Numerical Insights on Controlled Droplet Formation in a Microfluidic Flow-Focusing Device

TL;DR

This study uses a three-dimensional CLSVOF-based CFD model to predict droplet formation regimes and transitions in a square-cross-section flow-focusing microchannel, enabling flow regime maps and a unified scaling law for droplet length across a broad range of operating conditions. By explicitly resolving the liquid film around droplets and employing a CSF surface-tension model, the authors quantify the effects of continuous-phase viscosity, interfacial tension, dispersed-phase viscosity, and flow-rate ratios on droplet length, velocity, and volume. The key contributions include a validated model against existing experiments, a unified scaling relation $L_D/W_c=0.244\,Ca^{-0.430}$, and flow maps for two liquid–liquid systems, all of which inform design guidelines for high-throughput, on-demand droplet generation. The work underscores the importance of liquid-film thickness in controlling droplet dynamics and provides practical insights for droplet-based microfluidic applications such as drug delivery and materials synthesis.

Abstract

In this article, we have developed a computational model to determine the droplet formation regime and its transition in a square microfluidic flow-focusing device that eventually dictate the droplet shape, size, and its formation frequency. We have methodically explored the influences of various physicochemical parameters on the droplet dynamics and flow regime transition, which are essential in the development of new methods for on-demand droplet generation. On the basis of the droplet formation mechanism, we have formulated flow maps for different liquid-liquid systems, and have also proposed a scaling law to predict the droplet length for a wide range of operating condition resulting from the variation of flow rates, and viscosities of the continuous phase as well as the interfacial tension. This work can effectively contribute in providing helpful guidelines on the design and operations of droplet-based flow-focusing microfluidic systems.

Figures (18)

• Figure 1: Schematic of (a) computational domain, (b) typical droplet flow in a flow-focusing microchannel, (c) forces acting on the dispersed phase during droplet formation at the cross-junction, and (d) plug and spherical droplets with the definition of droplet deformation index (DI).
• Figure 2: (a) Computational grid with near wall mesh refinement, (b) comparison of parasitic currents around droplet interface through VOF and CLSVOF methods for oil– water system at $Q_w/Q_o=5$ and $Q_o$= 400 $\mu$L/min, (c) grid independence analysis with different mesh element sizes, and (d) comparison of droplet length predictions against the experimental results of wu2008three for $U_w$ =0.00252, $\gamma$ = 30 mN/m, and $\eta_w/\eta_o$ = 0.416.
• Figure 3: Droplet evolution in a flow-focusing microfluidic device containing (a) oil– water, and (b) oil– water+40% glycerol at $Q_w/Q_o=2$ and $Q_w$= 400 $\mu$L/min (blue: oil, red: water).
• Figure 4: Effect of continuous phase fluid viscosity on (a) non-dimensional droplet length, (b) droplet velocity, (c) droplet volume, and (d) pressure drop at $Q_w/Q_o=2$ and $Q_w$= 400 $\mu$L/min.
• Figure 5: (a) 3-D iso-surface view of simulated droplet formation in the dripping regime, where the droplet along with four vertical slices are shown in zoomed view, and (b) visualization of surrounding liquid film thickness around the droplet (left to right: rear to nose) for $Q_w/Q_o=2$ and $Q_w$= 400 $\mu$L/min.