Simulation of Droplet and Bubble Dynamics in Microfluidic Devices

FLOW-3D can be used as an effective tool for modeling the droplet/bubble dynamics in microfluidic devices. Here we will first discuss droplet formation in T-Junctions and bubble formation in a Co-flowing device, published recently in Sensors & Transducers journal [1]. Later on we will talk about simulations done for a novel device called the Hong Chamber.

Modeling T-Junction Devices

Figure 1. T-junction simulation setup

In a T-junction device, the disperse phase and the continuous phase are injected from the two branches of a "T." As a result, bubbles of the disperse phase are formed and carried forward by the continuous phase. For our simulations, water was used as the disperse phase and PFD as the continuous phase. The setup is shown in Fig. 1. Droplet formation was studied for various inlet conditions and the droplet size was compared with an analytical result known as the scaling law. Figure 2 shows the droplet size increases as the flow rate in one of the branches varies. Figure 3 shows the results compared with the scaling law. Here L and w are the length and width of the bubble.

Figure. 2. Increase in continuous phase flow rate (Qc) decreases bubble length.
(a: Qc = 1.8 µl/min, b: Qc = 2.7 µl/min, c: Qc = 3.6 µl/min, d: Qc = 7.2 µl/min)
Qd  = 3.9 µl/min for all cases.

Modeling Co-flowing Devices

Figure 3. (a) 3D and (b) 2D schematic
for co-flowing device

In this device, liquid and gas enter the device from the left-hand side (Fig. 4). They are separated by a barrier. The gas phase was found to form bubbles, which are carried forward by the liquid phase for certain combination of flow rates for the gas and the liquid.

In these simulations, air was used as the gaseous fluid. Water (viscosity μ = 0.92 mPa-s) and three aqueous solutions of glycerol, 50% (w/w) glycerol (μ = 7.31 mPa-s), 30% (w/w) glycerol (μ = 2.68 mPa s), and 10% (w/w) glycerol (μ = 1.19 mPa-s), were used as the liquids. To study the breakup process, a simulation was run with air and water flowing together in the co-flowing device described above. Figure 5 shows the comparison between experimental results [2] and the results obtained from simulation.

Figure 4. (a) 3D and (b) 2D schematic for Co-flowing device

Figure 5. Comparison of simulation results with
experimental data for a flow rate of water =
Ql=15 ml/hr and a flow rate of air = Qg =3 ml/hr.

When the liquid flow rate is increased beyond a certain critical value the flow dynamics of bubble formation is almost identical to that in a T-junction. In this regime, experiments in a co-flowing device agree quite well with the scaling law seen in the case of T-junctions [2].We investigated the size and frequency of bubble formation for water and air flow rates, where experiments show a good agreement with the scaling law. Air at flow rates of 2.1, 5.25, 10.5, 21 and 42 ml/hour above the separator and water at a fixed flow rate of 21 ml/hr below the separator were used. The bubble length was obtained near the exit of the channel once the bubble had reached a steady state. At this stage the bubble occupied the entire channel width due to the high surface tension.

In Fig. 6 the actual lengths observed for the cases simulated are compared with the values predicted on the basis of the scaling law. In Fig.7, the frequency of bubble formation is compared with an analytical expression for the frequency of bubbles generated in the co-flowing device derived by Xiong et al.[2].

Figure 6. Bubble lengths predicted using the scaling law compared against
bubble lengths from simulations

Figure 7. Bubble lengths predicted using the scaling law compared against
bubble lengths from simulations.

Understanding the Hong Chamber

The Hong Chamber is an innovative in-plane passive micromixer using modified Tesla structures, which are used as passive valves. This has been designed, simulated, fabricated and successfully characterized by Hong et al.[3].

Figure 9. The mixing pattern as a function of time at 0.04s, 0.2s, 0.5s, and 0.65s.

This novel micromixer has shown excellent mixing performance over a wide range of flow conditions in the micro scale. We simulated the Hong Chamber with two fluids coming in from the inlet, to look at the mixing patterns as a function of time. Figure 9 shows the mixing pattern as a function of time. The two streams represent two water based reagents.

Figure 10. The mixing pattern as a function of time at 0.003s, 0.02s, 0.06s and 0.1s.

The fluid fraction varies from 0 to 1, where 0 indicates a region completely occupied by fluid one and 1 indicates a region completely occupied by the second fluid (fluid 2). Fixed velocities were used at the inlet and an outflow boundary condition was used at the outlet. The initial region was filled with the blue fluid. Figure 10 shows results from the filling simulation. Here no fluid was defined in the initial region. Fixed velocities were used at the inlet boundary conditions and the adiabatic bubble model was used to trap bubbles. What is notable is that at each tesla valve unit, the flow in the reverse direction is prevented, which leads to the formation of bubbles.

References

[1] A. Chandorkar and S. Palit, Simulation of Droplet Dynamics and Mixing in Microfluidic Devices using a VOF-Based Method, Sensors & Transducers journal, ISSN 1726-5479 © 2009 by IFSA, Vol.7, October 2009, pp. 136-149.

[2] R. Xiong, M. Bai and J. Chung, "Formation of bubbles in a simple co-flowing micro-channel," Journal of Micromechanics and Microengineering, 17, 2007, pp.1002-1011.

[3] Chien-Chong Hong, Jin-Woo Choi and Chong H. Ahn, "A novel in-plane passive microfluidic mixer with modified Tesla  structures," Lab Chip, 2004, 4, 109 –113.