Potential-well model in acoustic tweezers.

Standing-wave acoustic tweezers are popularly used for non-invasive and non-contact particle manipulation. Because of their good penetration in biological tissue, they also show promising prospects for in vivo applications. According to the concept of an optical vortex, we propose an acoustics-vortex- based trapping model of acoustic tweezers. A four-element 1-MHz planar transducer was used to generate 1-MHz sine waves at 1 MPa, with adjacent elements being driven with a pi/2-rad phase difference. Each element was a square with a side length of 5.08 mm, with kerfs initially set at 0.51 mm. An acoustic vortex constituting the spiral motion of an acoustic wave around the beam axis was created, with an axial null. Applying Gor'kov's theory in the Rayleigh regime yielded the potential energy and radiation force for use in subsequent analysis. In the transverse direction, the vortex structure behaved as a series of potential wells that tended to drive a suspended particle toward the beam axis. They were highly fragmented in the near field that is very close to the transducer where there was spiral interference, and well-constructed in the far field. We found that the significant trapping effect was only present between these two regions in the transverse direction--particles were free to move along the beam axis, and a repulsive force was observed in the outer acoustic vortex. Because the steepness of the potential gradient near an axial null dominates the trapping effect, the far field of the acoustic vortex is inappropriate for trapping. Particles too close to the transducer are not sufficiently trapped because of the fragmented potential pattern. We suggest that the ideal distance from the transducer for trapping particles is in front of one-fourth of the Rayleigh distance, based on the superposition of the wavefronts. The maximum trapping force acting on a 13-mum polystyrene sphere in the produced acoustic vortex was 50.0 pN, and it was possible to trap approximately 10(6) particles within a plane; the maximum repulsive force was 24.5 pN, and this was reduced to less than 13 pN by smoothing the outer gradient. Most stiff and dense particles can be used in this model. The presence of transverse trapping and the long working distance make the model useful for 2-D manipulation, particularly in in vivo applications. This paper details the trapping properties in the acoustic vortex and describes methods for improving the design of the transducer. The results obtained support the feasibility of the potential-well model of acoustic tweezers.