Experimental and numerical investigation of steady-state and transient ultrasound directed self-assembly of spherical particles in a viscous medium

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.