# Evolution of Water-in-Oil Droplets in T-Junction Microchannel by Micro-PIV
## 3 Results and Discussion
### Internal Velocity Profile of Generated Water Droplets in Offset T-function Microchannel
In terms of the microchannel's size affecting the size of droplet, based from Figures 5-7, the droplets' size increases with an increase in the radius of the microchannels [32]. In the case of small differences between the offset T-junction microchannels, i.e., radiuses of 400 \(\upmu\)m and 500 \(\upmu\)m, there is no major difference in droplets' sizes that can be spotted in Figures 5 and 6. However, with a further increase in the microchannel's radius to 750 \(\upmu\)m (Figure 7), the water droplet's size with respect to flow velocity increases significantly. For the microchannel with a radius of 1000 \(\upmu\)m (Figure 8), the droplet's volume cannot be seen due to the limit of field of view and the exceedance of the observation area. From this discussion, it is clear that the change in the offset T-junction microchannel's radius exerts a major influence on the water droplet's size. On the other hand, the flow velocity vectors determined by micro-PIV are displayed as small arrows. The key features of the flow are illustrated by larger arrows for better visualization. At t = 91 ms and t = 1000 ms, the microchannel with a radius of 750 \(\upmu\)m (Figure 7) has an average velocity of 0.055 mm/s and 0.15 mm/s, which is 2.7 and 1.3 times smaller than the average velocity of the microchannel with a radius of 500 \(\upmu\)m (Figure 6), respectively. This is because in a bigger channel, the oil phase takes a longer time to break down the water phase into longer slugs. The interfacial area was decreased as channel size was increased. In contrast to that, for a smaller channel, an increase in the velocity with respect to time increases its inertial force which leads to the enhancement in its tendency to break down the water phase into smaller droplet form. In short, increasing the channel's size and cross-sectional area decrease the liquid's velocity compared to the ones in the smaller channel. This also can be proved by referring to the Hagen-Poiseuille equation [48] below:  
\[\text{Q}_{\text{HP}}=(\uppi\times\text{R}^{*}4\times\Delta\text{p})/(8\times \upmu\times\text{L}) \tag{1}\]  
where \(\text{Q}_{\text{HP}}\) is flow rate, R is the channel's radius, \(\Delta\text{p}\) is the pressure drop between the inlet and outlet, \(\upmu\) is the dynamic viscosity of the fluid and L is the channel's length. The velocity could then be shown as,  
\[\text{v}_{\text{HP}}=\text{Q}_{\text{HP}}/\text{ A}=(\text{R}^{*}2\times \Delta\text{p})/(8\times\upmu\times\text{L}) \tag{2}\]  
where \(\text{v}_{\text{HP}}\) is the average velocity and A is the channel's cross-sectional area. If Qexp is to be the flow rate measured in the experiment, the velocity can, thus, be written as,  
\[\mathrm{v_{exp}=Q_{exp}/A} \tag{3}\]  
The highest velocity which coloured in yellow region in velocity magnitude analysis is largely due to the vortex which localised towards the edge of the droplet, as the droplet grew bigger and the particles also moved to the edge. The interfacial tension between the droplet and the continuous oil phase pulls the resulting interface sideways more firmly, causing powerful vortex motions within the water droplet. The shear force causes these strong vortex motions within the droplet, located away from the centre to the edge of the front inner surface, deflecting the accelerated dispersed water phase [30]. Since gravitational forces have no significant impact in microfluidics, it can be concluded that the central region of the inner droplets exhibits low velocities, while the regions near the channel boundaries have higher velocities magnitude [26]. There might be minimal errors in the readings due to the channel's inner geometry and its surface roughness during the fabrication process.