3D ultrasound directed self-assembly of high aspect ratio particles: On the relationship between the number of transducers and their spatial arrangement

Ultrasound directed self-assembly (DSA) enables noninvasively aligning high aspect ratio particles in three-dimensional (3D) user-specified orientations, which finds application in a myriad of engineering applications, including manufacturing engineered materials. However, the number of ultrasound transducers and their spatial arrangement limit the accuracy of the particle alignment with any 3D user-specified orientation. We define a set of 3D user-specified orientations and use numerical simulations to quantitatively evaluate the effect of the number of ultrasound transducers, their spatial arrangement including a sphere, cube, and two parallel plates, and the size of the spatial arrangement on the orientation error of a high aspect ratio particle in a standing ultrasound wave field. We demonstrate that a spatial arrangement of ultrasound transducers with more than two unique wave propagating directions is required to orient a high aspect ratio particle in 3D, and we determine that the orientation error decreases with the increasing number of unique wave propagation directions. Furthermore, we show that in a spherical arrangement of ultrasound transducers, the orientation error is independent of the size of the arrangement of transducers. This knowledge facilitates using ultrasound DSA as a fabrication method for engineered composite materials that derive their function from the location and orientation of particle inclusions.