Inertia-driven jetting regimes in microfluidic coflows

Microfluidics have been used extensively for the study of flows of immiscible fluids, with a specific focus on the effects of interfacial forces on flow behavior. In comparison, inertia-driven flow of confined coflowing fluids has received scant attention at the microscale, despite the fact that the effects of microscale confinement are expected to influence inertia-driven flow behavior as observed in free jets. Herein, we report three distinct modes for breakup of coflowing, confined, microscale jets: the conventional Rayleigh mode and two additional inertia-driven modes occurring at higher Reynolds number flows, namely, a sinuous wave breakup and an atomizationlike mode. Each of the three modes is differentiated by a characteristic droplet size, size distribution, and dependence of the jet length as a function of the external fluid velocity $\left(v_{\text{ext}}\right)$. A unified phase diagram is proposed to categorize the jet breakup mechanisms and their transitions using, as a scale-up factor, the ratio of the jet inertial forces to the sum of the viscous and interfacial forces for both the inner and outer fluids. These results provide fundamental insights into the flow behavior of microscale-confined coflowing jets.

Figure 1

Coflowing setup developed for this study. $D$ and $d$ are the inner diameters of the outer and inner tubing, respectively. $L$ is the jet length, while $a$ is the droplets diameter.

Figure 2

(a) Optical images of the evolution of the jetting as a function of the outer fluid velocity: (a) dripping; (b),(c) Rayleigh jetting; (d),(e) sinuous wave breakup mode; (f),(g) atomizationlike mode. The pictures were obtained for $p=10\text{MPa}$, $T=20{}^{\circ }\mathrm{C}$; inner fluid: liquid ${\text{CO}}_2$; outer fluid: water, $v_{\text{int}\left({\text{CO}}_2\right)}=0.25\text{m}{\text{s}}^{-1}$. (h) Median plane visualization of the 3D numerical modeling of the atomizationlike jetting mechanism displaying the velocity vectors inside the core of the jet ($p=10\mathrm{MPa},T=20{}^{\circ }\mathrm{C},v_{\text{int}}\left({\mathrm{CO}}_2\right)=0.25\text{m}{\text{s}}^{-1}$; $v_{\text{ext}}$ (${\text{H}}_2\text{O}=4\text{m}{\text{s}}^{-1}$). The arrows represent the velocity vectors, whose magnitudes are proportional to their length, while the color represents the relative pressure ($P_r$) spatial variations (the total pressure can be calculated as $P=P_r+10\text{MPa}$).

Figure 3

Example of the regime characteristics used to categorize the breakup mechanisms. (a) Evolution of the jet length and the droplets mean size $\frac{\overline{a}}{d}$ as a function of $v_{\text{ext}}$ and (b) the droplets size distributions for different values of $v_{\text{ext}}$, corresponding to the yellow circled point in (a). The data were obtained for $p=10\text{MPa}$, $T=20{}^{\circ }\mathrm{C}$; inner fluid: liquid ${\text{CO}}_2$; outer fluid: water, $v_{\text{int}\left({\mathrm{CO}}_2\right)}=0.25\text{m}{\text{s}}^{-1}$.

Figure 4

Log-log plot of the ratio ($X$:$Y$) of the inertial forces over the sum of the viscous and interfacial forces for the $\mathrm{sc}\text{−}{\text{CO}}_2$–water ($p=10\mathrm{MPa}$, $T=48{}^{\circ }\mathrm{C}:\blacksquare$), pentane–water ($p=0.1\mathrm{MPa},T=20{}^{\circ }\mathrm{C}:▴$), and liquid ${\text{CO}}_2$–water ($p=10\mathrm{MPa}$, $T=20{}^{\circ }\mathrm{C}:•$) systems. The dripping regime is indicated in black, the Rayleigh type jets in green, the sinuous wave breakup mode is in blue, and the atomizationlike mode points are in red.