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Abstract Ultrasound‐directed self‐assembly (DSA) uses ultrasound waves to organize and orient particles dispersed in a fluid medium into specific patterns. Combining ultrasound DSA with vat photopolymerization (VP) enables manufacturing materials layer‐by‐layer, wherein each layer the organization and orientation of particles in the photopolymer is controlled, which enables tailoring the properties of the resulting composite materials. However, the particle packing density changes with time and location as particles organize into specific patterns. Hence, relating the ultrasound DSA process parameters to the transient local particle packing density is important to tailor the properties of the composite material, and to determine the maximum speed of the layer‐by‐layer VP process. This paper theoretically derives and experimentally validates a 3D ultrasound DSA model and evaluates the local particle packing density at locations where particles assemble as a function of time and ultrasound DSA process parameters. The particle packing density increases with increasing particle volume fraction, decreasing particle size, and decreasing fluid medium viscosity is determined. Increasing the particle size and decreasing the fluid medium viscosity decreases the time to reach steady‐state. This work contributes to using ultrasound DSA and VP as a materials manufacturing process. 

Ultrasound directed self-assembly (DSA) utilizes the acoustic radiation force (ARF) associated with a standing ultrasound wave to organize particles dispersed in a fluid medium into specific patterns. The ARF is a superposition of the primary acoustic radiation force, which results from the incident standing ultrasound wave, and the acoustic interaction force, which originates from single and multiple scattering between neighboring particles. In contrast with most reports in the literature that neglect multiple scattering when calculating the ARF, we demonstrate that the deviation between considering single or multiple scattering may reach up to 100%, depending on the ultrasound DSA process parameters and material properties. We evaluate a theoretical case with three spherical particles in a viscous medium and derive operating maps that quantify the deviation between both scattering approaches as a function of the ultrasound DSA process parameters. Then, we study a realistic system with hundreds of particles dispersed in a viscous medium, and show that the deviation between the ARF resulting from single and multiple scattering increases with decreasing particle size and increasing medium viscosity, density ratio, compressibility ratio, and particle volume fraction. This work provides a quantitative basis for determining whether to consider single or multiple scattering in ultrasound DSA simulations.