Autonomous propulsion of nanorods trapped in an acoustic field

Acoustic fields in a liquid medium can trap and suspend small particles at their pressure nodes. Recent measurements demonstrate that nanorods immersed in these fields generate autonomous propulsion, with their direction and speed controlled by both the particle's shape and density distribution. Specifically, slender nanorods with an asymmetric density distribution about their geometric centre are observed to move steadily with their low density end leading the motion; particle geometry exerts an equally significant and potentially opposing effect. In this article, we investigate the physical mechanisms underlying this combined density/shape induced phenomenon by developing a simple yet rigorous mathematical framework for axisymmetric particles. This only requires solution of the (linear) unsteady Stokes equations, which can be performed numerically or analytically. The theory holds for all particle shapes, particle aspect ratios (length/width) and acoustic frequencies. It is applied to slender dumbbell-shaped particles and asymmetric nanorods - these provide model systems to investigate the competing effects governing propulsion. This shows that geometric and density asymmetries in the particle generate axial jets that can produce motion in either direction, depending on the relative strengths of these asymmetries and the acoustic Reynolds number (dimensionless frequency). Strikingly, the propulsion direction is found to reverse with increasing frequency, an effect that is yet to be reported experimentally. The general theory and mechanism described here enable the a priori design and fabrication of nano-motors in fluid for transport of small-scale payloads and robotic applications.