Merged and alternating droplets generation in double T-junction microchannels using symmetrically inserted capillaries

Abstract

In this work, merged and alternating droplets generated in a microfluidic double T-junction are investigated using experiments and numerical simulations. The double T-junction is constructed by symmetrically inserting two capillaries into a microfluidic chip at specific positions. We explore the effects of the two-phase flow rate fraction, capillary tip distance (30 μm, 60 μm, and 200 μm), and fluid properties on droplet formation phenomena. Detailed observations reveal four distinct regimes during the dynamic evolution of the two-phase interface morphology: merged state, stable alternating droplets, droplet pairs, and jetting. Two phase diagrams are obtained to demonstrate that interfacial tension and dispersed phase viscosity significantly influence these regimes. Moreover, we find that as the flow rate fraction increases from 0.054 to 0.286, the length of generated droplets increases from 156 to 789 μm; we provide a theoretical prediction formula for dimensionless droplet length accordingly. Additionally, our simulations show fluctuating pressure in dispersed flows throughout the process of droplet generation. The simulated pressure in the dispersed flows fluctuates during the droplet generation process. The understanding of the underlying physics of the capillary-based double T-junction contributes valuable insights for various related applications.

Highlights

• An easy capillary-based double T-junction for droplet generation.

• Merged and alternating droplets are generated.

• Four regimes are observed as the merged, stable alternating droplet, droplet pairs, and jetting.

• Effects of two-phase flow rates, capillary tip distances, and fluid properties are investigated.

Graphical abstract

Appendix

1.1 Numerical simulation

To investigate the pressure variation in the two capillary tubes during the droplet generation process, three-dimensional numerical simulations were conducted by using VOF method (Bai et al. 2021) in ANSYS-Fluent 21.0. The governing equations for mass and momentum used to describe fluid movement are as follows:

$$\nabla \cdot u=0$$

(7)

$$\frac{\partial \rho u}{\partial t}+\nabla \cdot \rho uu=-\nabla P+\nabla \cdot \left(\mu \left(\nabla u+{\nabla }u^{T}\right)\right)+{F}_{s}$$

(8)

where u is the velocity, ρ is the average volume density, P is the pressure, μ is the average dynamic viscosity, and F_s is the surface tension force. The model size and inlet flow velocity were set to be identical to those used in the experiments. The fluid fraction function is implemented to derive the fractional volume H of the distinguished fluid phase, which ranges from 0 to 1 in a unit cell:

$$\frac{\partial H}{\partial t}+u\cdot \nabla H=0$$

(9)

The average density ρ and average viscosity μ are computed from the weighted average distribution of the fluid fraction of the dispersed phase H_d and the fluid fraction of the continuous phase H_c.

$$\rho ={\rho }_{d}{H}_{d}+{\rho }_{c}{H}_{c}$$

(10)

$$\mu ={\mu }_{d}{H}_{d}+{\mu }_{c}{H}_{c}$$

(11)

where ρ_d, ρ_c, μ_d, μ_c are the densities and the viscosities of the two phases.

Fig. 10

Model establishment and meshing. a Overall model construction. b Model meshing and pressure measurement points (A and B) for the dispersed phase. c Front close-up view of the model

Hypermesh2020 software was employed for dividing the hexahedral mesh of the model, as depicted in Fig. 2. For mesh refinement, the mesh at the intersection of the capillary and main channel was enhanced utilizing different bias factors (BF). A symmetrical boundary at the middle x–y plane was applied. Two phase fluids based on their physical parameters in Group A of Table 1 were selected. The velocity inlet and pressure outlet were chosen. Non-slip boundary conditions on wall surfaces were applied, while Presto and Quick schemes (Ngo et al. 2015) were utilized to minimize the computational costs. The geometric reconstruction method (piecewise linear interpolation calculation, PLIC) (Sajeesh et al. 2014) was used for determining the interface position within each unit cell.

The simulation errors of droplet lengths for different meshes are shown in Table 2, which is obtained by comparing with the experimental result. It can be found that the third and fourth cases exhibit minimal error values compared to other grids. Therefore, the mesh with approximately 2.45 million grid cells was selected for subsequent simulations. The pressure variations at points A (P_A) and B (P_B) in the two dispersed flows were monitored, as shown in Fig. 10b.

Table 2 Grid independence verification

1.2 Pressure change in dispersed flows

To investigate the influence of pressure on droplet generation under different regimes, we monitored the local pressure of the two dispersed flows using numerical simulation. Figure 11a illustrates the time-dependent pressure difference (ΔP = P_A − P_B) in the merged droplet regime at Ca = 0.03 and φ = 0.2. The beginning of one of the dispersed flows first entering the microchannel as the initial moment. It can be observed that there is a fluctuation around 0 Pa during the entire droplet generation process. Initially, this fluctuation is relatively pronounced but gradually diminishes over time (t > 0.06s). This result suggests that the pressures in both dispersed flows are nearly equal in the merged regime due to the large channel width employed in this study, preventing blockage by generated droplets.

The pressure changes during 7.5 periods (5.2 ms) in the jetting regime at Ca = 0.123, φ = 0.0465 are depicted in Fig. 11b. It can be observed that the pressure curves of the two dispersed flows exhibit sinusoidal behavior over time. A relatively stable phase difference exists between these curves, approximately half of the droplet generation period, due to a competitive relationship between the pressures of symmetrical dispersed flows during this process. Additionally, the pressure difference between the two dispersed flows also follows a sine law with time; when the upper droplet neck breaks, it decreases towards its minimum value and reaches its maximum at crest formation. These simulation results align well with experimental observations of droplet generation in the jetting regime and are consistent with previous studies (Ngo et al. 2015; Raja et al. 2021) where periodic fluctuations in pressure difference were reported. However, our study demonstrates relatively higher amplitude for this sinusoidal curve owing to smaller inner diameter (d = 50 μm) of our double T-junction capillary tube which generates higher pressures (~ 1250 Pa) within both dispersed flows during droplet generation process as similarly reported by Saqib et al. (2018), in tapered side channels.

Fig. 11

Pressure changes in two dispersed flows in term of time. a Merged regime. b Jetting regime