Equilibrium and Nonequilibrium States in Microfluidic Double Emulsions

We describe experimental and theoretical studies dedicated to establishing the physics of formation of double droplets in microfluidic systems. We show that the morphologies (complete engulfing, partial engulfing, and nonengulfing) obtained at late times minimize the interfacial energy of the system. We explain that nonequilibrium morphologies generated in the system can have long lifetimes. Remarkably, the physics of formation of the double droplets with microfluidics allows the synthesis of particles with new morphologies.

Figure 1

Double flow focusing geometry used in the experiment: a first structure $A/B$ is produced at the first junction. Downstream fluid $C$ engulfs the structure, and a structure $A/B/C$ is formed. The structure further moves into a reservoir. In the upper right figure, $N$ is the number of droplets encapsulated in a $\mathrm{\text{tetradecane}}/\mathrm{TPGDA}/\mathrm{\text{water}}+1\%\mathrm{SDS}$ system, and $Q_A$ and $Q_B$ are, respectively, the flow rates of fluids $A$ and $B$. I and III are monodisperse regimes and II (shaded region) represents polydisperse regimes for which the emulsion includes globules engulfing one or two droplets.

Figure 2

Two late time morphologies obtained in the experiments. On the left, partial engulfing (or Janus state) obtained using silicone oil and rapeseed oil, with distilled water as the external phase. On the right, complete engulfing obtained using fluorinated oil/silicone oil and $\mathrm{\text{water}}+\mathrm{SDS}$ as the external phase. The white bars represent $100\mu \mathrm{m}$.

Figure 3

Comparison between equilibrium and observed morphologies: Squares represent nonengulfing, circles engulfing, and triangles partial engulfing, as observed experimentally. The dotted line defines the boundary of a physically inaccessible region, as suggested by Girifalco’s formula, with the $\varphi$ parameter (cf. Ref. 13) equal to 0.92.

Figure 4

(a) Evolution from an encapsulated to a nonencapsulated state; using fluorinated $\mathrm{\text{oil}}/\mathrm{\text{water}}+\mathrm{SDS}/\mathrm{TPGDA}$. The entire process takes less than 1 ms. The arrow indicates the flow direction. (b) Evolution from a complete encapsulation to a Janus state, which represents the equilibrium in this case; the fluids are $\mathrm{\text{tetradecane}}/\mathrm{TPGDA}/\mathrm{\text{water}}+1\%\mathrm{w}/\mathrm{w}$ SDS. White bars represent $100\mu \mathrm{m}$.

Figure 5

Reduced distance $d/a$ from the center of the inner droplet to the interface of the host drop versus reduced time $t/\tau$ in the transient regime. Open circles, circles, and triangles are obtained, respectively, in the following conditions: (a) $a=65\mu \mathrm{m}$, $98\mu \mathrm{m}$, $92\mu \mathrm{m}$; (b) $\widehat{a}=26\mu \mathrm{m}$, $37\mu \mathrm{m}$, $40\mu \mathrm{m}$; (c) $\lambda =0.4$, 0.38, 0.43; $U=$ (a) $20.4\mathrm{mm}/\mathrm{s}$, (b) $10.3\mathrm{mm}/\mathrm{s}$, (c) $9.3\mathrm{mm}/\mathrm{s}$. For experiments a, b, and c, the viscosity of the inner droplet is ${\mu }_0=3\mathrm{mPa}\mathrm{s}$, that of the host drop is $\widehat{\mu }=15\mathrm{mPa}\mathrm{s}$; the viscosity of the continuous phase is $\mu =1\mathrm{mPa}\mathrm{s}$ for experiments a and b and $2.4\mathrm{mPa}\mathrm{s}$ for experiment c due to addition of glycerol. The typical lifetimes or the transient regimes are $\tau =$ (a) 0.68 s, (b) 0.78 s, and (c) 1.29 s while the predicted times are, respectively, 0.1 s, 0.2 s, and 0.1 s. The line shows the theoretical prediction developed in the paper.

Figure 6

SEM pictures of two different morphologies obtained with the same fluids, in the same chip, and cured under UV light: (a) nonequilibrium structure (cut with a razor blade so as to reveal full encapsulation), (b) equilibrium structure in the form of Janus particle. The fluids are tetradecane, acrylate monomer $+8\%$ Darocur, and water $+1\%$ SDS.