# Self-Propelled Aero-GaN Based Liquid Marbles Exhibiting Pulsed Rotation on the Water Surface

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Aero-GaN Preparation

_{3}gas reacted with each other in the next reaction zone, where at the beginning, the temperature was kept at 600 °C for 10 min to initiate nucleation of GaN on the surface of ZnO microtetrapods, and then increased up to T

_{g}= 850 °C for other 10 min to produce the high quality GaN layer. The flow rates of HCl (15 sml/min), NH

_{3}(600 sml/min) and H

_{2}(3600 sml/min) were maintained constant during the growth process.

#### 2.2. Aero-GaN Liquid Marbles Formation

## 3. Results and Discussions

_{r}= 2πrhrτ, where τ = μdv/dr = μω is the shear stress acting on its lateral surface, μ is the air viscosity, v and ω are the linear and angular velocity and, thus, C

_{r}= 2πr

^{2}hμω = cω. The driving torque C

_{m}can be modeled according to the discussed helicopter effect, assuming dC

_{m}/dt = k(ω

_{0}− ω), so as to have a linear decrement of its rate, where k and ω

_{0}are two constants. Imposing the dynamic equilibrium of the marble, we find Qd

^{2}ω/dt

^{2}+ cdω/dt + kω = kω

_{0}, where Q is the moment of inertia of the marble. In the experiments, no significant viscosity/damping effects are observed. Accordingly, the solution for c ≈ 0 is ω ≈ ω

_{0}+ AcosΩt + BsinΩt, where the fundamental angular frequency of the oscillations is predicted to be Ω = (k/Q)

^{1/2}. The moment of inertia Q scales as M

^{5/3}, where M is the marble mass (the moment of inertia scales as R

^{5}, with R being the characteristic size, while M scales as R

^{3}). The constant k does not have a clear scaling, but two limiting conditions could be envisioned: a negligible scaling, i.e., M

^{0}, or as proportional to c/t (i.e., C

_{r}scales, such as C

_{m}) and, thus, as M

^{1}. As a result, a scaling of the period T = 2π/Ω∝M

^{5/12–5/6}= M

^{0.42–0.83}is theoretically predicted, whereas we observe experimentally (from only the two available experiments; thus, this comparison has to be considered with caution) T∝M

^{0.60}, in agreement with this simple model. Fixing the origin of the time reference system at the stationary point for ω implies dω/dt(0) = 0, and thus, B = 0; accordingly, ω

_{0}represents the mean value of the angular velocity and A = Δω the amplitude of its oscillation, i.e., ω ≈ ω

_{0}+ Δω·cosΩt.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic representation of a single Aero-GaN microtetrapod exhibiting both hydrophobic and hydrophilic properties; (

**b**) an SEM picture taken from a network of Aero-GaN microtetrapods; (

**c**) cross-sectional views of individual microtubes, whose chemical compositions are presented in (

**d**).

**Figure 2.**Time dependence of the speed (r.p.s.—rotation per second) of uniform rotation for liquid marbles with different weights: (

**a**) 2.5 mg; (

**b**) 59.5 mg.

**Figure 3.**Time dependence of the speed of pulsed rotation for liquid marbles with different weights: (

**a**) 6.5 mg; (

**b**) 14.5 mg.

**Figure 4.**(

**a**) Liquid marble floating on water, where the inset represents a digital picture of an elongated liquid marble. (

**b**) Schematic interpretation of the liquid marble on the water surface; (

**c**) the same liquid marble when rotating at high velocities, leading to the formation of a water column.

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**MDPI and ACS Style**

Braniste, T.; Ciobanu, V.; Schütt, F.; Mimura, H.; Raevschi, S.; Adelung, R.; Pugno, N.M.; Tiginyanu, I.
Self-Propelled Aero-GaN Based Liquid Marbles Exhibiting Pulsed Rotation on the Water Surface. *Materials* **2021**, *14*, 5086.
https://doi.org/10.3390/ma14175086

**AMA Style**

Braniste T, Ciobanu V, Schütt F, Mimura H, Raevschi S, Adelung R, Pugno NM, Tiginyanu I.
Self-Propelled Aero-GaN Based Liquid Marbles Exhibiting Pulsed Rotation on the Water Surface. *Materials*. 2021; 14(17):5086.
https://doi.org/10.3390/ma14175086

**Chicago/Turabian Style**

Braniste, Tudor, Vladimir Ciobanu, Fabian Schütt, Hidenori Mimura, Simion Raevschi, Rainer Adelung, Nicola M. Pugno, and Ion Tiginyanu.
2021. "Self-Propelled Aero-GaN Based Liquid Marbles Exhibiting Pulsed Rotation on the Water Surface" *Materials* 14, no. 17: 5086.
https://doi.org/10.3390/ma14175086