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

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.