3.1. Characteristic Sizes of the Droplet Deformation
The characteristic-height (named C-height) and the characteristic-length (named C-length) of the droplet after deformation were recorded, as shown in
Figure 4. The C-height is the distance between the highest point and the lowest point of the droplet in the
XY plane, and the C-length is the contact length of the droplet and the upper surface in the
XZ view. Besides,
Figure 4 shows that when acceleration is 400 m/s
2, the droplets will flatten at 0.1 s, 0.2 s, and 0.3 s. It can be seen from the
XZ view that the flattened droplet expands and reaches the upper surface of the annular groove.
Here, the steady-state deformation of the droplet is the desired result, so that the relationship between the deformation of the droplet and the time step needs to be investigated. The transient performance of the step size from 0–0.3 s are simulated using the models with four accelerations of 100 m/s
2, 200 m/s
2, 300 m/s
2, and 400 m/s
2.
Figure 5 shows the relationship between the time step and the C-height of the droplets.
The results show that the C-height of the droplet from the time steps of 0.01 s to 0.18 s will increase and decrease periodically, which indicates that the droplet is flattened after the initial acceleration, and rebounds with an increased time step. This oscillation in height repeats for half a second before it settles. Acceleration is always present and does not change with time, but the deformation of the droplet oscillates at the beginning. When the time step exceeds 0.18 s, the height change of the droplets gradually becomes stable, which means the influence of the time step on the C-height gradually fades away. Therefore, the results after 0.3 s are used in the study.
More types of acceleration were applied to study the deformation of the droplet and verify whether the droplet will split at a large acceleration. The acceleration varies from 10 to 600 m/s
2, and several characteristic results at accelerations 30, 300, 500, and 600 m/s
2 are shown in
Figure 6.
Figure 7 shows the relationship between the C-height of the droplet deformation and the acceleration. The droplet in the annular groove is deformed by the acceleration, and the C-height of the droplet decreases as the acceleration increases. The C-height of the droplet is 1.658 mm at 10 m/s
2, and 0.246 mm at 600 m/s
2. Besides, it is observed that even when the acceleration reaches 600 m/s
2, the droplet remained in one piece and did not break.
The simulation results also show that as the acceleration increases, the droplet is gradually flattened and the C-length increases. The relationship between acceleration and C-length is shown in
Figure 8 (the red line represents the normalized data of C-length).
When the acceleration is lower than 50 m/s2, the little deformation is not enough for the droplet to be in contact with the upper surface of the annular groove. At this time, the C-length of the deformation is 0. When the acceleration reaches 60 m/s2, the droplet is deformed enough to contact the upper surface of the groove, and the C-length at this time is 0.863 mm. The length of the droplet gradually increases as the acceleration increases. When the acceleration is 600 m/s2, the C-length reaches 2.776 mm.
3.2. Effect of Material Properties in the Domain around the Droplet on Characteristic Sizes of the Deformation
In this section, the material properties surrounding the domain of the droplet are simulated.
Figure 9a–c respectively show the deformation of the droplet as the viscosity, density, and surface tension of the annular region increase. Meanwhile,
Figure 9d shows the deformation of the droplet when the material of the annular groove domain is water. Here, the acceleration is 300 m/s
2, the viscosity is four times larger than air, (7.16 × 10
−5 Pa.s), the density is three times bigger than air (3.9 kg/m
3), and the surface tension is 1.44.
The relationship between the deformation characteristic size and acceleration of the droplet in different materials property domains is shown in
Table 4.
It can be seen from
Table 4 that the material properties of the domain surrounding the droplet affect the characteristic size of the deformation. Increasing the viscosity and density of the material can increase the C-height of deformation and decrease the C-length of deformation. However, density and viscosity have little effect on the characteristic size of deformation. Besides, the effect of surface tension on the characteristic sizes of deformation is significant. Increasing the surface tension will increase the C-height, but the change of C-length is not obvious. The water domain has a higher density and higher viscosity than the air domain. Hence, the C-height of the mercury droplet in water is small and the C-length is large, which means that mercury is not easily deformed in water.
3.3. Experimental Setting and Results
The experiments for verifying the deformation of an accelerating droplet in the annular groove were designed, as shown in
Figure 10. The setting of the experiment consisted of a turntable, a silicon wafer with a SU-8 photoresist annular groove (the size of which was 2.5mm × 2.5mm) attached to the top surface of the turntable, and a glass slide as the lid of the groove [
23]. A mercury droplet of 2 mm in diameter was placed in the groove and surrounded by air. The contact angles between the droplet and the outer and lower surface in the annular groove surface and the glass substrate were 145°, 135°, and 150°, respectively. The deformation of the droplet was captured by a high-speed camera placed vertically above the turntable. The whole experiment bench was placed in the room temperature of 20 °C.
The centripetal acceleration is generated using the turntable. The distance between the initial position of the droplet and the center of the turntable is 20 mm, and different additional accelerations can be obtained by changing the speed of the turntable. The acceleration can be calculated with the following Equation:
where
a is the acceleration,
ω is the angular velocity of turntable, and
r is the distance between the initial position of the droplet and the center of the turntable.
Since the steady-state deformation model was required, the image of the droplet was acquired 60 s after the speed of the turntable became steady.
Figure 11 shows the shape of the droplet when the rotation speed reached 440, 1050, 1420, and 1710 rpm. These speeds correspond to accelerations of 42, 242, 438, and 640 m/s
2, respectively.
For comparison of the C-height in the experimental results with the C-height in the simulation results, the boundary conditions in the simulation needed to be improved. The modified boundary conditions, including the contact angle, are shown in
Table 5:
The wetted wall was added as a boundary condition in the Multiphysics coupling, reflecting the contact situation between the droplet, and the annular groove and other initial conditions and material properties remain unchanged in simulation. The simulation and experimental results of the droplet deformation when the accelerations were 42, 242, 438, and 640 m/s
2 are shown in
Table 6.
Figure 12a shows the relationship between the C-height of the droplet deformation and the acceleration. The black line represents the simulation results, and the red dots represent the experimental results. In addition,
Figure 12b shows the relationship between the C-length of the deformation and the acceleration, and the red line represents the normalized data of C-length.
By measuring the C-height of the droplet in
Figure 11 and calculating the C-height in the simulation models, the experimental results and simulation results of the C-height and acceleration are plotted shown in
Figure 12a. For the simulation models, the condition of adding the contact angles (wetted wall) will also cause the droplet to be squeezed under acceleration. However, compared with the sliding wall boundary condition, the C-height of the model with the contact angles boundary condition is increased under the same acceleration, which indicates that the contact angles boundary condition will reduce the deformation of the droplet. The C-height of the droplet was decreasing with the acceleration increases, as shown in
Figure 12a, and the droplet was still only flattened and did not break when the rotational speed reaches 1710 rpm. (The black line in
Figure 12a represents the numerical simulation results, and the red dots represent the experimental results.) This shows the same trend as the results of the simulation work. The relative error between the simulation and experimental results is 0.73% at 42 m/s
2, 4.72% at 242 m/s
2, 2.05% at 438 m/s
2, and 11% at 640m/s
2. The avenge amount of the relative error between the simulation and experimental results is 4.26%.
Figure 12b shows the simulation results of the relationship between acceleration and C-length with contact angle boundary (wetted wall boundary) conditions models. The droplet started to contact the upper surface of the annular groove at an acceleration of 80 m/s
2, and the C-length at this time was 1.148 mm. As the acceleration increases, the value of the C-length increases as the liquid is squeezed. When the acceleration value reaches 100 m/s
2, the increasing trend of C-length gradually slows down and stabilizes at about 2.24 mm. The results show that considering the contact angle boundary (wetted wall boundary) condition will increase the droplet C-height and decrease the C-length, which represents a reduction in the deformation amount of the droplet.