Bubble Formation in Yield Stress Fluids Using Flow-Focusing and $T$-Junction Devices

We study the production of bubbles inside yield stress fluids (YSFs) in axisymmetric $T$-junction and flow-focusing devices. Taking advantage of yield stress over capillary stress, we exhibit a robust break-up mechanism reminiscent of the geometrical operating regime in 2D flow-focusing devices for Newtonian fluids. We report that when the gas is pressure driven, the dynamics is unsteady due to hydrodynamic feedback and YSF deposition on the walls of the channels. However, the present study also identifies pathways for potential steady-state production of bubbly YSFs at large scale.

Figure 1

Top view of different devices: (a) $T$-junction, (b) flow focusing; $L$ is the exit channel length, $R$ the radius of all channels (inlet and exit). Pictures taken with $R=1\mathrm{mm}$, $L=10\mathrm{cm}$.

Figure 2

(a) Different stages of the break-up mechanism inside the $T$-junction, for a movie see Supplementary Materials [45]. (b) Spatiotemporal diagram of the break-up dynamic for a bubble train. The horizontal axis represents the ($OZ$) axis of the top picture in frame (a) and the vertical axis the time. The dashed blue lines illustrate the nearly constant speed regime of the YSF plug during the formation of different bubbles. (c) Typical evolution of the time to form one bubble $t_b$ (left vertical axis) and bubble length $\ell$ (right vertical axis) as a function of the time, with corresponding pictures of the spatiotemporal diagram. The dashed line stands for the divergence of bubble time formation when the system is completely filled with gas. The horizontal line highlights $t_b^{\min }$, the minimum time to form one bubble. In (a), (b), and (c) $R=1\mathrm{mm}$, $L=10\mathrm{cm}$, $Q=1.25\mathrm{ml}/\min$, $P=0.62\mathrm{bar}$, emulsion with ${\sigma }_y=100\mathrm{Pa}$).

Figure 3

$t_b$ as a function of the YSF flow rate in $T$-junction (left) and flow-focusing geometry (right), for Carbopol (${\sigma }_y=75\mathrm{Pa}$) both with channels’ radii of 1 mm and exit channel length of 10 cm. The red symbols correspond to steady regimes either obtained from pressure regulation (PR) or peristaltic pump (PP).

Figure 4

$t_b^{\min }$ as a function of $\mathrm{\Omega }/Q$ for $T$-junction (TJ) and the flow-focusing (FF) geometries. The different symbols are detailed in the inset; ($E$) stands for emulsion, ($C$) for Carbopol. The red symbols correspond to different steady state bubble production. TJ, FF, PR, and PP, respectively, stand for $T$-junction, flow focusing, pressure regulation, and peristaltic pump.