Measuring and Simulating the Local Packing Density Resulting From Ultrasound-Directed Self-Assembly of Spherical Microparticles into Specific Patterns

Ultrasound-directed self-assembly (DSA) enables organizing and orienting particles dispersed in a fluid medium into specific patterns, thus agglomerating them into pattern features with different packing density than when first dispersed in the fluid medium. In this paper, we theoretically derive and experimentally validate a three-dimensional model of the ultrasound DSA process to simulate and quantify the local packing density of spherical microparticles when assembled into pattern features. We study the packing density as a function of process parameters, including particle volume fraction, particle size, and medium viscosity. The results show that the local particle packing density increases with increasing particle volume fraction and reaches a maximum of 45% independent of medium viscosity. Also, the local particle packing density increases with decreasing particle size for constant particle volume fraction. The results shed light on the relationship between the process parameters and the local particle packing density within pattern features resulting from ultrasound DSA. This knowledge is useful in the context of using ultrasound DSA to manufacture engineered composite materials that require high particle packing density, or packing density gradients, e.g., to increase mechanical or electrical properties, or to tailor combustion of energetic particles, among other applications.