Dynamic properties of micro-particles in ultrasonic transportation using phase-controllable standing waves

Ultrasonic manipulation has become an attractive method for surface-sensitive objects in micro-technology. Related phenomena, such as radiation force, multiple scattering, and acoustic streaming, have been widely studied. However, in current studies, the behavior of micro-particles in potential force fields is always analyzed in a quasi-static manner. We developed a dynamic model of a dilute micro-particle in the commonly used two-dimensional ultrasonic manipulation system to provide a systemic and quantitative analysis of the transient properties of particle movement. In this model, the acoustic streaming and hydrodynamic forces, omitted in previous work, were both considered. The trajectory of a spherical silica particle with different initial conditions was derived by numerically solving the established nonlinear differential integral equation system, which was then validated experimentally. The envelope of the experimental data on the x-axis showed good agreement with the theoretical calculation, and the greater influence on the y-axis of the deviation between the actual sound field and the ideal distribution employed in our dynamic model could account for the differences in displacement in that direction. Finally, the influence of particle size on its movement and the effect of acoustic streaming on calculating the hydrodynamic forces for an isolated particle with motion relative to the fluid were analyzed theoretically. It was found that the ultrasonic manipulation system will translate from an under-damped system to an over-damped system with a decrease in particle size and the micro-scale acoustic streaming velocity was negligible when calculating the hydrodynamic forces on the particle in the ultrasonic manipulation system.