High-speed broadband elastic actuator in water using induced-charge electro-osmosis with a skew structure

An artificial cilium using ac electro-osmosis (ACEO) is attractive because of its large potentiality for innovative microfluidic applications. However, the ACEO cilium has not been probed experimentally and has a shortcoming that the working frequency range is very narrow. Thus, we here propose an ACEO elastic actuator having a skew structure that broadens a working frequency range and experimentally demonstrate that the elastic actuator in water can be driven with a high-speed ($\sim 10$ Hz) and a wide frequency range ($\sim 0.1$ to $\sim 10$ kHz). Moreover, we propose a simple self-consistent model that explains the broadband characteristic due to the skew structure with other characteristics. By comparing the theoretical results with the experimental results, we find that they agree fairly well. We believe that our ACEO elastic actuator will play an important role in microfluidics in the future.

Figure 1

A schematic view of an ACEO elastic actuator having a skew structure in water. Here, for structures A, B, and C, respectively, $L=1.75$, 4.25, and 4.04 mm; $L_2=3.68$, 3.81, and 3.67 mm; $H_1=0.10$, 0.90, and 0.10 mm; $H_2=0.20$, 1.59, and 0.74 mm; $d_L=0.11$, 0.54, and 0.50 mm; $d_H=0.10$, 0.69, and 0.64 mm; $d_W=0.37$, 0.27, and 0.89 mm; $d_0=0.40$, 0.92, and 1.20 mm; $W_1=1.00$, 2.10, and 1.20 mm; and $W_2=0.37$, 0.23, and 0.79 mm. $W=1$ mm and the thickness of the gold beams is $1\mu \mathrm{m}$; $L_c=30$ mm and $H_c=6$ mm. (a, b) Top and side views of the skew structure. (c) Mechanism and motion of the ACEO elastic actuator; “1” shows an ACEO flow at the edge of the gold elastic beam.

Figure 2

Initial structures and their motions (top view). In (a), (c), and (e), pictures show the top views of structures A, B, and C, respectively, at the initial state. Further, in (b), (d), and (f), the black regions of the tips of the beam edges show the motions during the initial and final states when we applied an ac voltage of $V_0=20$ V and $f=100$ Hz between electrodes.

Figure 3

Schematic view of the electrocircuit model on the skew structure.

Figure 4

Broadening of the working frequency due to a skew structure based on the simple model. (a) Dependences of $F^{\text{LPF}}$ and $F^{\text{HPF}}$ on $f$. (b) Dependence of $F^{\text{BPF}}$ on $f$. (c) Dependence of $F^{\text{max}}{d}_H/d_0$ on $d_w$. (d) Dependences of $f^{\text{LPF}}$ and $f^{\text{HPF}}$ on $d_w$.

Figure 5

Dependences of $h$ on $t$ for structures A to C. Here, lines show the theoretical results using Eq. (15), whereas characters show the experimental results. In (a), (c), and (e), $h_{\text{max}}^{\text{theory}}$ becomes large as $V_0$ increases. In (b), (d), and (f), thin (thick) lines denote $f=10$ to 1000 Hz ($f=10$ to 100 kHz) and the width of dots becomes larger as $f$ becomes larger. (a, c, e) Dependences of $h$ on $t$ for structures A, B, and C, respectively, at $f=100$ Hz. (b, d, f) Dependences of $h$ on $t$ for structures A, B, and C, respectively, at $V_0=20$ V.

Figure 6

Dependences of $h$ and $u_a$ on $V_0$ and $f$ for structures A to C. Here, a line shows the theoretical results using Eqs. (9) and (13), whereas characters show the experimental results using the image processing method and Eq. (10). (a, c) Dependences of $h_{\text{max}}$ and $u_a$, respectively, on $V_0$ at $f=100$ Hz. (b, d) Dependences of $h_{\text{max}}$ and $u_a$, respectively, on $f_0$ at $V=20$ V.