Vortex-ring-induced large bubble entrainment during drop impact

For a limited set of impact conditions, a drop impacting onto a pool can entrap an air bubble as large as its own size. The subsequent rise and rupture of this large bubble plays an important role in aerosol formation and gas transport at the air-sea interface. The large bubble is formed when the impact crater closes up near the pool surface and is known to occur only for drops that are prolate at impact. Herein we use experiments and numerical simulations to show that a concentrated vortex ring, produced in the neck between the drop and the pool, controls the crater deformations and pinchoff. However, it is not the strongest vortex rings that are responsible for the large bubbles, as they interact too strongly with the pool surface and self-destruct. Rather, it is somewhat weaker vortices that can deform the deeper craters, which manage to pinch off the large bubbles. These observations also explain why the strongest and most penetrating vortex rings emerging from drop impacts are not produced by oblate drops but by more prolate drop shapes, as had been observed in previous experiments.

Figure 1

Side view imaging of a prolate drop impacting into a pool ($D=$ 5.0 mm, $V=$ 0.9 m/s), observed below the pool surface at the following times after the first contact: 7.7, 8.7, 11, 13, 16, 20, 24, and 27 ms. A slightly different liquid is used in the drop (10.5% ${\text{MgSO}}_4$ solution with viscosity 1.96 cP and density $1.105\mathrm{g}/{\mathrm{cm}}^3$) and the pool (distilled water) to visualize their interface (hemispherical and curled line in the first frame). The dark region is the air cavity created by the impacting drop. The scale bar is 1 mm long.

Figure 2

Typical time sequence leading to large bubble entrapment, showing the following times: $t^{*}=-0.05$, 0.18, 0.41, 0.87, 1.80, 2.99, and 4.80. $D=$ 5 mm, $V=$ 1.0 m/s, $a=$ 0.9 ($\text{Re}=5000, \text{We}=69$). (a) The water originally in the drop (pool) is shown in red (blue), while the air is shown in green. The gray scales can be identified in the first image. The liquids in the drop and the pool are identical, without any material interface between them. (b) The corresponding vorticity field.

Figure 3

Influence of gravity on large-bubble entrapment. This sequence is for the same conditions as in Fig. 2, which includes gravity, while in this figure gravity has been excluded. $t^{*}=-0.05$, 0.18, 0.41, 0.87, 1.80, 2.99, and 4.80. $D=$ 5 mm, $V=$ 1.0 m/s, and $a=$ 0.9.

Figure 4

Role of gravity on regular bubble entrapment, at the bottom of the collapsing crater. Same impact conditions as in Fig. 2, but now for a spherical drop, $a=$ 1. With gravity (top) or without (bottom). $t^{*}=-0.05$, 0.18, 0.41, 0.87, 1.80, 2.99, 3.64, 4.80, 5.72, and 7.64. $D=$ 5 mm, $V=$ 1.0 m/s.

Figure 5

(a) Parameter space where a large bubble is entrapped ($▴$) or is not ($•$). All simulations are for a prolate water drop with a horizontal axis $a=D_h/D=0.9$. No large bubble entrapment was observed for other drop aspect ratios when $a$ is 0.95, 1, 1.05, and 1.1. (b) Equivalent spherical diameter of the large air bubble $D_b$, based on its total volume and normalized by the drop diameter ($D_b^{*}=D_b/D$), for $D=5\mathrm{mm}$ and $a=0.9.$

Figure 6

Time (a) and depth (b) of the large bubble entrapment. It is defined as the point where the liquid tongue first touches the opposite symmetrical liquid tongue on the axis of symmetry above the air cavity. The zero in depth (b) is set at the initial pool surface.

Figure 7

Effect of drop shape on the vortex interaction with the free surface: $D=$ 5 mm, $V=$ 1 m/s, over a range of aspect ratios from left to right, $a=$ 0.9, 0.95, 1, 1.05, and 1.1, which are shown in the insets (not to scale). First row: interface shapes at a fixed time $t/{\tau }_v=0.72$. Middle row: vorticity in the liquid at the same time. Bottom row: interface shapes shown at a later time $t^{*}=5.72$. The scale bars are $0.5D$ long.

Figure 8

Time evolution of the vorticity maximum in the main vortex ring shed behind the neck (a), and its location (b), starting near the center and then moving outward radially. Parts (c) and (d) show the time evolutions of its radial and vertical location. The red curve (with the +) represents the case in which the large bubble is entrapped. The + indicates the time of maximal radial location, corresponding to $t^{*}=$ 1.80 (fifth panel in Fig. 2).

Figure 9

Kinetic energy $EK$ in radial (a) and vertical (b) directions, normalized by the initial kinetic energy of the drop. The total combined kinetic energy is shown in Fig. S4 of the Supplemental Material [50].

Figure 10

Radial component of the momentum $M_R$, normalized by the norm of the initial vertical momentum of the drop. The dotted lines in (b) correspond to the cases in which gravity has been removed.

Figure 11

Large bubble entrapment for a drop of 6% ${\text{MgSO}}_4$, giving ${\rho }_d/{\rho }_p=$ 1.06 and ${\mu }_d=$ 1.3 cP for $D=5.0$ mm, $V=$ 0.94 m/s, and $H=$ 5.0 cm. The sequence shows the following times: $-2.3$, 7, 11, 17, and 25 ms after the first contact. The scale bar is 1 mm long.

Figure 12

(a) Large bubble entrapment for a drop of 10.5% ${\text{MgSO}}_4$ solution with viscosity 1.96 cP and density 1.105 $\mathrm{g}/{\mathrm{cm}}^3$, impacting into a pool of distilled water. Impact conditions: prolate drop, $D=$ 5.0 mm, $V=$ 1.30 m/s, and $H=$ 9.1 cm. The sequence shows the following times: $-1.3$, 5.4, 7, 11, and 20 ms after the first contact. The scale bar is 1 mm long. (b) Sequence in the same conditions as in Fig. 2, but higher impact velocity, and thus similar conditions as in the experiments of Fig. 12. $t^{*}=-0.05$, 0.18, 0.41, 0.87, 1.80, 2.99, and 4.80. $D=$ 5 mm, $V=$ 1.30 m/s, and $a=$ 0.9.

Figure 13

Crater evolution for oblate drops, which never entrap a large bubble. Drop composition: 10.5% ${\text{MgSO}}_4$ solution with viscosity 1.96 cP and density $1.105{\mathrm{g}/\mathrm{cm}}^3$; pool: distilled water. Impact conditions: oblate drop, $D=$ 5.0 mm. (a) For $V=$ 1.11 m/s, $H=$ 6.8 cm. The sequence shows the following times: $-2$, 2.7, 7.7, 12.7, 24.3, 29, 37, and 67.7 ms after the first contact. (b) For $V=$ 1.24 m/s, $H=$ 8.3 cm. The sequence shows the following times: $-1.5$, 3.5, 8.5, 13.5, 25.2, 29.8, 37.8, and 50.8 ms after the first contact. The scale bars are 1 mm long.

Figure 14

Emergence of the vorticity from the growing neck connecting the drop and the pool. The last row is zoomed on the point of highest curvature of the interface, where the vorticity is produced.

Figure 15

Strength of the vortex ring as in Fig. 8 but rescaled with the vertical extension of the drop $b$.