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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. 

Abstract Ultrasound‐directed self‐assembly (DSA) utilizes the acoustic radiation force associated with a standing ultrasound wave field to organize particles dispersed in a fluid medium into specific patterns. State‐of‐the‐art ultrasound DSA methods use single‐frequency ultrasound wave fields, which only allow organizing particles into simple, periodic patterns, or require a large number of ultrasound transducers to assemble complex patterns. In contrast, this work introduces multi‐frequency ultrasound wave fields to organize particles into complex patterns. A method is theoretically derived to determine the operating parameters (frequency, amplitude, phase) of any arrangement of ultrasound transducers, required to assemble spherical particles dispersed in a fluid medium into specific patterns, and experimentally validated for a system with two frequencies. The results show that multi‐frequency compared to single‐frequency ultrasound DSA enables the assembly of complex patterns of particles with substantially fewer ultrasound transducers. Additionally, the method does not incur a penalty in terms of accuracy, and it does not require custom hardware for each different pattern, thus offering reconfigurability, which contrasts, e.g., acoustic holography. Multi‐frequency ultrasound DSA can spur progress in a myriad of engineering applications, including the manufacturing of multi‐functional polymer matrix composite materials that derive their structural, electric, acoustic, or thermal properties from the spatial organization of particles in the matrix.