Theoretical framework to predict the acoustophoresis of axisymmetric irregular objects above an ultrasound transducer array

Acoustophoresis of monodisperse oil droplets in water: Effect of symmetry breaking and non-resonance operation on oil trapping behavior

Acoustic manipulation of particles in microchannels has recently gained much attention. Ultrasonic standing wave (USW) separation of oil droplets or particles is an established technology for microscale applications. Acoustofluidic devices are normally operated at optimized conditions, namely, resonant frequency, to minimize power consumption. It has been recently shown that symmetry breaking is needed to obtain efficient conditions for acoustic particle trapping. In this work, we study the acoustophoretic behavior of monodisperse oil droplets (silicone oil and hexadecane) in water in the microfluidic chip operating at a non-resonant frequency and an off-center placement of the transducer. Finite element-based computer simulations are further performed to investigate the influence of these conditions on the acoustic pressure distribution and oil trapping behavior. Via investigating the Gor'kov potential, we obtained an overlap between the trapping patterns obtained in experiments and simulations. We demonstrate that an off-center placement of the transducer and driving the transducer at a non-resonant frequency can still lead to predictable behavior of particles in acoustofluidics. This is relevant to applications in which the theoretical resonant frequency cannot be achieved, e.g., manipulation of biological matter within living tissues.

Soundiation: A software in evaluation of acoustophoresis driven by radiation force and torque on axisymmetric objects

Acoustic radiation force and torque arising from wave scattering are commonly used to manipulate micro-objects without contact. We applied the partial wave expansion series and the conformal transformation approach to estimate the acoustic radiation force and torque exerted on the axisymmetric particles. Meanwhile, the translational and rotational transformations are employed to perform the prediction of the acoustophoresis. Although these theoretical derivations are well-developed [Tang and Huang, J. Sound Vibr. 532, 117012 (2022), Tang and Huang, Phys. Rev. E 105, 055110 (2022)], coding the required systems, including generation of the wave function, implementation of the transformations, calculations between modules, etc., is non-trivial and time-consuming. Here, we present a new open-source, matlab-based software, called Soundiation [GitHub Repository: https://github.com/Tountain/SoundiationAcoustophoresis, GPL-3.0 license], to address the acoustic radiation force and torque while supporting the dynamic prediction of non-spherical particles. The implementation is basically generic, and its applicability is demonstrated through the validation of numerical methods. A graphical user interface is provided so that it can be used and extended easily.

Acoustic levitation of axisymmetric Mie objects above a transducer array by engineering the acoustic radiation force and torque

Transducer arrays are a versatile tool for the contactless manipulation of spherical Rayleigh objects. Here we propose an analytical model for stable levitation of axisymmetric Mie objects through directly engineering the desired radiation force and torque. Acoustic contributions from multiple transducers are superimposed through the translation addition theorem, and the nonspherical objects are mapped into a sphere using the conformal transformation technique so that the scattered field can be asymptotically obtained. Then we give the acoustic radiation force and torque applied to a rigid nonspherical Mie object, which can be reconstructed as a series of quasiexplicit functions of the transducer (amplitude and phase) parameters. Through specifying the desired radiation force and torque exerted on the objects, a system of nonlinear equations is produced, which could be iteratively solved to retrieve appropriate transducer parameters that stabilize the object in an equilibrium position. Practically, we demonstrate several examples of stable levitation of a sphere, a spheroid, and a disk with an averaged radius of a=7mm (size parameter of ka≈5.18) above a transducer array. The absolute acoustic pressure field surrounding the objects simulated by the finite-element method is illustrated to verify the trapping results. The developed analytical model provides an alternative approach to retrieve the transducer parameters for levitating macroscopic nonspherical rigid objects, which may help design the systematic dynamical manipulation of Mie particles.