Collisions of drops with an immiscible liquid jet

We investigate the collisions of a regular stream of drops with a continuous immiscible liquid jet. By varying the jet and drop diameters, their velocities, and relative orientation, we observe a broad variety of liquid structures, some of which have a high applicability for capsule and advanced fiber production. First, these structures are described and classified into four regimes that account for potential liquid fragmentation and the resulting liquid distribution. Fragmentation mechanisms are proposed based on a physical analysis accounting for the problem geometry, the system inertia, and the system's surface energy. Corresponding dimensionless numbers are built, which are used to draw two-dimensional regime maps that can very well distinguish the experimental outcomes. Finally, the effects of viscosity, qualitatively evidenced by employing various liquid pairs, are discussed.

Figure 1

Experimental setup enabling the production and observation of collisions between a regular drop stream and a continuous immiscible liquid jet. The signal generator provides the signal S driving the drop generator and a synchronous TTL signal to trigger the illumination.

Figure 2

Geometric and kinetic parameters of the collision.

Figure 3

Sketch representing the four regimes observed after the collision of a drop stream (dark) with a continuous immiscible jet (bright gray): (a) Encapsulated drops, (b) Drops in the jet, (c) Mixed fragmentation, and (d) Fragmented drops in the jet.

Figure 4

Examples of drops in the jet outcomes with (a) $D_d=205\mu \mathrm{m}, D_j=192\mu \mathrm{m}, L_j/D_j=3.04, U_{\perp }=5.02\mathrm{m}{\mathrm{s}}^{-1}, U_{\parallel }=-4.81\mathrm{m}{\mathrm{s}}^{-1}$, and $L_{\mathrm{dij}}/L_d=0.86$; (b) $D_d=206\mu \mathrm{m}, D_j=300\mu \mathrm{m}, L_j/D_j=2.03, U_{\perp }=3.96\mathrm{m}{\mathrm{s}}^{-1}, U_{\parallel }=-2.33\mathrm{m}{\mathrm{s}}^{-1}$, and $L_{\mathrm{dij}}/L_d=1.05$; and (c) $D_d=216\mu \mathrm{m}, D_j=500\mu \mathrm{m}, L_j/D_j=1.35, U_{\perp }=3.33\mathrm{m}{\mathrm{s}}^{-1}, U_{\parallel }=-2.41\mathrm{m}{\mathrm{s}}^{-1}$, and $L_{\mathrm{dij}}/L_d=1.20$.

Figure 5

Plot of $L_{\mathrm{dij}}/L_d$ as a function of $m_j/m_d$ and $u_j/u_d$ for $\alpha ={60}^{\circ }$. The central line corresponds to Eq. (4) and represents the conditions for which the spacing between the drops is unchanged by their encapsulation into the jet.

Figure 6

Examples of fragmented drops in the jet with (a) $D_d=205\mu \mathrm{m}, D_j=300\mu \mathrm{m}, L_j/D_j=2.03, U_{\perp }=4.97\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=-4.76\mathrm{m}{\mathrm{s}}^{-1}$; (b) $D_d=197\mu \mathrm{m}, D_j=180\mu \mathrm{m}, L_j/D_j=1.81, U_{\perp }=5.59\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=-0.63\mathrm{m}{\mathrm{s}}^{-1}$; and (c) a partially continuous structure and $D_d=209\mu \mathrm{m}, D_j=280\mu \mathrm{m}, L_j/D_j=1.00, U_{\perp }=6.37\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=1.62\mathrm{m}{\mathrm{s}}^{-1}$.

Figure 7

Examples for encapsulated drops: (a) G5 and SOM3 with $D_d=200\mu \mathrm{m}, D_j=280\mu \mathrm{m}, L_j/D_j=2.50, U_{\perp }=3.95\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=-2.61\mathrm{m}{\mathrm{s}}^{-1}$; (b) G5 and SOM5 with $D_d=207\mu \mathrm{m}, D_j=192\mu \mathrm{m}, L_j/D_j=3.04, U_{\perp }=1.98\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=-0.91\mathrm{m}{\mathrm{s}}^{-1}$; (c) G5 and SOM5 with $D_d=210\mu \mathrm{m}, D_j=192\mu \mathrm{m}, L_j/D_j=3.04, U_{\perp }=4.56\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=-3.09\mathrm{m}{\mathrm{s}}^{-1}$; and (d) G13 and SOM5 with $D_d=225\mu \mathrm{m}, D_j=205\mu \mathrm{m}, L_j/D_j=3.25, U_{\perp }=3.84\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=-1.10\mathrm{m}{\mathrm{s}}^{-1}$.

Figure 8

Regime of mixed fragmentation (a) with oil satellites and $D_d=223\mu \mathrm{m}, D_j=193\mu \mathrm{m}, L_j/D_j=4.38, U_{\perp }=5.82\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=3.86\mathrm{m}{\mathrm{s}}^{-1}$; (b) without oil satellites and with $D_d=228\mu \mathrm{m}, D_j=275\mu \mathrm{m}, L_j/D_j=1.91, U_{\perp }=6.06\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=-1.91\mathrm{m}{\mathrm{s}}^{-1}$; (c) with $D_d=231\mu \mathrm{m}, D_j=210\mu \mathrm{m}, L_j/D_j=2.65, U_{\perp }=7.69\mathrm{m}{\mathrm{s}}^{-1}$, and $U_{\parallel }=4.24\mathrm{m}{\mathrm{s}}^{-1}$ from the view of the collision plane; and (d) from the normal view of the framed part of (a) observed from the jet side.

Figure 9

Regime maps built using (a) $L_j/D_j$ and (b) $L_{\mathrm{dij}}/D_{\mathrm{dij}}$ as a function of $U_{\parallel }/U$ to distinguish the encapsulated drops (red diamonds) from the drops in the jet (gray circles) and the fragmented drops in the jet (blue triangles). All points were obtained with SOM5 and G5. The insets are close-ups of the transition showing the variation of ${\mathrm{\Lambda }}_c$ and ${\mathrm{\Omega }}_c$ with $U_{\parallel }/U$. The dashed and solid lines are symmetric around $U_{\parallel }/U=0.12$ and $U_{\parallel }/U=0$, respectively, and are guides to the eye.

Figure 10

Regime maps for G5 drops and SOM5 jets aiming to distinguish the encapsulated drops (red diamonds) and the drops in the jet (gray circles) from the fragmented drops in the jet (blue triangles) and the mixed fragmentation (black stars) using (a) ${\text{We}}^{*}$ and $D_{\mathrm{dij}}{L}_{\mathrm{dij}}/D_d^2$. Also shown are the same points plotted for ${\text{We}}^{*}{D}_d^2/D_{\mathrm{dij}}{L}_{\mathrm{dij}}\propto D_{\max }^2$ and (b) $D_j/D_d$; or (c) $L_j/D_j$. The solid and dashed lines are guides to the eye.

Figure 11

Regime maps featuring encapsulated drops (diamonds), drops in the jet (circles), fragmented drops in the jet (triangles), and mixed fragmentation (stars) for various liquid pairs: (a) G5 and SOM20, (b) G13 and SOM20, (c) G5 and SOM3, and (d) G13 and SOM3. The solid and dashed lines are guides to the eye and correspond to the capillary and inertial fragmentation thresholds observed for G5 and SOM5.