UC Merced

This dissertation investigates the acoustic radiation forces arising from wave scattering between closely-situated sound-hard spheres, with direct implications for the phenomenon of acoustic binding. Motivated by experimental findings in the Kleckner Lab at UC Merced, we develop a numerical and analytical framework to compute surface fields and resulting forces with high precision, even in the challenging near-field regime. Using boundary integral equations (BIEs) and spherical harmonic expansions, we resolve the scattering problem for two spheres in regimes where multiple scattering and coupling effects are non-negligible. We begin by establishing a boundary integral formulation that allows direct computation of surface fields, circumventing the need for full domain discretization. We then expand the field using a spherical harmonic basis and derive a Galerkin discretization scheme capable of capturing both independent and coupled scattering behaviors. A key contribution is the decomposition of the acoustic field and radiation force into individual components, revealing the dominant role of cross-terms in determining equilibrium configurations. Specifically, when the incident and scattered fields are decomposed into their even and odd components with respect to symmetry, the acoustic radiation force integral contains terms representing all pairwise products of these components (such as the interaction between the even part of the incident field and the odd part of the scattered field). Among these terms, it is the mixed even-odd interactions that contribute significantly to the net force, while other terms cancel due to symmetry. This insight provides a framework for approximating the force using only the most relevant interactions. Numerical simulations give results that show the complex behavior of these acoustic radiation forces as a function of the distance between the two spheres. To interpret these results, we analytically determine individual components of the acoustic radiation force and consider how different orders of multiple scattering (including independent, first-order, and higher-order effects) influence them. Building on this, we propose a first-order correction using the Block-Jacobi method, which captures essential multiple scattering effects with improved accuracy and stability. Numerical results highlight the emergence of oscillatory force patterns and equilibrium saturation phenomena as the inter-sphere distance tends to zero. These findings offer theoretical insight into the mechanisms driving acoustic binding and provide a robust computational toolset for the study of particle assembly in structured materials.