Figure 1

Passive breakup at T junctions. Droplets flow into a T junction, sketched in (a), where the flow is split into two sidearms. The narrow portion of the two side arms, of lengths ${\ell }_1$ and ${\ell }_2$, control the relative flow resistance of the paths and, hence, the relative sizes of the two daughter drops as shown in the photomicrographs of (b), (c), and (d); the ratios of arm lengths are, respectively, ${\ell }_1/{\ell }_2=1:1$, $1:5.2$, and $1:8.1$, corresponding to daughter drop volume ratios of (b) $1:1$, (c) $1:5.2$, and (d) $1:7.5$.Reuse & Permissions

Figure 2

Critical conditions for breaking drops at T junctions. In a channel of width $w_0$, droplets having length ${\ell }_0$ and velocity $v$ enter a T junction and either break or do not break. An example of nonbreaking drops, corresponding to the circled point below the curve in (k), enter the T junction in (a), stretch in (b), reach a maximum extension in (c), and then move alternatively left and right out of the junction in (d). At maximum extension, shown in (e), the extended length ${\ell }_e$ and width $w_e$ give $\epsilon ={\ell }_e/(\pi w_e)=0.95$. A similar series for breaking conditions corresponding to the circled point above the critical line are shown in (f)–(i). In this case, the maximum extension shown in (j) is $\epsilon =1.15$. In (k), open circles indicate when drops of a given capillary number $\mathcal{C}=\eta v/\gamma$ and initial extension ${\epsilon }_0={\ell }_0/(\pi w_0)$ break, and squares indicate when they do not. A model for the critical capillary number for breaking ${\mathcal{C}}_{\mathrm{c}\mathrm{r}}$ provides the curve ${\mathcal{C}}_{\mathrm{c}\mathrm{r}}=\alpha {\epsilon }_0(1/{\epsilon }_0^{2/3}-1{)}^2$ shown in (k) with fitting parameter $\alpha =1$.Reuse & Permissions

Figure 3

Sequential application of passive breakup. In (a) drops are formed at high dispersed phase volume fractions (drop formation not shown) and are sequentially broken to form small drops. In (b) the droplets flow downstream with nearly defect-free hexagonal-close-packed ordering.Reuse & Permissions

Figure 4

Obstruction mediated passive breakup. (a) Schematic diagram of a square obstruction in a microchannel. The obstacle is a $60\mu \mathrm{m}$ square; $a=15\mu \mathrm{m}$. (b) The obstacle is approximately in the center of the channel so that the ratio $a/b$ is $1:1.2$. (c) The channel width is $120\mu \mathrm{m}$ and the ratio $a/b$ is $1:2.7$. (d) As in (c) but every second drop breaks when a two-layer pattern encounters an off-center obstruction.Reuse & Permissions