On the shape-dependent propulsion of nano- and microparticles by traveling ultrasound waves

Abstract

We address the propulsion mechanism of ultrasound-propelled nano- and microparticles that are exposed to a traveling ultrasound wave. Based on direct computational fluid dynamics simulations, we study the effect of two important aspects of the particle shape on the propulsion: rounded vs. pointed and filled vs. hollow shapes. We also study the flow field generated around such particles. Our results reveal that pointedness leads to an increase of the propulsion speed, whereas it is not significantly affected by hollowness. Furthermore, we show that the flow field near to ultrasound-propelled particles can look similar to the flow field generated by pusher squirmers.

Fig. 1. Setup for the simulations. A traveling ultrasound wave is entering the fluid domain Ω_f at the inlet, where it is prescribed by an inflow velocity v_in(t) and pressure p_in(t). The width of the fluid domain is l₁ and the rigid particle, constituting a particle domain Ω_p, is placed at a distance l₂ from the inlet. At the particle boundary a no-slip condition is prescribed and for the lateral boundaries of Ω_f slip boundary conditions are used. The ultrasound exerts on the particle a time-averaged propulsion force with a component F_∥ parallel to and a component F_⊥ perpendicular to the particle orientation and after a further distance l₂ the domain Ω_f ends with an outlet.

Fig. 2. Simulation data for the time-dependent forces F_∥,p(t) and F_∥,v(t) acting on a particle with the shape of a hollow half ball as well as an extrapolation of the forces with the fit function f(t). The extrapolation of the total propulsion force parallel to the particle orientation F_∥(t) = F_∥,p(t) + F_∥,v(t) converges against c_∥,p + c_∥,v, where c_∥,p and c_∥,v are the offset fit coefficients in f(t) for F_∥,p(t) and F_∥,v(t), respectively. Its limiting value is consistent with corresponding experimental data from Soto et al. that can be tied to the interval [F^exp_min, F^exp_max] = [0.163 fN, 1.63 fN].

Fig. 3. The considered particle shapes: (a) half ball, (b) cone, (c) hollow half ball, and (d) hollow cone. All particles have diameter σ and the hollow particles have wall width σ/5. The center of mass (CoM), the center of resistance (CoR), the direction of the propulsion-force component F_∥ and corresponding propulsion-velocity component v_∥, which are parallel to the symmetry axes of the particles and perpendicular to the main direction of sound propagation, and the direction of the components F_⊥ and v_⊥, which are perpendicular to the symmetry axes of the particles and parallel to the main direction of sound propagation, are indicated. For each particle shape, the values of F_∥ = F_∥,p + F_∥,v and F_⊥ = F_⊥,p + F_⊥,v, the pressure components F_∥,p and F_⊥,p, the viscous components F_∥,v and F_⊥,v, and v_∥ and v_⊥ are given.

Fig. 4. The time-averaged mass-current density 〈ρv⃑〉 and reduced pressure 〈p − p₀〉 for all considered particle shapes (see Fig. 3). (a) The far field is shown for a half-ball particle and looks similar for the other particle shapes; (b)–(e) the near field is shown for each particle shape.