1. the Relation Between the Plug Length and Its Volume

Supplementary materials

1. The relation between the plug length and its volume.

To determine the volumes of the free ruptured droplets, the relation between the plug length and its volume was investigated as shown in Fig. S1. The volumes were gotten from the liquid/liquid dispersion experiments and calculated by dividing the incoming flow rates of oil phase to the generation frequencies. As shown in the figure the length (LO) and the volume (vO) have a linear relationship. Correlated from the experimental data the volume of the droplet can be expressed by a linear equation:

(S1)

Since the cross-section area of the channel is 0.126 mm2, it can be seen that the slope of Eq. S1 is almost equal to the cross-section area, which means the oil droplets almost abound the cross-section of the channel. To simplify the calculation of the droplet volume the slope was chosen as the cross-section area of the channel (0.126 mm2) in the article. The intercept of Eq. S1 can be seemed as the redundant volume (Vr ) out of the hemispherical end of the plugs. Thus, the volume of the droplet can be represented by the following equation:

(S2)

fig s1

Fig. S1 The relation between the plug length and its volume. The dots are the results from experiments and the line is the linear fitting of the experimental results.

2. The effect of droplet generation on the bubble generation

To determine the volumes of the bubbles, the effect of the break-up of oil phase on the break-up of gas phase should also be considered. Fig. S2 gives the generating frequency of the bubbles at different flow rates of the oil phase. It can be seen that there are little effect of droplet generation on the bubble generation process. So the break-up of the bubbles can be seemed independent with the introduction of oil phase.

fig s2

Fig. S2 The generating frequencies of gas phase with the variation of the incoming flow rates of oil phase. The flow rate of water phase in the figure is 300μL/min, and the flow rates of gas phase are shown on the right side of the figure.

3. The dynamic contact angle at the rupturing moment of the gas phase

The dynamic contact angle is an important value to determine the size law of gas phase. It was statistically measured from the recorded images as shown in Fig. S3a. From the measurement results it can be seen that the dynamic contact angle are independent with flow rates of the two phases and fixes at a value of 41º as shown in Fig. S3b.

(a)

(b)

Graph2

Fig. S3 a The schematic diagram of the dynamic contact angle. b The measured results at different flow rates of the gas phase and water phase.