To Split or Not to Split: Dynamics of an Air Disk Formed under a Drop Impacting on a Pool

When a drop falls and impacts on a liquid pool, it entraps an air disk below the drop, which then contracts into a central bubble. Here, we use high-speed imaging and high-resolution numerical simulations to characterize the air-disk contraction dynamics for different liquid properties. We show that the air disk can contract into a single central bubble, form a toroidal bubble, or split vertically into two smaller bubbles. We demonstrate that the transitions between the different regimes can be separated by an Ohnesorge number, ${\mathrm{Oh}}_e$, based on the air-disk thickness. For the lowest ${\mathrm{Oh}}_e$, we find a new regime, where vortex shedding from the rim of the contracting air disk breaks the vertical symmetry and prevents the bubble from splitting in two.

Figure 1

(a),(b) Schematic of the experimental setup: (a) side view, (b) bottom view. (c) Axisymmetric numerical configuration. (d)–(f) Typical experimental images at the beginning of air-disk entrapment: side view of (d) Milli-Q water, (e) silicone oil 20 cSt, and (f) bottom view of glycerin 60%. Scale bars are $100\mu \mathrm{m}$ long. (g) Simulation of Flutec PP1 drop impact and entrapped air disk (inset). The liquid originally in the drop (red) and in the pool (blue) are distinguished by using a passive tracer, while in the simulations they are in the same liquid phase separate from the air (green) [56].

Figure 2

Morphological changes of the entrapped air disk. (a),(b) Toroidal bubble for 0.65 cSt silicone oil: (a) bottom-view experiment; (b) simulation. Frame 1 is $60\mu \mathrm{s}$ after contact and time interval between snapshots is $10\mu \mathrm{s}$. (c),(d) Vertical splitting for 1.5 cSt silicone oil: (c) side view experiment; (d) simulation. Frame 1 is $23\mu \mathrm{s}$ after contact and time interval between snapshots is $33\mu \mathrm{s}$ except for the last two frames, where it is $17\mu \mathrm{s}$. Scale bars are $100\mu \mathrm{m}$ long. Colors are the same as in Fig. 1. Videos available online [56].

Figure 3

Parameter space for (a) toroidal bubble and (b) vertical splitting. Our simulations (filled symbols) and experiments (empty symbols). Numbered points are our experimental observations, 1: silicone oil 20 cSt; 2: glycerin 60%; 3: silicone oil 1.5 cSt; 4: ethanol; 5: glycerin 20%; 6: Flutec PP1; 7: silicone oil 0.65 cSt; 8: Milli-Q water. +: Vertical splitting observed experimentally for deionized water in [12]. ×: No vertical splitting in [48]. Blue dashed lines are experimental data for 5, 10, 20 cSt silicone oil in [16]. Experimental error bars for Re and We are smaller than 2 and 4%, respectively [56].

Figure 4

Vortex shedding from the edge of the contracting air disk. Snapshots of (a) tracers and (b) vorticity at $t^{*}=0.01$, 0.03, 0.05, 0.06, 0.08, 0.15 for ${\mathrm{Oh}}_e=0.092$, $\mathrm{Re}=5000$, $\mathrm{We}=100$. Scale bars are $100\mu \mathrm{m}$ long. The white dashed line indicates the initial pool surface position. Colors in (a) are the same as in Fig. 1. Videos available online [56].

Figure 5

Temporal evolution of the entrapped air disk size and vertical motion from the simulations, varying the Weber number We at three different Reynolds numbers Re: (a),(d) $\mathrm{Re}=1000$ ($0.460<{\mathrm{Oh}}_e<1.838$), (b),(e) 3000 ($0.153<{\mathrm{Oh}}_e<0.613$), (c),(f) 6000 ($0.077<{\mathrm{Oh}}_e<0.306$). (a),(b),(c) Maximal diameter of the air disk ($D_{\max }/D_b$). Insets show the ratio $D_{\max }/D_s$. (d),(e),(f) $Z$ coordinate of the bubble center of mass ($z_{\mathrm{cm}}^{*}$). Insets show $z$ coordinate of the $D_{\max }$ point reset by $z_{D_{\max }}^{*}-z_s^{*}$, where $z_s^{*}=-0.58t^{*}+0.005$. NVS denotes no vertical splitting.