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.