Viscous torque on spherical micro particles in two orthogonal acoustic standing wave fields.

This paper reports the experimental results of the acoustic rotation of spherical micro particles because of two orthogonal standing waves. When the standing waves are excited at equal frequency but with a phase shift between two external voltage signals there is an acoustic streaming around the particles. This streaming is due to a time averaging of the acoustic wave field and produces a nonzero viscous torque on the particles, driving them to rotate. The work investigates the micro-particle rotation due to the viscous torque and predict the particle's steady state rotational velocity. The previous theoretical discussions [Nyborg, J. Acoust. Soc. Am. 85, 329-339 (1958); Lee and Wang, J. Acoust. Soc. Am. 85, 1081-1088 (1989)] of the viscous torque on a non-rotating sphere are expanded to allow free rotations. The analytical calculations provide a deeper understanding of the viscous torque and explain the experimental observations of rotating particles. A macroscopic experimental device is designed to provide the necessary boundary conditions for the viscous torque to rotate spherical particles. The experiments not only show good agreement with the analysis, but also demonstrate that the viscous torque due to acoustic streaming may dominate for the case of near-spherical particle dynamics.

Bring It to the Pitch: Combining Video and Movement Data to Enhance Team Sport Analysis.

Analysts in professional team sport regularly perform analysis to gain strategic and tactical insights into player and team behavior. Goals of team sport analysis regularly include identification of weaknesses of opposing teams, or assessing performance and improvement potential of a coached team. Current analysis workflows are typically based on the analysis of team videos. Also, analysts can rely on techniques from Information Visualization, to depict e.g., player or ball trajectories. However, video analysis is typically a time-consuming process, where the analyst needs to memorize and annotate scenes. In contrast, visualization typically relies on an abstract data model, often using abstract visual mappings, and is not directly linked to the observed movement context anymore. We propose a visual analytics system that tightly integrates team sport video recordings with abstract visualization of underlying trajectory data. We apply appropriate computer vision techniques to extract trajectory data from video input. Furthermore, we apply advanced trajectory and movement analysis techniques to derive relevant team sport analytic measures for region, event and player analysis in the case of soccer analysis. Our system seamlessly integrates video and visualization modalities, enabling analysts to draw on the advantages of both analysis forms. Several expert studies conducted with team sport analysts indicate the effectiveness of our integrated approach.

Numerical simulation of micro-particle rotation by the acoustic viscous torque.

We present the first numerical simulation setup for the calculation of the acoustic viscous torque on arbitrarily shaped micro-particles inside general acoustic fields. Under typical experimental conditions, the particle deformation plays a minor role. Therefore, the particle is modeled as a rigid body which is free to perform any time-harmonic and time-averaged translation and rotation. Applying a perturbation approach, the viscoacoustic field around the particle is resolved to obtain the time-averaged driving forces for a subsequent acoustic streaming simulation. For some acoustic fields, the near-boundary streaming around the fluid-suspended particle induces surface forces on the nonrotating particle that integrate into a non-zero acoustic viscous torque. In the equilibrium state, this torque is compensated by an equal and opposite drag torque due to the particle rotation. The rotation-induced flow field is superimposed on the acoustic streaming field to obtain the total fluid motion around the rotating particle. In this work, we only consider cases within the Rayleigh limit even though the presented numerical model is not strictly limited to this regime. After a validation by analytical solutions, the numerical model is applied to challenging experimental cases. For an arbitrary particle density, we consider particle sizes that can be comparable to the viscous boundary layer thickness. This important regime has not been studied before because it lies beyond the validity limits of the available analytical solutions. The detailed numerical analysis in this work predicts nonintuitive phenomena, including an inversion of the rotation direction. Our numerical model opens the door to explore a wide range of experimentally relevant cases, including non-spherical particle rotation. As a step toward application fields such as micro-robotics, the rotation of a prolate ellipsoid is studied.

Imaging the position-dependent 3D force on microbeads subjected to acoustic radiation forces and streaming.

Acoustic particle manipulation in microfluidic channels is becoming a powerful tool in microfluidics to control micrometer sized objects in medical, chemical and biological applications. By creating a standing acoustic wave in the channel, the resulting pressure field can be employed to trap or sort particles. To design efficient and reproducible devices, it is important to characterize the pressure field throughout the volume of the microfluidic device. Here, we used an optically trapped particle as probe to measure the forces in all three dimensions. By moving the probe through the volume of the channel, we imaged spatial variations in the pressure field. In the direction of the standing wave this revealed a periodic energy landscape for 2 µm beads, resulting in an effective stiffness of 2.6 nN m(-1) for the acoustic trap. We found that multiple fabricated devices showed consistent pressure fields. Surprisingly, forces perpendicular to the direction of the standing wave reached values of up to 20% of the main-axis-values. To separate the direct acoustic force from secondary effects, we performed experiments with different bead sizes, which attributed some of the perpendicular forces to acoustic streaming. This method to image acoustically generated forces in 3D can be used to either minimize perpendicular forces or to employ them for specific applications in novel acoustofluidic designs.

Direct 2D measurement of time-averaged forces and pressure amplitudes in acoustophoretic devices using optical trapping.

Ultrasonic standing waves are increasingly applied in the manipulation and sorting of micrometer-sized particles in microfluidic cells. To optimize the performance of such devices, it is essential to know the exact forces that the particles experience in the acoustic wave. Although much progress has been made via analytical and numerical modeling, the reliability of these methods relies strongly on the assumptions used, e.g. the boundary conditions. Here, we have combined an acoustic flow cell with an optical laser trap to directly measure the force on a single spherical particle in two dimensions. While performing ultrasonic frequency scans, we measured the time-averaged forces on single particles that were moved with the laser trap through the microfluidic cell. The cell including piezoelectric transducers was modeled with finite element methods. We found that the experimentally obtained forces and the derived pressure fields confirm the predictions from theory and modeling. This novel approach can now be readily expanded to other particle, chamber, and fluid regimes and opens up the possibility of studying the effects of the presence of boundaries, acoustic streaming, and non-linear fluids.