(474j) Modeling and Simulation of High-Throughput Droplet Generation in Shear-Thinning Fluids

Droplet-based microfluidics hold immense promise in a wide range of applications such as emulsions, drug delivery, material synthesis, and lab-on-a-chip technologies. The increasing need for near-monodisperse emulsion production, especially for advanced microcapsule fabrication, has driven interest in controlled droplet generation techniques. Among them, computational fluid dynamics (CFD) offers a powerful platform to explore and optimize droplet dynamics under varying operating and fluid conditions. This study focuses on a three-dimensional, transient CFD simulation of droplet formation in a flow-focusing microfluidic device. To capture the interface between the immiscible fluids involved in droplet generation, the Coupled Level Set and Volume of Fluid (CLSVOF) method was employed. This hybrid approach leverages the mass conservation accuracy of the Volume of Fluid (VOF) method and the precise curvature tracking capability of the Level Set (LS) method, enabling smooth and accurate modeling of the evolving interface. The primary objective of this study is to investigate the effects of shear-thinning, non-Newtonian fluids-specifically sodium carboxymethyl cellulose (CMC) solutions on the formation of mineral oil droplets. The continuous phase (CMC solution) exhibits shear-thinning behavior and follows the power-law model, where viscosity (μ) is expressed as μ = Kγ̇ⁿ⁻¹, with K as the consistency index and n as the flow behavior index. The dispersed phase is Newtonian mineral oil, introduced through the main inlet, while the CMC enters through two side inlets of the microfluidic device.

The geometry of the device consists of square channels, with inlet and outlet channel widths and heights set to 600 µm. The entrance lengths for both phases are 1800 µm, and the main channel extends 6000 µm downstream. A schematic representation of the device and droplet dimensions is provided for clarity (see Figure 1 A). Rheological properties of CMC were analyzed for concentrations of 0.1%, 0.25%, 0.5%, and 1.0%, with corresponding variations in the parameters K and n. These concentrations significantly affect the flow behavior and droplet dynamics. The simulations captured key droplet parameters, such as length, velocity, formation frequency, pressure distribution, and flow regimes. Model validation was carried out by comparing the CLSVOF simulation results with the experimental work of Fu et al. on droplet formation under similar conditions. Specifically, the model reproduced the temporal evolution of oil droplet formation in the dripping regime, at flow rates of 300 µL/min (oil) and 2000 µL/min (water), closely matching both qualitative and quantitative experimental observations (Figure 1 B). After validation, systematic simulations were conducted to examine the effect of CMC concentration: Increasing concentration strengthens shear-thinning effects, decreasing droplet size due to greater viscous resistance (Figure 1 C). Increasing the continuous phase flow reduces droplet length, while higher dispersed phase flow produces longer droplets (Figure 1 D-E). Higher interfacial tension resists droplet breakup, leading to larger droplet sizes (Figure 1 F). The developed CFD model successfully captured the liquid film thickness as shown in Fig. 1 G. At lower concentrations of CMC, the generated droplets are plug-shaped and span the width of the channel a characteristic of the squeezing regime. As the concentration increases, the regime transitions from squeezing to dripping and eventually to jetting. These transitions are mapped out to form flow regime diagrams that help visualize operational boundaries as shown in Fig. 1 H. In addition to geometric and flow variables, this study explores non-dimensional numbers that govern droplet formation physics. The Weber number (We) and a modified Capillary number (Ca*) were defined as functions of the flow rate and interfacial tension. These dimensionless parameters help generalize the behavior across various operating conditions and fluid properties, offering a robust framework for droplet design. Pressure distribution along the channel was analyzed to understand the driving forces responsible for droplet detachment and transport. Simulations revealed pressure drops across the interface, indicating the role of capillary and viscous stresses in the breakup process. Additionally, the influence of viscosity gradients due to the shear-thinning nature of CMC was clearly visible in the droplet formation zones. The study also highlights the formation and thickness of the liquid film between the droplet and the channel wall, which varies with flow conditions and fluid properties. A thinner film correlates with higher shear rates and stronger confinement, influencing both the velocity and shape of the droplets. Quantitative results demonstrated that droplet length decreases consistently with rising continuous phase flow rates and increasing CMC concentrations. Conversely, dispersed phase flow rate and interfacial tension increase the size of droplets. These insights are valuable for applications where precise control over droplet size and frequency is crucial.

In conclusion, this study presents a robust CFD-based approach to analyzing droplet generation in a flow-focusing microchannel using shear-thinning fluids. By integrating the CLSVOF method for accurate interface capturing and validating the results with experimental data, the study provides a detailed understanding of droplet dynamics under varying conditions. The systematic exploration of parameters like fluid rheology, flow rates, and interfacial tension, along with pressure and velocity fields, offers valuable design guidelines for microfluidic systems. The results not only enhance fundamental knowledge but also serve practical applications across multiple industries requiring precise droplet control.