The Limits of Primary Radiation Forces in Bulk Acoustic Standing Waves for Concentrating Nanoparticles

Abstract

Acoustic waves are increasingly used to concentrate, separate, and pattern nanoparticles in liquids, but the extent to which nanoparticles of different size and composition can be focused is not well‐defined. This article describes a simple analytical model for predicting the distribution of nanoparticles around the node of a 1D bulk acoustic standing wave over time as a function of pressure amplitude, acoustic contrast factor (i.e., nanoparticle and fluid composition), and size of the nanoparticles. Predictions from this model are systematically compared to results from experiments on gold nanoparticles of different sizes to determine the model's accuracy in estimating both the rate and the degree of nanoparticle focusing across a range of pressure amplitudes. The model is further used to predict the minimum particle size that can be focused for different nanoparticle and fluid compositions, and those predictions are tested with gold, silica, and polystyrene nanoparticles in water. A procedure combining UV‐light and photoacid is used to induce the aggregation of nanoparticles to illustrate the effect of nanoparticle aggregation on the observed degree of acoustic focusing. Overall, these findings clarify the extent to which acoustic resonating devices can be used to manipulate, pattern, and enrich nanoparticles suspended in liquids.

Protocol for assembling micro- and nanoparticles in a viscous liquid above a vibrating plate

“…The effect of transporting particles in external acoustic fields, acoustophoresis, has been used to assemble a variety of microparticles [ 15 , 16 ], nanoparticles [ 17 , 18 ] and biological samples [ 19 , 20 ]. The acoustic field can act on a variety of material combinations so long as a density and compressibility difference between the assembling particles and the medium exists.…”

Nanomaterial Patterning in 3D Printing

“…This often inhibits focusing smaller particles, resulting in a wider FWHM. Reyes et al extended this observation to polystyrene and silica nanoparticles, concluding that the FWHM of the distribution of the nanoparticles decreased as the acoustic contrast factor, pressure amplitudes, and size of the nanoparticles increased 291. With this knowledge, an acoustic field‐assisted nanomaterial patterning system can be designed to target certain particle size ranges.…”

“…This force depends upon the size and position of the particles, as well as the energy associated with the wave 290. More specifically, the acoustic force is positively affected by increases in particle volume, particle density and speed of sound in the particle, as well as decreases in fluid density and speed of sound in the fluid, as described with the equation where k is the wavenumber, V is the particle volume, E ac is the acoustic energy density, ϕ is the acoustic contrast factor, and x is the position of the particle on the x ‐axis 291…”

“…Moreover, analytical models that account for interparticle interactions and secondary acoustic radiation forces could predict the limit of particle size that can be manipulated acoustically. Reyes et al analytically and experimentally investigated the size limit of gold nanoparticles that can be focused on a fluid using ultrasonic radiation forces 291. It was shown experimentally that the distribution of larger particles (100–200 nm) features a narrow full width at half‐maximum (FWHM) (43.2–25 µm) and smaller sized particles (60 nm) exhibit a wider distribution, with an FWHM of 140 µm under 700 kPa.…”

Flexible Conductive Composites with Programmed Electrical Anisotropy Using Acoustophoresis

“…Stochastic approaches such as freeze‐casting or laser‐directed alignment show promise for improving material properties of composites, but these are generally restricted to specific material systems and microstructural configurations. Another advantage of acoustophoresis is that it is highly scalable, able to assemble µm‐ to mm‐size structures in seconds, in contrast to diffusion‐limited self‐assembly processes that are prohibitively slow to assemble > 10 µm structures …”