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Abstract
We numerically demonstrate acoustophoretic separation of spherical solid particles in air by means of an acoustic Fresnel lens. Beside gravitational and drag forces, freely-falling millimeter-size particles experience large acoustic radiation forces around the focus of the lens, where interplay of forces lead to differentiation of particle trajectories with respect to either size or material properties. Due to the strong acoustic field at the focus, radiation force can divert particles with source intensities significantly smaller than those required for acoustic levitation in a standing field. When the lens is designed to have a focal length of 100 mm at 25 kHz, finite-element method simulations reveal a sharp focus with a full-width at half-maximum of 0.5 wavelenghts and a field enhancement of 18 dB. Through numerical calculation of forces and simulation of particle trajectories, we demonstrate size-based separation of acrylic particles at a source sound pressure level of 153 dB such that particles with diameters larger than 0.5 mm are admitted into the central hole, whereas smaller particles are rejected. Besides, efficient separation of particles with similar acoustic properties such as polyethylene, polystyrene and acrylic particles of the same size is also demonstrated.
Highlights
Acoustic trapping can be achieved without the involvement of a standing field
Since the radiation force is size dependent, the node displacement was utilized by Skotis et al.[33] through controlling the relative phases of two opposing speakers so that polystyrene beads of 2 mm and 5 mm diameters are translated at different rates
Acoustic-Solid Interaction and the Particle Tracing for Fluid Flow modules of the COMSOL Multiphysics software, which is an implementation of finite-element method (FEM), are employed for the former and latter, respectively
Summary
Acoustic trapping can be achieved without the involvement of a standing field. For instance, levitation of a large polystyrene ball over three Langevin transducers positioned in a tripod fashion is demonstrated[27]. Rapid translation of millimeter-size polystyrene particles by controlling the distance between the radiating plate and the reflector in a standing-field configuration is demonstrated[15]. Acoustic particle manipulation through focused waves discussed above by means of curved transducer surfaces[28,29,30] can alternatively be achieved by flat acoustic lenses in air. Acoustic focusing in 2D can be achieved by optimizing the positions of a finite number of aperiodic scatterers in air[37,38]. While these approaches lead to focusing acoustic energy on a plane, fully three-dimensional (3D) lenses should be considered to focus on a point. Acoustic Fresnel lenses with perforations can be a good means for acoustophoretic separation of particles, as they may possess central perforations size of which can be designed for the desired separation efficiency
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