Ultrasound directed self-assembly (DSA) relies on the acoustic radiation force associated with a standing ultrasound wave to organize particles dispersed in a fluid medium into specific patterns. State-of-the-art ultrasound DSA methods can only organize particles into (quasi-)periodic patterns, limited by the use of single-frequency ultrasound wave fields. Acoustic holography and acoustic waveguides provide alternatives to assembling complex patterns of particles, but generally provide low spatial accuracy and are not re-configurable because they require custom hardware for each specific pattern of particles, which is impractical. We introduce multi-frequency ultrasound wave fields to organize particles in non-periodic patterns. We theoretically derive and experimentally validate a solution methodology to determine the operating parameters (frequency, amplitude, phase) of any number and spatial arrangement of ultrasound transducers, required to assemble spherical particles dispersed in an inviscid fluid medium into any specific two-dimensional pattern. The results show that multi-frequency ultrasound DSA enables the assembly of complex, non-periodic patterns of particles with substantially fewer ultrasound transducers than single-frequency ultrasound DSA, and without incurring a penalty in terms of accuracy. The results of this work fundamentally transform the state-of-the-art knowledge of ultrasound DSA. Multi-frequency ultrasound wave fields enable a near-unlimited complexity of patterns of particles that can be assembled, increasing the relevance of the technology to practical implementation in engineering applications such as manufacturing of engineered composite materials that derive their properties from the spatial organization of the filler in the matrix material. Although this work focuses specifically on ultrasound wave fields, the theoretical model is valid for all wave phenomena. / Master of Science / Ultrasound directed self-assembly (DSA) is the process where particles dispersed in a fluid medium assemble into specific patterns due to their interactions with a sound wave and/or other particles. Current ultrasound DSA methods use a single-frequency ultrasound wave to assemble particles into specific patterns, which creates repeating patterns within the fluid medium. Other methods of assembling particles that allow for more complex, non-repeating patterns generally provide low spatial accuracy and do not allow dynamically changing the pattern as they require custom hardware for each specific pattern of particles, rendering these methods impractical. We use many ultrasound waves each with a different frequency to organize particles into complex, non-repeating patterns, which we call multi-frequency ultrasound DSA. We theoretically derive and experimentally validate a method that allows us to assemble any specific two-dimensional pattern of particles using multi-frequency ultrasound DSA. The results show that multi-frequency ultrasound DSA enables the assembly of complex, non-repeating patterns of particles with substantially resources than single-frequency ultrasound DSA, and without incurring a penalty in terms of accuracy. Multi-frequency ultrasound DSA enables a near-unlimited complexity of patterns of particles that can be assembled, increasing the relevance of the technology to practical implementation in engineering applications.

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. The ability to tailor the organization and packing density of spherical particles using ultrasound DSA in a viscous fluid medium is crucial in the context of (additive) manufacturing of engineered materials with tailored properties. However, the fundamental physics of the ultrasound DSA process in a viscous fluid medium, and the relationship between the ultrasound DSA process parameters and the specific patterns of particles that result from it, are not well-understood. Researchers have theoretically described the acoustic radiation force and the acoustic interaction force that act on spherical particles in a standing ultrasound wave field in both inviscid and viscous media. In addition, they have solved the forward and inverse ultrasound DSA problem in an inviscid medium, in which they relate the patterns of particles and the ultrasound DSA operating parameters. However, no theoretical model exists that allows simulating the steady-state and transient local particle packing density in a viscous medium during ultrasound DSA. Thus, in this dissertation, we (i) theoretically derive and experimentally validate a model to determine the steady-state locations where spherical particles assemble during ultrasound DSA as a function of medium viscosity and particle volume fraction. (ii) We also theoretically derive and experimentally validate a model to quantify the steady-state and transient local packing density of spherical particles within the pattern features that result from ultrasound DSA. Using these models, we quantify and predict the locations where spherical particles assemble during ultrasound DSA in a viscous medium, considering the effects of medium viscosity and particle volume fraction. We demonstrate that the deviation between locations where particles assemble in viscous and inviscid media first increases and then decreases with increasing particle volume fraction and medium viscosity, which we explain by means of the sound propagation velocity of the mixture. In addition, we quantify and predict the steady-state and transient local packing density of spherical particles within the pattern features, using ultrasound DSA in combination with vat photopolymerization (VP). We show that the steady-state local particle packing density increases with increasing particle volume fraction and increases with decreasing particle size. We also show that the transient local particle packing density increases with increasing particle volume fraction, decreasing particle size, and decreasing fluid medium viscosity. Increasing particle size and decreasing fluid medium viscosity decreases the time to reach steady-state. Finally, we implement single and multiple scattering in the calculation of the acoustic radiation force for spherical particles in a viscous medium and quantify their relative contributions to the calculation of the acoustic radiation force as a function of ultrasound DSA operating parameters and material properties. We demonstrate that the deviation between considering single and multiple scattering may reach up to 100%, depending on the ultrasound DSA process parameters and material properties. Also, increasing the particle volume fraction increases the need to account for multiple scattering. Quantifying and predicting the local packing density of spherical particles during ultrasound DSA in a viscous medium, as a function of ultrasound DSA process parameters is crucial towards using ultrasound DSA in engineering applications, in particular (additive) manufacturing of engineered polymer matrix composite materials with tailored properties whose properties depend on the spatial organization and packing density of particles in the matrix material. / Doctor of Philosophy / Ultrasound directed self-assembly (DSA) is a technique that uses ultrasound waves to arrange small particles submerged in a fluid into specific patterns. When combined with other manufacturing techniques, ultrasound DSA can be used to fabricate composite materials that derive their properties from the spatial organization of particles in a matrix material. However, ultrasound DSA in viscous fluids is not well-understood. Researchers have studied the forces associated with ultrasound waves that move small spherical particles in an inviscid fluid medium (fluids that experience little to no internal resistance to flow), and they have demonstrated intricate control of the patterns of particles that form using ultrasound DSA. However, that knowledge is not currently available for ultrasound DSA in viscous media. In this dissertation, we develop and evaluate theoretical models to understand ultrasound DSA of small spherical particles in a viscous fluid medium. We simulate where particles organize and how densely they pack together. We also determine the difference of the time-dependent motion of particles in a viscous fluid compared to that in an inviscid fluid medium and relate the difference to the number of particles submerged in the fluid and the viscosity of the fluid. Additionally, we examine the effect of particle size and fluid viscosity on the speed by which the particles reach their final location. We also study how ultrasound waves interact with multiple small particles in a viscous fluid, focusing on the forces that move these particles. We explore two models that account for single and multiple ultrasound wave scattering. Scattering is the process by which ultrasound waves deflect in different directions when they encounter a particle. The results show that the difference between single and multiple scattering models can be significant, depending on the ultrasound DSA process parameters and the properties of the fluid and particles. In general, the importance of accounting for multiple scattering increases with the number of particles submerged in the fluid. Understanding particle packing density when using ultrasound DSA in a viscous fluid is essential in many engineering applications, in particular manufacturing of composite materials that derive their properties from the spatial arrangement of particles in a matrix material.