Particulate Projectiles Driven by Cavitation Bubbles

The removal of surface-attached particles with cavitation bubbles is usually attributed to the jetting or shear stresses when bubbles collapse. In this Letter, we report an unexpected phenomenon that millimeter-sized spherical particles made of heavy metals (e.g., stainless steel), when initially resting on a fixed rigid substrate, are suddenly accelerated like projectiles through the production of nearby laser-induced cavitation bubbles of similar sizes. We show experimentally and theoretically that the motion of a particle with radius $R_p$ is determined by the maximum bubble radius $R_{b,\max }$, the initial distance from the laser focus to the center of the particle $L_0$, and the initial azimuth angle ${\phi }_0$. We identify two dominant regimes for the particle’s sudden acceleration, namely, the unsteady liquid inertia dominated regime and the bubble contact dominated regime, determined by $R_{b,\max }{R}_p/L_0^2$. We find the nondimensional maximum vertical displacement of the particle follows the fourth power and the square power scaling laws for respective regimes, which is consistent with the experimental results. Our findings can be applied to nonintrusive particle manipulation from solid substrates in a liquid.

Figure 1

Experimental configuration (side view) and notation.

Figure 2

Image sequences showing the sudden acceleration of a stainless steel particle (radius $R_p=2.5\mathrm{mm}$) from a substrate made of stainless steel by cavitation bubbles for (a) case A, ${\phi }_0=3.4°$, $L_0/R_p=1.17$, $R_{b,\max }/R_p=0.83$; (b) case B, ${\phi }_0=31°$, $L_0/R_p=1.20$, $R_{b,\max }/R_p=0.84$; (c) case C, ${\phi }_0=56°$, $L_0/R_p=1.04$, $R_{b,\max }/R_p=0.89$; and (d) case D, ${\phi }_0=35°$, $L_0/R_p=2.37$, $R_{b,\max }/R_p=0.81$. The regions focused on the bottoms of the particles are enlarged in the fourth column. The last column displays the superimposition of the outlines of the particle at the initial position (“1”), at the maximum height (“2”), and the snapshot of impact of the fallen particle on the plate (“3”). The trajectory of the center of the particle in each case is visualized by the solid line. Videos are provided in the Supplemental Material [16].

Figure 3

Experimental and theoretical results for the particle’s sudden acceleration. (a) Theoretical model. (i) Sketch of the method of images. Hydrodynamic forces on the particle (ii) at the bubble generation and (iii) when the bubble’s volume growth rate $Q(t)$ slows down. (b) Evolution of the normalized bubble radius. The black line is based on the solution to the Rayleigh equation for a spherical bubble. The forces exerted on the particle are shown in the (c) vertical and (d) horizontal directions. The yellow areas highlight the time period of the force conversion. The normalized particle displacements are shown in the (e) vertical and (f) horizontal directions.

Figure 4

Scaling laws controlling the particle acceleration. (a) Nondimensional time-averaged lift force estimated from experimental results versus $R_{b,\max }{R}_p/L_0^2$ for two dominant regimes. (b) Nondimensional maximum vertical displacement of the particle with $\mathrm{\Delta }{z}_0$ defined by Eq. (3) versus $R_{b,\max }/L_0$. Solid lines indicate the scaling laws for the unsteady liquid inertia dominant regime and dashed lines for the bubble contact regime.