Figure 7. BCA channel simulation results, (A) Simulation result of particle density movement due to each cilia and field. The color scale shows the concentration of particles and (B) Relative number of particles counted according to the x-axis position throughout time; (i) Symmetric BCA + Strike Magnetic Field, (ii) Asymmetric BCA + Strike Magnetic Field, (iii) Symmetric BCA + Rotating Magnetic Field, and (iv) Asymmetric BCA + Rotating Magnetic Field
The particle distributions of the simulation confirmed that the motion of the fluid flow was largely divided according to the applied field type (strike and rotating field) (Figure. 7 and Movie S7 ). When the strike magnetic field was applied, the fluid was pumped, which generally moved the particles forward. When the rotating magnetic field was applied, the fluid was mixed, which quickly dispersed the particles (Figure. 7A). This is similar to the experimental results (Figure. 6A), and could also be verified by the change in the number of particles (Figure. 7B). When the strike magnetic field was applied, in the symmetric BCA channel, the position where the particle number peaks had a strong property of moving forward rather than spreading (Figure. 7B(i)). In contrast, in the asymmetric BCA channel, the particles did not move forward but stayed in the middle (Figure. 7B(ii)). When the rotating magnetic field was applied, the particles were evenly dispersed throughout the symmetric BCA channel but did not spread well up to the inlet and outlet (Figure. 7B(iii)). However, it was found that the particles were evenly distributed up to the inlet and outlet throughout the asymmetric BCA channel (Figure. 7B(iv)). Through the simulations, it was also verified that when the strike magnetic field was applied, the symmetric BCA channel could show strong fluid pumping, and when the rotating magnetic field was applied, the asymmetric BCA could show distinct fluid mixing.
3. Discussion
The proposed RMS cilia array can be easily and conveniently fabricated using a self-assembly method, and the magnetization direction of the cilia can be reprogrammed. The fabricated cilia had a large aspect ratio (approximately 10), similar to the actual in vivo cilia, and could mimic the shape and movement of the actual cilia compared to previously reported studies. However, the size of the fabricated cilia (approximately 1–3 mm in length) is considerably larger than that of the actual cilia (approximately 4–10 µm in length). The size of the proposed cilia could be significantly affected by the particle size of the NdFeB powder, the external magnetic field, and the viscosity of the silicone. [36] Therefore, if NdFeB powder with small particle size, strong external magnetic field, and low silicon viscosity is used, it is expected that cilia with a smaller size can be fabricated. However, in this study, we attempted to mimic the shape and movement of real cilia through the RMS cilia array using the proposed self-assembly method and reprogramming.
The UCA channel was constructed using the RMS cilia array, and when two types of magnetic fields (strike and rotating magnetic fields) were applied to the channel, the asymmetric movement of the natural cilia could be mimicked and the generated fluid flow in the UCA channel was observed. When a rotating magnetic field is applied, MCW can be implemented; however, when a strike magnetic field is applied, MCW cannot be realized. However, in both types of magnetic fields, it was confirmed that the moving direction of the fluid changed sequentially, advancing the flow. When a magnetic field was applied, the fluid slowly moved forward as the fluid stagnation zone moved intermittently according to the movement of the cilia (Figure. 3C). However, when the rotating magnetic field was applied, the cilia moved to form an MCW, which moved the stagnation zone of the fluid sequentially (Figure. 3D). Therefore, the fluid in the UCA channel can advance faster under a rotating magnetic field.
In this study, symmetric and asymmetric BCA channels were constructed using the RMS cilia array, and when two types of magnetic fields (strike and rotating magnetic fields) were applied to each channel, the fluid flow was observed through experimentation and simulation. First, in the symmetric BCA channel, the upper and lower cilia arrays have the same magnetization direction along the x-axis and opposite magnetization directions along the y-axis. Therefore, when the strike magnetic field was applied, the upper and lower cilia arrays moved symmetrically, thereby creating a propelling fluid flow. On the other hand, when the rotating magnetic field was applied, the upper and lower cilia arrays showed propagation of the MCW in the same direction, but a phase difference occurred, which caused the rotating fluid flow rather than the propelling fluid flow. Additionally, in the asymmetric BCA channel, the upper and lower cilia arrays had opposite magnetization directions on both the x- and y-axes. Therefore, when the strike magnetic field was applied, the upper and lower cilia arrays moved in the opposite direction, which caused the fluid flow to return to the middle instead of advancing. In contrast, when the rotating magnetic field was applied, the upper and lower cilia arrays exhibited MCW propagation in opposite directions, resulting in a strong rotating fluid flow that caused the mixing of the fluid in the channel. As a result, when the strike magnetic field was applied to the symmetric BCA channel, the advancing fluid flow was generated owing to the symmetrical movement of the two cilia arrays, which is advantageous for fluid pumping. When a rotating magnetic field was applied to the asymmetric BCA channel, the propagation directions of the MCW of the upper and lower cilia arrays were reversed, resulting in an asymmetrically rotating fluid flow, which is advantageous for fluid mixing.
All fluid experiments were conducted in a rectangular open channel with the inlet and outlet of 8 mm x 5 mm, and we used 70% glycerol diluted with distilled water which has a density of 1182.7 kg/m3 and a viscosity of 22.25 cp.[37] Herein, when the images of the UCA and BCA channel test results were analyzed, the flow velocity caused by the RMS cilia array has ranged from a minimum of about 0.2758 mm/s to a maximum of about 0.8328 mm/s. Based on the results, the Reynolds numbers in the experiments were calculated as the ranges from a minimum of 0.3222 to a maximum of 0.9728, which corresponds to the laminar flow section. Therefore, it is expected that repeatable results can be obtained when the experiment is executed under the above conditions.
In this study, to verify the experimental results, we conducted a simulation that showed trends very similar to those of the experiments. However, compared to the experimental results, the fluid flow for each magnetic field showed a similar trend, but there was a difference in the velocity of the fluid. This could be because of the limitations of the simulation. That is, a simplified model of the RMS cilia array was used in the simulation, but this model is not exactly equivalent and differs in terms of the pitch between the cilium, cilia length, and cilia thickness. In addition, the simulation was performed in a two-dimensional space, and because the cilia were recognized as a wall, the particles used could not pass through the cilia, and the fluid flow was significantly affected by the cilia structure. However, because the cilia array used in the experiment was arranged in a three-dimensional space, the particles in the fluid could pass through the space between cilia. In the future, for a more accurate simulation, it will be necessary to construct a precise simulation model with a shape similar to the cilia array used in the experiment and analyze the three-dimensional space of the simulation model.
4. Conclusion
In this study, the RMS cilia array was fabricated using a simple self-assembly method and had a shape and motion that was more similar to that of the natural cilia array than in previous studies. Using the RMS cilia array, a UCA channel was constructed, and by applying strike and rotating magnetic fields, the motion of the RMS cilia array and the resulting fluid flows were confirmed through experiments and simulations. Consequently, when the rotating magnetic field was applied, a clear MCW appeared, and the advancing movement of the particles in the fluid was also prominent. In addition, symmetric and asymmetric BCA channels were prepared and operated by applying strike and rotating magnetic fields, and the motion of the RMS cilia array in the BCA channels and the resulting fluid flows were confirmed through experiments and simulations. As a result, when the strike magnetic field was applied to the symmetric BCA channel, fluid pumping was observed, and when the rotating magnetic field was applied to the asymmetric BCA channel, fluid mixing was observed. Based on the above results, it is expected that the proposed RMS cilia array can be applied quickly and easily to lab-on-a-chip or microfluidic channels that require fluid mixing or pumping.
5. Experimental Section/Methods