**3.1.1 Vibrating droplet under the zero gravity**

In order to verify the potential of the advanced interface tracking method, 3-dimensional analyses of the vibration of a liquid drop under zero gravity were carried out. Initial arrangement of the droplet is shown in Fig.3. In the simulations, two computational grids

We try to validate the TPFIT with the advanced interface tracking method developed in this

Before validate the TPFIT for fluid mixing phenomena, we check basic performance of the TPFIT for two-phase flow by performing numerical simulation in simple flow configuration

7.5mm5mm

X,Z Y

(a) Case A (b) Case B

In order to verify the potential of the advanced interface tracking method, 3-dimensional analyses of the vibration of a liquid drop under zero gravity were carried out. Initial arrangement of the droplet is shown in Fig.3. In the simulations, two computational grids

3

4

Length(mm)

5

0 0.02 0.04

Time (s)

Δt=2.5×10–5 Δx=8.33×10–4 9×9×9

X,Z Y

**3. Validation of TPFIT for fluid mixing phenomena** 

**3.1 Verification and validation of TPFIT for simple flow configuration** 

study for fluid mixing phenomena.

Fig. 3. Initial arrangement of droplet.

0 0.02 0.04

Fig. 4. Time change of diameters of droplet.

**3.1.1 Vibrating droplet under the zero gravity** 

Time (s)

Δt=2.5×10–6 Δx=1.83×10–4 41×41×41

3

4

Length(mm)

5

were used, one is a fine grid (41×41×41, case A) and another is a course grid (9×9×9, case B). Time changes of diameters of the droplet are shown in Fig.4. The vibration cycle is about 0.022 seconds and agrees with the theoretical value that expressed as following equation (Rayleigh, 1879).

$$
\pi = \pi \sqrt{\frac{\rho\_\circ r^\circ}{2\sigma}} \tag{14}
$$

The results of the case A and those of the case B are almost the same, and the effect of the different grid number is small. The diffusion at the gas-liquid interface was not observed. Then we confirmed the effectiveness of the advanced interface tracking method.
