Fig. 3.

Nonreciprocal and multibody effects in acoustic interactions. Net forces on individual and groups of particles in a levitated, seven-particle cluster, contrasted with a pair-wise additive interaction (the LJ force) on the same configuration. For acoustically interacting clusters, the displacement of a single particle from its force-balanced position leads to nonreciprocal forces that promote the shearing of close-packed layers. (A) Various forces (obtained from LBM simulation) in an acoustically interacting cluster as the central particle is displaced by an amount Δx from its stable position. Insets show individual forces (black) and net forces on layers parallel to the displacement direction (red, force scale eight times smaller than the black arrows). The sum of all individual forces is shown in the main panel (blue points), along with the difference of net forces on the top and middle layers (red points). Acoustic clusters have nonconservative forces that promote shearing of particle layers in the direction of point displacements. (B) The same configuration interacting through pair-wise additive LJ forces has no nonconservative force component (blue points) and the opposite behavior for layer shear forces (red points). Here, all forces act to restore the cluster toward its undisturbed configuration, unlike for particles interacting acoustically. (C) Time-averaged streaming flow of magnitude v_st around the minimal cluster in the x–y plane for Δx/D = 0.3, obtained from COMSOL simulation. Green and purple arrows denote the force contributed by viscous streaming repulsion and scattering attraction, respectively. (D) Magnitude of the net force from LBM simulation on the central, displaced particle (black) and the sum of net forces on all particles in the x direction (blue) for different acoustic energy density E₀ normalized by mgk², where m = πρD³/6 and g = 9.8 m/s². As in Fig. 2C, all acoustic forces reported here are normalized as $\widetilde{f_i}=f_i/(E_0{D}^6{k}^4)$, and Lennard-Jones (LJ) interactions are normalized as $\widetilde{f_i}=f_i/(ϵ/\sigma )$, where ϵ and σ are characteristic energy and length scale of the potential.