Cavity Ripples Observed during the Impact of Solid Objects into Liquids

We report the experimental observation of a well-defined rippling of the air cavity entrained by a rapidly moving solid object entering the free surface of a liquid (water or ethanol). The ripples are fixed in the lab frame, and begin just after the pinch-off (deep seal) of the cavity, simultaneous with the acoustic emission. This acoustic resonance corresponds approximately to the Minnaert frequency for volume oscillations of the bubble. We present an irrotational model which explains the ripples as a spatial rectification of these volume oscillations by the surface of the moving object.

Figure 1

The onset of rippling after the pinch-off of a cavity formed by a $d=1/2\mathrm{in}.$ steel sphere with impact velocity $U_i\simeq 4\mathrm{m}/\mathrm{s}$ ($\mathrm{Fr}=128$, $\mathrm{Re}=5.1\times {10}^4$, $\Delta t=3.2\mathrm{ms}$).

Figure 2

Ripple-induced breakup of the entrained bubble behind a $1/2\mathrm{in}.$ diameter steel sphere, $U_i=4.1\mathrm{m}/\mathrm{s}$.

Figure 3

Cavity rippling behind a brass cone ($d=1/2\mathrm{in}.$, $U_i=4.5\mathrm{m}/\mathrm{s}$), brass hemisphere ($d=1/2\mathrm{in}.$, $U_i=5.7\mathrm{m}/\mathrm{s}$), and teflon sphere ($d=3/4\mathrm{in}.$, $U_i=4.1\mathrm{m}/\mathrm{s}$).

Figure 4

Plot of the product of the ripple wavelength and acoustic frequency $f$ versus the speed of the sphere. The straight line shows $\lambda f=U_0$. Inset: Pressure oscillations after cavity pinch-off for a $3/4\mathrm{in}.$ steel sphere ($U_0=4\mathrm{m}/\mathrm{s}$, $\mathrm{Fr}=86$).

Figure 5

Left: Dependence of the rippling transition on cavity dimensions for different spheres. The dashed line approximates the transition boundary. Right: The transitional pulsing or rippling state ($d=3/4\mathrm{in}.$ teflon, $U_i=1.5\mathrm{m}/\mathrm{s}$, $\mathrm{Fr}=12$).