^{1,a)}, Guillaume Petit-Pierre

^{1}and Jurg Dual

^{1}

### Abstract

Contactless rotation of non-spherical particles has been modeled and experimentally achieved using ultrasonic manipulation. For this purpose an acoustic radiation torque was generated by a time-varying pressure field resulting in a change of orientation of the potential well. The rotation method is based on amplitude modulation of two orthogonal ultrasonic modes. The force potential field has been used to evaluate the different modes and actuations to achieve rotation. Experiments have been performed in micro devices with copolymer particles and glass fibers at frequencies in the megahertz range. A continuous rotation was successfully demonstrated and the method allowed to stop the rotation at arbitrary angular positions.

I. INTRODUCTION

II. THEORY

III. EXPERIMENTAL SETUP

IV. RESULTS

V. CONCLUSION

### Key Topics

- Torque
- 30.0
- Acoustic waves
- 17.0
- Acoustic standing waves
- 12.0
- Ultrasonics
- 12.0
- Viscosity
- 9.0

## Figures

Contour plot sequence of the Gor'kov force potential as a result of amplitude change in the *x* and *y* direction, resulting from superposition of two in phase cosine functions with identical frequency and amplitudes *A* _{1} and *A* _{2}. The bright gray lines are potential maxima, the black lines are indicating the potential minima. The black arrow is representing a fiber located at one of the force potential minima.

Contour plot sequence of the Gor'kov force potential as a result of amplitude change in the *x* and *y* direction, resulting from superposition of two in phase cosine functions with identical frequency and amplitudes *A* _{1} and *A* _{2}. The bright gray lines are potential maxima, the black lines are indicating the potential minima. The black arrow is representing a fiber located at one of the force potential minima.

(a) Definition of the rotation angle *α* for a fiber. (b) Rotation angle and corresponding amplitudes for a variation of one of the amplitudes while the other is set to 1. (c) Sinusoidal variation of the amplitudes leads to a linear variation of the angle *α* for equal maximum amplitudes (black). The influence of unbalanced amplitudes is shown with the gray curves.

(a) Definition of the rotation angle *α* for a fiber. (b) Rotation angle and corresponding amplitudes for a variation of one of the amplitudes while the other is set to 1. (c) Sinusoidal variation of the amplitudes leads to a linear variation of the angle *α* for equal maximum amplitudes (black). The influence of unbalanced amplitudes is shown with the gray curves.

Linear amplitude variation of *A* _{1} and *A* _{2} for a rotation of 180°. *A* _{1} and *A* _{2} are varied over half a rotation cycle *T _{M} * between 1 and −1.

Linear amplitude variation of *A* _{1} and *A* _{2} for a rotation of 180°. *A* _{1} and *A* _{2} are varied over half a rotation cycle *T _{M} * between 1 and −1.

Contour plot sequence of the mean square fluctuations of (a) the pressure and (b) the velocity for one wavelength in the *x* and *y* direction. The amplitude *A* _{1} is varied from 1 to 0 and *A* _{2} is maintained constant at 1.

Contour plot sequence of the mean square fluctuations of (a) the pressure and (b) the velocity for one wavelength in the *x* and *y* direction. The amplitude *A* _{1} is varied from 1 to 0 and *A* _{2} is maintained constant at 1.

(Color online) (a) Exploded view of the micromanipulation device with a detailed view of the bottom electrode of the piezoelectric transducer with its strip electrodes. (b) Picture of the device showing the cone shaped inlet channels and the fluidic chamber (3 × 3 mm^{2}). (c) Picture of the device from the bottom showing the piezoelectric transducer with the strip electrodes and the wire connections.

(Color online) (a) Exploded view of the micromanipulation device with a detailed view of the bottom electrode of the piezoelectric transducer with its strip electrodes. (b) Picture of the device showing the cone shaped inlet channels and the fluidic chamber (3 × 3 mm^{2}). (c) Picture of the device from the bottom showing the piezoelectric transducer with the strip electrodes and the wire connections.

(Color online) A 180° rotation of clumps of copolymer particles (Ø17 *μ*m) with amplitude modulation and an excitation frequency of 1689kHz. The applied voltage is 30 V. The pictures [(a)–(i)] are 0.86 × 0.86 mm^{2} details of a whole cavity and the elapsed time is given in each part.

(Color online) A 180° rotation of clumps of copolymer particles (Ø17 *μ*m) with amplitude modulation and an excitation frequency of 1689kHz. The applied voltage is 30 V. The pictures [(a)–(i)] are 0.86 × 0.86 mm^{2} details of a whole cavity and the elapsed time is given in each part.

Angular position of a particle clump plotted over time for a rotation of 360°. The black dots represent the angle of the clump for each frame in the video. The gray line is the average expected angular position at a rotation speed of 44 rpm (rotation time *T _{M} * = 1.36 s).

Angular position of a particle clump plotted over time for a rotation of 360°. The black dots represent the angle of the clump for each frame in the video. The gray line is the average expected angular position at a rotation speed of 44 rpm (rotation time *T _{M} * = 1.36 s).

(Color online) A 180° rotation of a glass fiber. The images are taken from a video. They correspond to a 0.5 × 0.5 mm^{2} area inside the chamber. The actuation frequency is 1085 kHz.

(Color online) A 180° rotation of a glass fiber. The images are taken from a video. They correspond to a 0.5 × 0.5 mm^{2} area inside the chamber. The actuation frequency is 1085 kHz.

Angular position of the fiber plotted over time for two complete rotations (720°). The black dots represent the angle of the fiber for each frame in the video. The gray line is the average expected angular position at a rotation speed of 36 rpm (rotation time *T _{M} * = 1.67 s).

Angular position of the fiber plotted over time for two complete rotations (720°). The black dots represent the angle of the fiber for each frame in the video. The gray line is the average expected angular position at a rotation speed of 36 rpm (rotation time *T _{M} * = 1.67 s).

Force potential plot for a (4,2) and (2,4) mode used for rotation of a glass fiber with amplitude modulation. The black arrow is representing a fiber, located at one force potential minimum like in the experiment.

Force potential plot for a (4,2) and (2,4) mode used for rotation of a glass fiber with amplitude modulation. The black arrow is representing a fiber, located at one force potential minimum like in the experiment.

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