Ultrasound directed self-assembly of three-dimensional user-specified patterns of particles in a fluid medium

Abstract

We use ultrasound directed self-assembly to organize particles dispersed in a fluid medium into a three-dimensional (3D) user-specified pattern. The technique employs ultrasound transducers that line the boundary of a fluid reservoir to create a standing ultrasound wave field. The acoustic radiation force associated with the wave field drives particles dispersed in the fluid medium into organized patterns, assuming that the particles are much smaller than the wavelength and do not interact with each other. We have theoretically derived a direct solution method to calculate the ultrasound transducer operating parameters that are required to assemble a user-specified 3D pattern of particles in a fluid reservoir of arbitrary geometry. We formulate the direct solution method as a constrained optimization problem that reduces to eigendecomposition. We experimentally validate the solution method by assembling 3D patterns of carbon nanoparticles in a water reservoir and observe good quantitative agreement between theory and experiment. Additionally, we demonstrate the versatility of the solution method by simulating ultrasound directed self-assembly of complex 3D patterns of particles. The method works for any 3D simple, closed fluid reservoir geometry in combination with any arrangement of ultrasound transducers and enables employing ultrasound directed self-assembly in a myriad of engineering applications, including biomedical and materials fabrication processes.

Acoustic Hologram Enhanced Phased Arrays for Ultrasonic Particle Manipulation

“…This effect is most well known in optics but has previously been demonstrated successfully in underwater ultrasound using threedimensional (3D) printed holograms [3]. In ultrasound, the traditional technique for generating a desired sound field is to use a phased array consisting of a number of independently controlled elements [4][5][6][7][8][9]. However, the hologram offers two key advantages; the first is the simplification of the driving electronics, as it only requires a single channel [10], and the second is the increased phase fidelity, which is only limited by the print or machining resolution.…”

Approximation by Herglotz Wave Functions

“…The problem of designing Helmholtz equation solutions for which the minima of the acoustic radiation potential are close to a desired pattern has been studied numerically and experimentally in both 2D and 3D settings [8,14]. The numerical approach in [8,14] allows for a broader range of particle and fluid parameters than the one we consider here and also accounts for having finitely many transducers lining the reservoir. The design problem is formulated as a constrained minimization problem in [8].…”

Particle separation by phase modulated surface acoustic waves

“…21 In multi-transducer bulk devices, the control of the trapping position can either be achieved by a carefully designed matching layer 2,4,22 or by calculations of the required phase and amplitude of the transducers' signals, 23,24 providing thereby the possibility to pattern any user-specified pattern in 2D 25 or even in 3D. 26 Surface acoustic wave devices offer flexibility, as no matching layer or complex design is required to achieve patterning by frequency or phase control, and such devices can produce one-dimensional, 3,5,18,[27][28][29][30][31][32] two-dimensional, 3,5,33,34 or three-dimensional 35 patterns.…”