Controlled Multidirectional Particle Transportation by Magnetic Artificial Cilia

Abstract

Manipulation of particles in a controllable manner is highly desirable in many applications. Inspired by biological cilia, this article experimentally and numerically demonstrates a versatile particle transportation platform consisting of arrays of magnetic artificial cilia (MAC) actuated by a rotating magnet. By performing a tilted conical motion, the MAC are capable of transporting particles on their tips, along designated directions that can be fully controlled by the externally applied magnetic field, in both liquid and air, at high resolution (particle precision), with varying speeds and for a range of particle sizes. Moreover, the underlying mechanism of the controlled particle transportation is studied in depth by combining experiments with numerical simulations. The results show that the adhesion and friction between the particle and the cilia are essential ingredients of the mechanism underlying the multidirectional transportation. This work offers an advanced solution to controllably transport particles along designated paths in any direction over a surface, which has potential applications in diverse fields including lab-on-a-chip devices, in vitro biomedical sciences, and self-cleaning and antifouling.

Keywords: adhesion and friction; directional microparticle transportation; magnetic artificial cilia; particle manipulation; rotating magnetic field.

Figure 1

Experimental results, showing schematically the magnetic artificial cilia (MAC) fabrication and actuation, as well as the resulting MAC, cilia motion, and particle transportation. (A) Schematic drawing of the fabrication process of the MAC (see Materials and Methods). CIP represents the used magnetic particles carbonyl iron powder. (B) Top- and side-view scanning electron microscopy images of a fabricated MAC array; the MAC have a diameter, length, and pitch of 50, 350, and 450 μm, respectively. (C1,C2) Schematics of the actuation setup with MAC integrated in a circular-channel chip placed on a supporting plate and underneath a microscope (see Figure S1 for more details). Reproduced with permission from ref (35). Copyright 2018 Elsevier B.V. (C3) Schematic drawing of a rotating cilium performing a tilted conical motion in perspective view; the direction of the effective stroke (ED, red arrow), the tilting direction (TD, yellow arrow), and the amplitude of the cilia motion (α, in this article α = 36°) are indicated. (D) Top view of actuated MAC: 25 superposed frames completing one full rotation cycle; the MAC perform a tilted conical motion with the effective stroke direction (red arrow) and the tilting direction (yellow arrow) as indicated in the image. (E) Top-view time-lapse trajectory of a particle transported along one direction (blue arrow) in deionized water. The particle is a 500 μm polylactic acid particle and the MAC have a pitch of 450 μm, with the cilia performing a tilted conical motion at 1 Hz; the effective stroke direction and the tilting direction are indicated in the image and are the same as in panel D. The image is an overlay of 14 images of the particle at different locations during the transportation. See Movie S1. (F) Top-view time-lapse trajectory of a transported particle along a “z”-shaped trajectory in deionized water. During this experiment, the direction of the effective stroke and the tilting direction were changed a number of times to change the direction of the particle motion. The image is an overlay of 22 images of the particle at different locations. See Movie S2.

Figure 2

Particle transportation mechanism. (A–E) Perspective view of a particle transportation cycle, shown in snapshots taken from our simulations. The cilia are represented as strings of beads. The particle is made semitransparent to show the particle and cilia positions clearly—see the text for a detailed explanation. (F) Snapshots from both the simulations (top view and side view) and the experiments (top view), in which a 500 μm PLA particle is transported one cilia pitch. The red arrow, yellow arrow, and blue arrow are the effective stroke direction, cilia tilting direction, and particle transportation direction, respectively; see Movie S1. From panel A to panel F, all computational parameters are as stated in Table 1 except the adhesive strength which is D = 8 × 10^–13 J and the cilia rotational frequency is 7 Hz. (G) Top-view time-lapse computed trajectory of a particle transported along one direction at 1 Hz; see Movie S1. (H) Top-view time-lapse computed trajectory of a transported particle along a “z”-shaped trajectory using the same protocol as in the experiment shown in Figure 1F at 7 Hz; see Movie S3. For panels G and H, all computational parameters are stated in Table 1.

Figure 3

Transportation of PLA particles in deionized water. (A) Transportation speed as a function of the actuation frequency (equal to the rotation frequency of the cilia) for both the experiments and the numerical simulations. Each experimental data point was obtained by averaging the results of at least three identical but separately performed experiments; the error bar represents the standard deviation. The numerical results were obtained with C_fr = 1 × 10^–1 N/m and two values for the adhesive strength: D = 3.2 × 10^–13 J and D = 8 × 10^–13 J (and all other parameters as stated in Table 1). (B) Transportation inefficiency as a function of the actuation frequency for both the experiments and the numerical simulations based on the data from panel A. This quantity is defined as the average number of rotation cycles of the cilia needed to advance the particle one cilia pitch forward. The larger the number, the less efficient the transportation. The error bars are the standard deviations of at least three identical but independent experiments. In panels A and B, the particle is a 500 μm PLA particle with a pitch of 450 μm. (C) Particle transport speed as a function of adhesive strength D and friction constant C_fr, as found from the numerical simulations, for a fixed actuation frequency of 7 Hz. The current experiments are best fitted using D = 3.2 × 10^–13 J and C_fr = 1 × 10^–1 N/m, indicated in the graph as the left white asterisk. The right white asterisk corresponds to D = 8 × 10^–13 J and C_fr = 1 × 10^–1 N/m. Both adhesive strengths correspond to panels A and B. All other parameters are as stated in Table 1. (D) Transportation speed as a function of the particle size to cilia pitch ratio in both water (red bars) and air (blue bars) at an actuation frequency of 1 Hz. The PLA particles have a size range from 400 to 800 μm, and the cilia arrays have a pitch of 350, 450, or 550 μm. The error bars are the standard deviations of at least three identical but independent experiments.

Figure 4

Multidirectional particle transportation over a ciliated surface by changing the actuation mode of the cilia. (A) Different modes of cilia motion, in which the tilting direction is varied in the four different panels between 0, 90, 180, and 270° (yellow arrow); for each TD, there are two possible effective stroke directions indicated by the dashed black and white arrows; the corresponding particle transportation directions are indicated by the solid black and white arrows. (B) Particle trajectories obtained from numerical simulations, starting at the area center, in which the tilting direction and the effective stroke direction were varied. The parameters used were those in Table 1, and the rotation frequency was 1 Hz. (C) Superposed time sequence images (top view) of a 500 μm PLA particle transported on a cilia array with a pitch of 450 μm, rotating at a frequency of 1 Hz. By changing mode of actuation between situations shown in panel A during the experiment, the particle is made to travel along a “z”-shaped trajectory (see also Movie S2, in which the effective stroke, tilting directions and particle transportation direction are shown over time). The blue arrows show particle transportation direction.