Volume of Fluid (VOF) Method as a Suitable Method for Studying Droplet Formation in a Microchannel

Abstract

Microfluidics is a rapidly advancing field focused on optimizing microdevices for applications such as organ-on-a-chip systems and enhancing laboratory analyses. Understanding the physical parameters of droplet generation is crucial for these devices. Computational fluid dynamics (CFD) techniques are essential for providing insights into the limitations and efficiency of numerical methods for studying fluid dynamics and improving our understanding of various application conditions. However, the influence of different numerical methods on the analysis of physical parameters in problems involving droplet generation in microchannels remains an area of ongoing research. This study implements the Volume of Fluid (VOF) method to investigate key physical parameters, including droplet size and the effect of the capillary number on fluid regimes, in droplet generation within a microchannel featuring a T-junction geometry. We compare the VOF method with the widely used Level Set Method (LSM) to evaluate its suitability for this context. The results show that the VOF method agrees with the LSM in fundamental outcomes, such as the reduction in droplet diameter as the flow rate ratio increases and the identification of the capillary number's influence on fluid regime classification. The VOF method provides a clearer understanding of transitions between fluid regimes by detecting stages of non-uniformity in droplet size. It identifies a transition region between regimes with variations in droplet size, proving to be effective at mapping fluid flow regimes. This study highlights the potential of the VOF method in offering more detailed insights into instabilities and transitions between fluid regimes at the microscale.

Keywords: computational fluid dynamics; level set method; microchannel; microfluidics; volume of fluid method.

Figure 1

Schematic of the t-junction microchannel. A lateral channel is used for the inlet of the dispersed phase, while the continuous phase flows through the main channel. At the junction, the two phases converge, initiating the droplet formation process. The arrows in the schematic indicate the direction of the flows.

Figure 2

Meshing applied to the modeled geometry.

Figure 3

Dimensions of the channels in the T-junction geometry used in the simulations. The inlet channel for the dispersed phase has a width of $60\mathsf{\mu }\mathrm{m}$, while the inlet channel for the continuous phase has a width of $100\mathsf{\mu }\mathrm{m}$.

Figure 4

Mesh independence study. A 5 $\mathsf{\mu }$m mesh was selected as it offered a good balance between accuracy and computational cost, with no significant differences in the analyzed parameter compared to finer meshes.

Figure 5

Comparison of droplet length for flow velocity ratios between the present study and the validation model (Bashir et al., 2011 [11]), which includes experimental and numerical data.

Figure 6

Dimensionless droplet length as a function of the velocity ratio ($U_c/U_d$). A general decreasing trend in droplet size is observed as $U_c/U_d$ increases, except near $U_c/U_d\approx 4$, where an irregular pattern emerges with an unexpected increase in droplet length.

Figure 7

Phase diagram illustrating the different droplet formation regimes as a function of the continuous phase velocity ($U_c$) for a fixed dispersed phase velocity ($U_d=0.012\mathrm{m}/\mathrm{s}$). The regimes are defined over the following intervals of $U_c$: squeezing regime ($0.015\le U_c<0.060\mathrm{m}/\mathrm{s}$), transition regime ($0.060\le U_c<0.085\mathrm{m}/\mathrm{s}$), dripping regime ($0.085\le U_c<0.115\mathrm{m}/\mathrm{s}$), and jetting regime ($0.115\le U_c\le 0.140\mathrm{m}/\mathrm{s}$).

Figure 8

Dimensionless droplet length ($L_d/W_c$) as a function of the capillary number (Ca). The results indicate a general decrease in droplet length as the capillary number increases. A slight increase in droplet length is observed around $Ca\approx 0.012$, representing a local deviation from the overall decreasing behavior.

Figure 9

Droplet break up for different capillary numbers. The breakup moments of the dispersed phase at the junction were captured under different capillary number ($Ca$) conditions. These observations provide valuable insights into the droplet formation regimes as a function of the capillary number.

Figure 10

Phase diagram of fluid regimes depending on the capillary number. The squeezing regime is observed in the range of $0.003<Ca<0.012$. A transition region, associated with unstable droplet formation, occurs in the range of $0.012<Ca<0.023$. The dripping regime appears within $0.023<Ca<0.032$, and for $Ca>0.032$, the system enters the jetting regime.