Simulation

In this chapter, we to design a worm trapper by two phases flow in microfluidic channels. For more understanding the fluidic phenomenon, some simulation results were discussed by using COMSOL Multiphysics® Modeling Software. At the beginning, we set a π-structure for analyzing the oil bulges expansion at the junction with different oil (FC-43) input pressures. The fluidic parameters are in (Table 3-3). The inlet and outlet pressures of the water were both set in an atmospheric condition, and the oil inlet pressure was from 103100 Pa to 104300 Pa. The trapping time was stop at 0.005 second, which is much faster than the C. elegans swimming velocity (~ 0.2 mm/s) [129, 130]. In (Figure (3-17)

(3-18)

3-8), the expanding oil bulges pushed the water outward; and the bulges completely sealed the water channel if the oil inlet pressure is larger than 104300 Pa (Figure 3-9).

Table 3-3. Specifications and material properties of the π-channels structure.

(a) (b)

Figure 3-8. The x- and y- directional velocities, (a) u and (b) v, when the oil bulges expand from inlet pressure 103500 Pa at time=0.005s.

Fluid properties Symbol Size (mm) Water

(a) (b)

(c) (d)

Figure 3-9. The volume fraction of water and oil bulges with different oil inlet pressures (103100 Pa, 103500 Pa, 103900 Pa, 104300 Pa) at 0.005 second.

In next simulation, we set the oil pressure as 104300Pa, which can totally block the static water channel. We then change the water inlet pressure from 102700 Pa to 105100 Pa. In a flowing water channel, the oil bulges are difficult to expand. If the water pressure is too high, the oil might even shrink back to the π-channels (Figure 3-10).

Thus with the same oil inlet pressure, the biggest bulges can be made in a static water channel.

(a) (b)

(c) (d)

Figure 3-10. The volume fraction of water and FC-43 droplets with different water inlet pressures (102700, 103500 Pa, 104300 Pa, 105100 Pa) at 0.005 second.

However in a real case, the Laplace pressure theory should be considered. It happens when the roughness of the two parallel channels surfaces are different (Figure 3-11a). This difference makes one big and one small bulge at the beginning. Because the pressure is inversely proportional to the droplet curvature, the pressure is smaller in the larger droplet. Thus the oil flows from the small droplet to the big one. Finally, the big one unlimitedly expands until it blocks the water channel (Figure 3-11b).

(a) (b)

Figure 3-11. (a) The structure of the π-channel structure. (b)A real case of an extremely large bubble blocking the water channel due to Laplace pressure.

To solve the Laplace pressure issue, we modified the π-structure to be a donut shape.

The pushing ability of a PZT plate, which can generate ~10⁵ Pa pressure with ~70 µm central deformation in one millisecond was simulated [131, 132]. (Figure 3-12) shows the central deformation at different applied voltages. (Figure 3-13a) shows the flow velocity after triggering the PZT. With a central pillar, the flow was separated from one to two streams when it hit the pillar. It is clear that these two streams are almost independent to push the water out of the channels. Finally, a water droplet was made at the bottom of the donut structure. However, in real testing, the response time is very short during the making of the water droplet (in millisecond scale). Sometimes the droplet shifted a little toward the left or the right side, it means the flow velocities are not symmetric in a few

milliseconds around the pillar (Figure 3-13b). This might pose a potential risk of losing the worm. To improve the donut structure, we added three symmetric fingers at the bottom (Figure 3-13c). When compared to the donut structure, the pushing velocity happened only at the upper half of the donut. In the fingers-donut structure, the pushing velocity went deeper toward the lower half of the donut. It means that we have more opportunity to keep a symmetric water droplet at the bottom (Figure 3-13d).

Figure 3-12. The deformation measurement from laser vibrometer (Keyence, LK-H080).

(a) (b)

(c) (d)

Figure 3-13. The x-directional velocity simulation of (a) the donut structure and (c) the fingers-donut structure with 150µm channel height. The water is static, and the oil inlet pressure is 261300 Pa. Figure (b) and (d) are the photos with water droplet at the bottom

in the donut and 45° fingers-donut structure, respectively.

The time dependent water flow from 0.001 s to 0.005 s in the donut structure and the fingers-donut structure was simulated in (Figure 3-14 and 3-15). In the donut structure, the direction and the value of the flow velocity at the junctions were similar from start to 0.005 s. The water in the donut was continuously pushed outside, and it was almost static at the bottom. Because in microfluidic devices, the flow rate is zero at the channel walls, the lower half circle of the donut is almost static. Regarding the fingers-donut structure, besides the velocity was much larger; the flow was more active in the lower half donuts.

The reason is that the flow rate is not zero at the opening end of these fingers. It’s clear to see at the beginning, i.e., t=0.001s, immediately after the pressure came from the oil inlet, the oil went outward and downward.

Considering the three fingers spread with 30°, 45° and 60° in (Figure 3-15) for finding the optimal structure to make sure trapping C. elegans in the donut. In the 30°

fingers-donut channel, although the flow went downward to the lower half of circle, making an active fluidic field around the fingers. The flow was still unstable at 0.005s might has difficulty forming water droplet with C. elegans inside. For the spreading angles of 45° and 60°, their flows were also active at beginning then tended to be stable finally. Furthermore, comparing these results at 0.005s, the flow went deeper in the 45°

fingers-donut (Figure 3-16). Thus we verified that the 45° fingers-donut structure provides the best efficiency to trap C. elegans.

(a) (b) t=0.001s (c) t=0.002s

(d) t=0.003s (e) t=0.004s (f) t=0.005s

Figure 3-14. (a) The flow direction in the donat. (b)~(f) The pushing flow velocity of the donut structure from 0.001 s to 0.005 s.

t=0.001s t=0.001s t=0.001s

t=0.002s t=0.002s t=0.002s

t=0.003s t=0.003s t=0.003s

t=0.004s t=0.004s t=0.004s

t=0.005s t=0.005s t=0.005s

Figure 3-15. The flow direction in the donut. And the pushing flow x-directional velocity of the 30°, 45°, and 60° fingers-donut structures from 0.001 s to 0.005 s.

(a)

Fingers angle: 45°

(b)

Fingers angle: 60°

Figure 3-16. The comparison of the flow at the junctions of (a) 45° and (b) 60°

fingers-donut structure at 0.005s.