Experimental and Computational Analysis of the Hydrodynamics of Droplet Generation in a Cylindrical Microfluidic Device

Abstract

This study investigates the hydrodynamics of droplet formation in a T-shaped cylindrical microfluidic device using micro-PIV experiments and CFD simulations. Devices of 150 micro-m internal diameter were fabricated from PDMS via a cost-effective embedded templating method. Flow visualization was conducted using immiscible silicone oil and deionized water, forming water-in-oil droplets. A mathematical model coupling the Navier-Stokes and conservative level-set equations was solved using the finite element method. Detailed flow fields (velocity, pressure, and phase distribution) were obtained over a wide range of flow-rate ratios (0.1-10) and capillary numbers (0.001-0.1) to characterize droplet formation mechanisms. Phase evolution revealed distinct breakup stages (lag, filling, necking, and pinch-off) and multiple regimes (squeezing, dripping, sausage flow, and parallel flow with tip streaming). A regime map delineating droplet and non-droplet regions was developed. Droplet size, curvature, and internal flow profiles exhibited strong dependence on Ca and Qr. Scaling analysis showed linear dependence of droplet size on Qr in the squeezing regime, with curvature nearly independent of Qr. In contrast, both size and curvature followed power-law dependence on Ca and Qr in the dripping regime. Velocity fields inside droplets were laminar and parabolic in the core. Fully developed plug-like profiles appeared in squeezing, whereas front and rear regions remained developing in dripping. Correlations for droplet length, curvature, and film thickness, including a novel thin-film model incorporating visco-inertial and capillary effects, enable predictive design within the studied range. These findings advance fundamental understanding of confined droplet dynamics and provide quantitative guidelines for optimizing droplet-based microfluidic systems.

Figures (20)

• Figure 1: Schematic representation of the droplet formation in the two-phase cross-flow through a T-junction cylindrical microfluidic device.
• Figure 2: (a) Fabricated sample of T-junction cylindrical microchannel inside a PDMS block. (b) Measured contact angle of water on PDMS block.
• Figure 3: Schematic representation of experimental $\mu$-PIV setup.
• Figure 4: The dimensionless instantaneous pressure, $P^{\ast}(t^{\ast})$, profiles at a probe point ($L_{\text{u}} + D_{\text{c}}, 0$) as a function of domain length ($L_{\text{u}}$, $L_{\text{d}}$, and $L_{\text{v}}$) and mesh size ($\lambda_\text{m}= h_\text{max}$) at the fixed flow rates ($Q_{\text{c}}=\hbox{0.03}$ mL/h, $Q_{\text{d}}=\hbox{0.03}$ mL/h).
• Figure 5: Comparison of present experiment and simulation results in terms of Dimensionless droplet length ($L^{\ast}=L/D_\text{c}$).