Effects of viscosity on liquid structures produced by in-air microfluidics

This paper experimentally investigates the effect of viscosity on the outcomes of collisions between a regular stream of droplets and a continuous liquid jet. A broad variation of liquid viscosity of both the drop and the jet liquid is considered, keeping other material properties unchanged. To do so, only two liquid types were used: aqueous glycerol solutions for the drop and different types of silicone oil for the jet liquid. Combining these liquids, the viscosity ratio $\lambda ={\mu }_{\mathrm{drop}}/{\mu }_{\mathrm{jet}}$ was varied between 0.25 and 3.50. The collision outcomes were classified in the form of regime maps leading to four main regimes: drops in jet, fragmented drops in jet, encapsulated drops, and mixed fragmentation. We demonstrate that, depending on the drop and jet viscosity, not all four regimes can be observed in the domain probed by our experiments. The experiments reveal that the jet viscosity mainly affects the transition between drops in jet and encapsulated drops, which is shifted towards higher drop spacing for more viscous jets. The drop viscosity leaves the previous transition unchanged but modifies the threshold of the drop fragmentation within the continuous jet. We develop a model that quantifies how the drop viscosity affects its extension, which is at first order fixing its shape during recoil and is, therefore, determining its stability against pinch-off.

Figure 1

(a) Experimental setup for the drop/jet collision experiments. (b) Geometric and kinetic parameters of the collisions. Figure adapted from Ref. [50].

Figure 2

(a) Collision outcomes of the reference case G5/SO5 classified in the form of a regime map with $W{e}_d$ and $L_j/D_j$ as the scaling parameters. (b) Recorded collision pictures (front view—camera 2) of the structures produced by drop-jet collisions. A, B, C, and D correspond to the data marked in red in (a). (c) Schematic of the structures. Adapted from Ref. [50].

Figure 3

(a) Studied liquid combinations with the corresponding drop/jet Ohnesorge numbers Oh and associated viscosity ratio $\lambda ={\mu }_d/{\mu }_j$. (b)–(f) The collision outcomes of the sets of experiments with changing drop or jet liquid in the form of regime maps with ${\mathrm{We}}_d$ and $L_j/D_j$ as the scaling parameters—(b) drop liquid: G1, jet liquid: SO5; (c) drop liquid: G20, jet liquid: SO5; (d) drop liquid: G5, jet liquid: SO1; (e) drop liquid: G5, jet liquid: SO3; (f) drop liquid: G5, jet liquid: SO20. The colored (solid or dashed) lines represent the boundaries for the respective liquid pair, whereas black lines indicate the boundaries for the reference case.

Figure 4

(a) Recorded collision picture in orthogonal view with the three major instants at drop jet collisions and the maximum extension of the elongated drop $L_{\max }$. See Supplemental Material for an illustrative movie [66]. (b) The aspect ratio $\zeta =L_{\max }/D_d$ as a function of ${\mathrm{We}}_d$ for all liquid pairs. (c) The critical aspect ratio ${\zeta }_{\mathrm{crit}}$ at which fragmentation occurs against the viscosity ratio $\lambda$. The dashed-dotted line is a fit function given by ${\zeta }_{\mathrm{crit}}=0.007{\lambda }^4-0.078{\lambda }^3+0.422{\lambda }^2-0.759\lambda +3.447$. (d) The critical Weber number ${\mathrm{We}}_{d,\mathrm{crit}}$ at which the drop fragments as a function of the drop Ohnesorge number ${\mathrm{Oh}}_d$. The dashed-dotted line is a guide for the eyes. (b)–(d) All the investigated configurations are accounted for corresponding to $1.1<L_j/D_j<2.3$.

Figure 5

Collision pictures in (a) front view and (b) orthogonal view with $D_{\mathrm{lam}}^{\max }$, the maximum diameter of the bent lamella, and $t_d^{\max }$, the instant of maximal extension. (c) The maximum surface of the deformed drop ${\mathrm{\Sigma }}_d^{\max }$ normalized by ${\mathrm{\Sigma }}_{d,0}$ as a function of ${\mathrm{We}}_d$ for all six liquid combinations. (d) Instant of maximal extension $t_d^{\max }$ normalized by $t_{d,\mathrm{osc}}$. (e) Normalized maximum drop surface ${\mathrm{\Sigma }}_d^{\max }/{\mathrm{\Sigma }}_{d,0}$ as a function of ${\mathrm{We}}_d{\mathrm{Re}}_d^{2/5}$ where (Re) is the Reynolds number. The inset: The aspect ratio $\zeta$ as a function of ${\mathrm{We}}_d{\mathrm{Re}}_d^{2/5}$.

Figure 6

Inertial fragmentation threshold in the form of ${\mathrm{We}}_{d,\mathrm{crit}}{\mathrm{Re}}_{d,\mathrm{crit}}^{2/5}$ as a function of $\lambda$. Symbols: experimental data, dashed-dotted line: Eq. (9).

Figure 7

Collision pictures illustrating the three droplet fragmentation processes observed for G5/SO20 in front (upper picture) and orthogonal (picture below) view: (a) $L_j/D_j\approx 1.4$, (b) $L_j/D_j\le 1.3$, and (c) $L_j/D_j\ge 1.75$.