The effect of medium viscosity and particle volume fraction on ultrasound directed self-assembly of spherical microparticles

Abstract

Ultrasound directed self-assembly (DSA) allows organizing particles dispersed in a fluid medium into user-specified patterns, driven by the acoustic radiation force associated with a standing ultrasound wave. Accurate control of the spatial organization of the particles in the fluid medium requires accounting for medium viscosity and particle volume fraction. However, existing theories consider an inviscid medium or only determine the effect of viscosity on the magnitude of the acoustic radiation force rather than the locations where particles assemble, which is crucial information to use ultrasound DSA as a fabrication method. We experimentally measure the deviation between locations where spherical microparticles assemble during ultrasound DSA as a function of medium viscosity and particle volume fraction. Additionally, we simulate the experiments using coupled-phase theory and the time-averaged acoustic radiation potential, and we derive best-fit equations that predict the deviation between locations where particles assemble during ultrasound DSA when using viscous and inviscid theory. We show 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. This work has implications for using ultrasound DSA to fabricate, e.g., engineered polymer composite materials that derive their function from accurately organizing a pattern of particles embedded in the polymer matrix.