Gravity-induced double encapsulation of liquids using granular rafts

We experimentally investigate a millimetric armored droplet of a water-isopropyl alcohol solution sedimenting through oil and approaching a water layer at the bottom of the container. Upon reaching the oil-water interface, the droplet is shown to rupture and coalesce with the water either for low droplet densities (floating rupture) or for low oil viscosities (sinking rupture). By contrast, for sufficiently large drop density or oil viscosity, the oil covering the armored drop pinches off in the underlying water, as the armored drop continues to sink. This leads to the double encapsulation of an aqueous solution in water, which can be utilized to transport desired ingredients within a wet environment. We show that a simplified quasistatic model of a rigid sphere successfully captures the limit of the floating rupture behavior. We also rationalize the transition from the sinking rupture to oil pinch-off, by comparing the timescales of the film drainage versus sinking. Our results demonstrate that an effective Bond number and an effective Ohnesorge number are the two key dimensionless parameters that characterize the pinch-off threshold in good agreement with the experiments.

Figure 1

(a) The 3D schematic of the stratified system where particles are slowly added from the top. (b) The schematic of the granular raft forming on an IPA-oil interface prior to the formation of the armored drop. (c) The armored drop sediments in oil and approaches the water-oil interface.

Figure 2

Time sequential images for (a) [$d_{\mathrm{s}}=125\mu \mathrm{m}$, ${\rho }_{\mathrm{s}}=2500\mathrm{kg}/{\mathrm{m}}^3$, ${\mu }_{\mathrm{o}}=0.097$ Pa s]: The armored drop approaches the interface ($t_0=0$ s) and comes to an apparent rest ($t_1=0.12$ s), until the thin film ruptures ($t_2=0.6$ s). After rupture, some particles sink and some particles float and surf under a Marangoni flow ($t_3=0.72$ s), as illustrated in the inset schematic. (b) [$d_{\mathrm{s}}=500\mu \mathrm{m}$, ${\rho }_{\mathrm{s}}=3800\mathrm{kg}/{\mathrm{m}}^3$, ${\mu }_{\mathrm{o}}=0.097$ Pa s]: The interface deforms strongly ($t_0=0$ s); the armored drop continues to push the interface downward into water ($t_2=0.02$ s), until the oil film ruptures ($t_3=0.035$ s). Then, all particles sink in water ($t_4=0.07$ s), as highlighted in the inset schematic. (c) [$d_{\mathrm{s}}=350\mu \mathrm{m}$, ${\rho }_{\mathrm{s}}=2500\mathrm{kg}/{\mathrm{m}}^3$, ${\mu }_{\mathrm{o}}=0.485$ Pa s]: The interface deforms strongly ($t_0=0$ s); the armored drop continues to push the interface downward into water ($t_1=0.3$ s and $t_2=0.6$ s) until the encapsulating oil pinches off ($t_4=0.68$ s). The inset schematic highlights the resultant double encapsulation in the pinch-off behavior. All scale bars show 2 mm.

Figure 3

Schematics for two-phase experiments (a) before and (b) after formation of the armored drop. (c) The armored drop equivalent density, ${\rho }_{\mathrm{eq}}-{\rho }_{\mathrm{i}}$, as a function of ${\rho }_{\mathrm{s}}{d}_{\mathrm{s}}/{\ell }_{\mathrm{c}}$ for varying particle sizes, $d_{\mathrm{s}}=4\text{–}1000\mu \mathrm{m}$, and particle densities, ${\rho }_{\mathrm{s}}=2500\mathrm{kg}{\mathrm{m}}^{-3}$ (half-filled) or ${\rho }_{\mathrm{s}}=3800\mathrm{kg}{\mathrm{m}}^{-3}$ (filled). The dashed line corresponds to the total mass calculation with particle packing fraction, $\varphi =0.76$. Inset: The armored drop equivalent radius, $a$, for varying ${\rho }_{\mathrm{s}}{d}_{\mathrm{s}}/{\ell }_{\mathrm{c}}$.

Figure 4

(a) Schematics of a sphere in equilibrium at a fluid-fluid interface. (b) An armored drop [${\rho }_{\mathrm{s}}=2500\mathrm{kg}{\mathrm{m}}^{-3}$, $d_{\mathrm{s}}=125\mu \mathrm{m}$, ${\mu }_{\mathrm{o}}=0.485\mathrm{Pa}\mathrm{s}$] before the onset of rupture.

Figure 5

The phase diagram showing Bo vs $\mathrm{\Gamma }$ for the particle density, ${\rho }_{\mathrm{s}}=2500\mathrm{kg}/{\mathrm{m}}^3$ (half-filled), or ${\rho }_{\mathrm{s}}=3800\mathrm{kg}/{\mathrm{m}}^3$ (filled), and varying particle sizes (corresponding varying symbol sizes). Error bars are smaller than symbol sizes. The dotted-dashed line and the dashed line correspond to the upper bounds (i.e., ${\mathrm{\Gamma }}_{\max }$) of the floating behavior from the quasistatic force balance [25, 30] for $\theta =\pi /2$ and $\theta =3\pi /5$, respectively.

Figure 6

Schematics of a sinking armored drop approaching pinch-off.

Figure 7

The schematic of a sphere settling toward a shear free planar boundary.

Figure 8

The phase diagram showing ${\mathrm{Bo}}_{\mathrm{eff}}$ vs ${\mathrm{Oh}}_{\mathrm{eff}}$ for the particle density, ${\rho }_{\mathrm{s}}=2500\mathrm{kg}/{\mathrm{m}}^3$ (half-filled), or ${\rho }_{\mathrm{s}}=3800\mathrm{kg}/{\mathrm{m}}^3$ (filled), and varying particle sizes (corresponding varying symbol sizes). Error bars are smaller than the symbol sizes. The dotted-dashed line and the dashed line correspond to ${\mathrm{Bo}}_{\mathrm{eff}}\approx 3(1-cos\theta )/4$ for $\theta =\pi /2$, and $\theta =3\pi /5$, respectively. The solid line shows ${\mathrm{Oh}}_{\mathrm{eff}}=0.4{\mathrm{Bo}}_{\mathrm{eff}}/\sqrt{{\mathrm{Bo}}_{\mathrm{eff}}-1}$.

Figure 9

A snapshot of an armored drop sinking in oil.