Calculating the acoustic radiation force on spherical particles in a standing ultrasound wave field considering single and multiple scattering

Abstract

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.