Fig. 2.

Short-ranged repulsive interactions from viscous effects. (A) Acoustic scattering potential, U_sc, in the x–z plane. The interaction is attractive in the equatorial and repulsive in the polar direction. The white circle represents the particle. (B) Time-averaged microstreaming flow of magnitude v_st in the x–z plane around a 45-μm sphere levitated at ω/(2π)=34.7 kHz, obtained from COMSOL simulation. The direction of flow-induced forces in the levitation plane is opposite to that in A. (C) Magnitude of the net force in the equatorial direction F_r as a function of radial distance r for various particle diameters D, from lattice fluid simulation. Here, k = 2π/λ, where λ is the wavelength of the generated acoustic wave. The black curve represents the force from the scattering expansion following ref. 14. (D) Magnitude of the microstreaming repulsive interaction, approximated by subtracting the scattering expansion from the net force in C. The purple dashed line represents an exponential decay, exp(−(r − D)/δ_ν), with δ_ν = 12 μm. (E) Time-averaged steady-state separation ⟨r⟩/D for a particle pair as function of Stokes number Ω. Blue errorbars represent the uncertainties for selected data points (SI Appendix, Fig. S2).