Role of the Channel Geometry on the Bubble Pinch-Off in Flow-Focusing Devices

The formation of bubbles by flow focusing of a gas and a liquid in a rectangular channel is shown to depend strongly on the channel aspect ratio. Bubble breakup consists in a slow linear 2D collapse of the gas thread, ending in a fast 3D pinch-off. The 2D collapse is predicted to be stable against perturbations of the gas-liquid interface, whereas the 3D pinch-off is unstable, causing bubble polydispersity. During 3D pinch-off, a scaling $w_m\sim {\tau }^{1/3}$ between the neck width $w_m$ and the time $\tau$ before breakup indicates that breakup is driven by the inertia of both gas and liquid, not by capillarity.

Figure 1

(a) Sketch of the flow-focusing setup. (b) Scanning electron micrograph of the imprint in the PDMS slab of the channel of width $30\mu \mathrm{m}$ and height $6\mu \mathrm{m}$. (c) Snapshot of the flow-focusing process: the central gas thread is squeezed by the surrounding liquid flow, releasing monodisperse microbubbles, shaped almost as disks because of the confinement in the third dimension.

Figure 2

Snapshots of the gas thread in two regimes of collapse described in the text [18]. (a) The gas thread is first squeezed inwards from the sides by the surrounding liquid; $w_m$ is its minimal width in the processed region (white dashed rectangle). This regime is sketched in cross section in (b). The gas thread experiences finally a fast pinch-off (c), where it is squeezed radially in the cross section (d).

Figure 3

Evolution of the minimum width of the gas thread $w_m$ as a function of the time $\tau =t_c-t$ remaining until final breakup, for the following cross sections ($W\times H$, both in $\mu \mathrm{m}$) (a) $30\times 6$, (b) $30\times 20$, (c) $20\times 20$. The liquid flow rates are (a) 20, (b) 20, and (c) $70\mu \ell /\min $. Each curve results from the superposition of independent events (indicated by different symbols in cases b and c), which collapse on the same master curve, showing the excellent reproducibility of the system. The two regimes described in the text correspond to different fits: first a linear one, and then a power law. Dashed lines in (a) and (b) indicate the transition between the two regimes, where the fitting curves intersect. The transition value between 2D and 3D collapses is $6.1\mu \mathrm{m}$ in case a ($H=6\mu \mathrm{m}$), and $19.1\mu \mathrm{m}$ in case b ($H=20\mu \mathrm{m}$). The instant of this transition gives the duration ${\tau }_{3\mathrm{D}}$ of the 3D collapse: $22\mu \mathrm{s}$ in case a, $25\mu \mathrm{s}$ in case b, and $19\mu \mathrm{s}$ in case c.

Figure 4

Logarithm of the minimum width of the gas thread $w_m$ as a function of the logarithm of the time $t_c-t$ until final breakup. The line represents the best fit of the data: its slope is (a) 0.33 (cross section $30\times 20\mu {\mathrm{m}}^2$) and (b) 0.30 (cross section $20\times 20\mu {\mathrm{m}}^2$). Different symbols represent independent experiments. We do not present the results for the channel of cross section $30\times 6\mu {\mathrm{m}}^2$, for which only three data points are in the 3D collapse regime: in that case, the slope is 0.35.