Motion of Micrometer Sized Spherical Particles Exposed to a Transient Radial Flow: Attraction, Repulsion, and Rotation

It is now accepted that the physical forces in ultrasonic cleaning are due to strongly pulsating bubbles driven by the sound field. Here we have a detailed look at bubble induced cleaning flow by analyzing the transport of an individual particle near an expanding and collapsing bubble. The induced particulate transport is compared with a force balance model. We find two important properties of the flow which explain why bubbles are effectively cleaning: During bubble expansion a strong shear layer loosens the particle from the surface through particle spinning and secondly an unsteady boundary layer generates an attractive force, thus collecting the contamination in the bubble’s close proximity.

Figure 1

(a)–(c) 12 stacked high-speed recordings taken at $540000\mathrm{frames}/\mathrm{s}$ of the bubble-particle dynamics for different distances of the particle from the bubble center ${\delta }^{\prime }$. The final (dimensional) displacement is $\Delta x^{\prime }$. (a) Repulsion of the particle, $\Delta x^{\prime }>0$, (b) neutral displacement, $\Delta x^{\prime }=0$, (c) attraction, $\Delta x^{\prime }<0$. Particle rotation in (a): Rotation is evident by comparing the picture of the particle before (circle 1), during (circle 2), and after the bubble oscillation (circle 3). Scale bar in the upper left is $50\mu \mathrm{m}$.

Figure 2

(a) Plots of the particle displacement as a function of the initial distance from the bubble. Master curve obtained by nondimensionalizing the initial distance with the maximum bubble radius, $\delta ={\delta }^{\prime }/R_{\max }$, and the displacement with the particle diameter, $\Delta x=\Delta x^{\prime }/d_p$. Inset: Displacement of 4 different particles plotted in dimensional coordinates. Panels (b) and (c) depict the simulation results (see text) in the rejection and attraction regime, respectively.

Figure 3

Particle translation for consecutive experiments. (a) The position of a single $4.5\mu \mathrm{m}$ particle located initially $73\mu \mathrm{m}$ from the bubble center as a function of number of bubble oscillations $N$. (b) Agglomeration of many particles on an annular ring after 50, 100, and 400 laser induced bubbles. The circles have a radius of $0.7R_{\max }$ and $1R_{\max }$ respectively; $R_{\max }=51\mu \mathrm{m}$. A video of the particle dynamics is available in the Supplemental Material [12].

Figure 4

(a) Comparison of the particle trajectory (circles) with the force balance model including the boundary layer approximation (solid lines) and ignoring the boundary layer (dashed lines) for $d=2\mu \mathrm{m}$ and $R_{\max }\approx 50\mu \mathrm{m}$. (b) Snapshots of the boundary layer velocity profile for times $t=5,15,25\mu \mathrm{s}$ at position $r=60\mu \mathrm{m}$.