures, the forward and recovery response times were τ f ≃ 1 s and τr ≃ 1.5 s, respectively, although there was an overshoot in a forward stroke at V 0 = 40 V. Figure 3(c) shows the dependence of the maximum velocity V h ≡ dh dt on V 0 . From Fig. 3(c), we found that there is a nonlinearity in V h corresponding to the characteristic of ICEO. Note that the carbon fiber has a conductivity, 14  counter ions) is formed at the tip, and the ions in the double layer moves along the tangential electric field Et. As a result, the ICEO flow velocity 15 is proportional to E 2 0 , and thus, V h (due to the ICEO flow) is also proportional to E 2 0 . Therefore, the behavior shown in Fig. 3(c) is expected under ICEO, and the underlying physics that drive this behavior are considered to be a hydrodynamic interaction due to ICEO. Figure 3(d) shows a picture composed of the six images in Fig. 2 translucently stacked. From Fig. 3(d), we understood that asymmetric motion cannot be observed for the carbon ICEO cilium with a simple structure.
B. Beating motions of the carbon ICEO cilium with a branching structure Figure 4 (Multimedia view) shows the beating motions of the carbon ICEO cilium with a branching structure. As shown in Figs. 4(a)-4(c) (Multimedia view), the shorter branch responded faster than the longer branch to the electric field by the ICEO effect. This is because the bundle fiber structure of the shorter branch produces much ICEO flow than the thin fiber structure of the longer branch. Furthermore, as shown in Figs. 4(d)-4(f) (Multimedia view), the recovery of the deformation near the common root of the cilium was observed at t = 5 s, and then, the shorter and longer branches return while attracting each other until t = 7 s through the interaction due to the tangled thin wires. This is why the shorter branch seems to come back late at t = 7 s. Probably, the interaction between branches and the difference in the ICEO driving force are the origin of the asymmetric motion of the carbon ICEO cilium with a branching structure. Figure 5 shows the characteristics of the ICEO cilium with a branching structure. Specifically, Fig. 5(a) shows the dependence of h on t under the AC electric field, whereas Fig. 5(b) shows the dependence without the AC electric field. In Figs. 5(a) and 5(b), h 1 (t) ≡ |X 2,1 (t) − X 2 (0)| and h 2 (t) ≡ |X 2,2 (t) − X 2 (0)|, where X 2,1 and X 2,2 denote the tip positions of the longer and shorter branches, respectively. As shown in these figures, the forward and recovery response times of X 2,1 were τ f ≃ 1 s and τr ≃ 4 s, respectively, whereas the forward and recovery response times of X 2,2 were τ f ≃ 0.5 s and τr ≃ 4 s, respectively. Note that although the recovery speed of X 2,2 was slower than that of X 2,1 until t = 5 s, their recovery times were almost the same. Figure 5(c) shows the dependence of V h on f. From Fig. 5(c), we found that V h of the carbon ICEO cilium is approximately constant at f ≤ 10 5 Hz although it becomes small at f > 10 5 Hz because of its insufficient charging time to the electric double layer. Figure 5(d) shows a picture composed of the six images in Fig. 5 translucently stacked. From Fig. 5(d), we found that asymmetric motion can be observed for the carbon ICEO cilium with a branching structure.

IV. DISCUSSION
A. Possibility of metachronal motion Here, an elastic force of the carbon wire makes the cilium return to the initial state, and the balance between the elastic force and the flow resistance determines the returning velocity. Thus, we may control the returning time by controlling the synthesis parameters.

B. Meaning of our study
In this study, we have reported that fibrous carbon wires produced by the self-organization process show cilium motions due to ICEO under AC electric fields in water although self-assembled cilia using magnetic beads were already reported. 7 This carbon ICEO cilium intrinsically does not require large equipment for fabrication, driving, and repairment. Thus, it is suitable for total miniaturization of systems. In particular, since the carbon cilium can be produced by a simple self-organization process, 14 we may produce a channel covered with the fine cilium (or the cilia) at a low cost in the future.

C. Possibility of miniaturization
Although we have demonstrated the carbon ICEO cilium using a carbon rod, 14 the carbon rod is not always required. In other words, we may use various carbon self-wiring processes 16 for making a channel covered with our carbon ICEO cilium. In fact, a bundle of carbon wires can be produced between Cu electrodes without the carbon rod if graphite material exists in the solution [please see Fig. 5(a) of our previous paper 14 ]. Thus, we may develop the path to miniaturization of the carbon cilium in the future. Here, we emphasize that the path to miniaturization offers interesting potential applications like low Re pumps although challenges remain for realization, as outlined in Sec. IV D.

D. Outstanding challenges
Many challenges remain for the self-organization process that produces carbon wires, e.g., the control of (1) thickness, (2) length, (3) direction, (4) position, and (5) pattern. In particular, it is a great challenge to make carbon wires grow in a regular pattern, ordered by length. Potential approaches to overcome these challenges are, e.g., (i) to control the carbon concentration, (ii) to control the growing time, (iii) to control the direction of the electric field, and (iv) to place seeds (e.g., graphite films) in the desired positions. Furthermore, by achieving a periodic pattern of electric fields, we may obtain a regular pattern of carbon wires. For example, by applying a voltage between a rectangular electrode and a wire placed above the edge of the rectangular electrode, we obtain asymmetrical electric fields. Thus, we may obtain a regular pattern by arranging the units since the carbon wire grows in the direction of the electric fields. By these approaches, we will obtain the desired applications, that is, in the future, we will demonstrate actual metachronal waves of a bundle of carbon wires growing in a regular pattern and will observe the net flow due the metachronal motion. Note that a net flow with a hair-like structure such as the structure of carbon wires has not been demonstrated yet although Hanasoge et al. 4 showed a net flow with a plate-like cilium structure.

V. CONCLUSION
In conclusion, we have demonstrated that fibrous carbon wires produced by the self-organization process show cilium motions due to ICEO under AC electric fields in water. In particular, we have demonstrated that the carbon ICEO cilium with a branching wire structure shows asymmetric beating motion. Furthermore, through the discussion of carbon ICEO cilia, we have shown the possibility ARTICLE scitation.org/journal/adv that the carbon ICEO cilium with a simple wire structure shows different response times due to the difference in the wire length, and thus, it can be applied to a metachronal motion.

DATA AVAILABILITY
The data that support the findings of this study are available within the article.