Bidirectional Wave-Propelled Capillary Spinners

The design of novel and tunable experimental systems for synthetic active materials is of immense interest. We present one such design that uses the physics of self-generated waves to realize a tunable active spinner system.
Bidirectional Wave-Propelled Capillary Spinners
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Introduction

Active matter systems are comprised of active particles which convert energy from the environment into directed propulsion. Synthetic active systems have recently gained prevalence as a means to study out-of-equilibrium behavior in a controlled manner. One such experimental system which could serve as a tunable platform is particles at a vibrating liquid interface which, coupled with some form of symmetry-breaking, can lead to self-propulsion. The relative motion between the object and the fluid leads to the generation of surface waves which in turn propel the object.  In this study, we used a vibrating liquid interface, coupled with floating chiral objects called spinners, to study how stable, bidirectional, rotational motion can be achieved.

Main Results

We found that by designing spinners with size on the order of a centimeter, the object would steadily spin when the liquid bath is vertically vibrated at a frequency, f, and acceleration amplitude, γ. The angular velocity of the spinner is influenced by the driving parameters (f and γ), the geometric design of the spinner, and the fluid's material properties. To produce the spinners, a readily available silicone rubber was utilized, which is commonly found in most art stores. By exploiting the material's inherent hydrophobicity, the spinners are able to float on the surface supported by buoyancy and surface tension forces. A step-by-step Instructables tutorial on how to make such floaters can be found here.

In this study, we focused on varying the size of the spinner, frequency, and acceleration to understand the underlying physics governing the observed rotation. We used a 5-arm design for the entire study, but observed the same qualitative phenomena for different chiral geometric designs in preliminary experiments. We quickly were met with the surprising observation that as the frequency increased, the speed of the spinner varied non-monotonically, and at a critical frequency, f*, the rotation speed came to a halt (Ω=0). Further increasing the frequency, the spinner rotated in the opposite direction! In Figure 1, we summarize these findings, and we conclude that the phenomena comes down to a balance of length-scales between the wavelength (itself being a function of the driving frequency) and the size of the spinner (which we characterized by L, the wedge opening size). Specifically, the emitted waves' spatial structure, leading to regions of constructive interference (emanating from the center of each wedge) and destructive interference led to the observed bidirectionality.

Figure 1: Bidirectional rotation and the flipping frequency.  (a) Plot of the flipping frequency f* at which  Ω= 0 for spinners of multiple sizes. For f < f* the spinner rotates counterclockwise and clockwise for f > f*. In (b-d), we use a shadowgraph imaging technique to visualize the wave field generated by the oscillating spinner. In (e-g) by distributing tracer particles at the interface, surface flows are visualized demonstrating qualitative changes below, at, and above the flipping frequency.

Given our understanding of the relationship between geometry and wave-propulsion for a chiral object, we generalized the idea to a Chiral Active Particle (CAP) capable of both translating and rotating. To design such a particle, we decided on a "Pac-man" like shape which combined the asymmetric chiral wedge of the spinner with a fore-aft asymmetry leading to rotation and translation respectively. Now by varying the frequency in real-time, 2D steering on the vibrating surface was possible as shown in Figure 2.

Figure 2: Remote steering of a "Pac-Man''-shaped chiral active particle (CAP) via modulation of the driving frequency. The CAP translates in the direction of the wedge opening, but simultaneously rotates with a frequency-dependent direction. By changing the driving frequency in real-time, the CAP is able to navigate a small obstacle course.

Perspectives and Future Directions

With a picture of the underlying physics at the single active particle now established, we hope to consider questions relating to collective motion where multiple spinners are able to interact via their waves and surface flow-fields. Such long-range hydrodynamic interactions between active particles allow us to probe questions in collective motion and out-of-equilibrium physics at intermediate Reynolds’ number in a controllable table-top setup.

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