3.1. Experimental Observation
Firstly, high-speed camera is used to photograph the surface through the glass window at the top of the channel to investigate the bubble attachment phenomenon on different wettability surfaces in the turbulent flow field downstream of the backward-facing step, as shown in
Figure 8. On the super hydrophilic surface (
Figure 8a), the attached bubbles are hardly seen and small, and the small bubbles are basically gathered on the surface of the corner vortex region beside the backward-facing step. On the hydrophilic surface (
Figure 8b), a large number of bubbles with small volume are seen. Most of the bubbles are distributed in the recirculating flow region, and the volume of bubbles on the surface of the corner vortex region is slightly larger than that in other regions. On the hydrophobic surface (
Figure 8c), the bubbles are mostly distributed on the surface of the recirculating flow region. Several large bubbles are gathered in the corner vortex region beside the backward-facing step, and the bubbles in other regions are small. On the superhydrophobic surface (
Figure 8d), only a very large bubble appeared on the surface of the recirculating flow region.
It is worth noting that the quartz glass window with a static contact angle of 52° also has some bubbles adhering to the surface at a lower Reynolds number. However, the transparency of the bubbles attached on the surface of the glass window (B
1) and the bubbles attached on the copper surface (B
2) are different and can be distinguished, as shown in
Figure 8a,b. Since there are more bubbles attached to the glass window at low Reynolds number, the top view at the Reynolds number of 5000 working condition is selected for comparison. In addition, the direction indicated by the arrow in
Figure 8 is the mainstream direction.
In the experiment, the Reynolds number in the channel is adjusted by controlling the flow velocity.
Figure 9 shows that, only under the condition that turbulent (Re > 2300) flow passes the superhydrophobic surface downstream of the backward-facing step, a stable large bubble would appear on the surface (
Figure 9a), while large bubbles did not appear in laminar and transitional flow (Re < 2300) (
Figure 9b).
Figure 10 shows the bubble attachment on the superhydrophobic surface at different Reynolds numbers beside the backward-facing step. It is worthwhile to note that the bubble is constantly changing with time, so, at each Reynolds number, the maximum volume and the closest hemispherical shape of the bubble are selected at the corresponding flow rate. It can be observed from the experiment that Reynolds number has large impacts on the size, position, shape, oscillation amplitude, detachment, and splitting of bubbles, which will be further analyzed below.
3.2. Cause of Bubbles
It can be seen from the experimental observation that there is a stable bubble on the superhydrophobic surface beside the backward-facing step, and the reason for the stable bubble in the liquid can only be boiling and cavitation. Under normal temperature conditions, boiling is impossible in the liquid, so the experimental observed phenomenon can only be cavitation. The cavitation is defined as [
20] the gasification process that occurs when the local pressure in the liquid at room temperature decreases to the saturated vapor pressure of the liquid. In other words, cavitation is the formation, development, and collapse of gas bubbles inside or at the liquid-solid interface.
In order to verify the reliability of the experiments and to investigate the causes of the experimental phenomena, numerical simulations of the backward-facing step two-dimensional flow field have been performed using Fluent software. Based on the previous studies [
21,
22], the Reynolds averaging approach was chosen in this paper to simulate the turbulent flow field on the superhydrophobic surface downstream of the step. The pressure solver is selected, the SIMPLIC algorithm is chosen for the coupling of velocity and pressure, the second order format is chosen for the pressure discretization format, the second order upwind format is chosen for the momentum and turbulence discretization, and the convergence factors of pressure and momentum are kept as default. The standard k-ε model was used, the geometric model was the same as the dimensions of the test section, the bottom surface after the step was set as a slip surface, and the distribution of the pressure in the flow field of the backward-facing step was obtained, as shown in
Figure 11. From the numerical simulation results, the minimum gauge pressure
pmin of the flow field can be obtained (where
h is the height of the step,
x is the distance from the step, and
x/h is the dimensionless distance), as shown in
Table 1.
It can be found from
Table 1 that the minimum pressure in the backward-facing step flow field decreases with the increase of Reynolds number. It can be seen from the water saturated vapor pressure gauge that, when the experimental temperature is 20 °C, the saturated vapor pressure of water is 2338 Pa. The minimum pressure (gauge pressure) in the experiment is −1110 Pa, that is, the absolute pressure is 100,215 Pa, which is much higher than the saturated vapor pressure of water at 20 °C. Therefore, it is impossible to have phase transition in the channel. It can be known from the definition of cavitation that hydrodynamic cavitation cannot occur in the flow of the experimental pipeline. Anubhav Bhatt et al. [
23] explored the cavitation phenomenon in the backward-facing step flow field through experiments, and the captured cavitation image is quite different from the bubble phenomenon in this experiment. The cavitation phenomenon in the experiment of Anubhav Bhatt et al. is not just a bubble; it is the formation and violent bursting of a large number of non-spherical bubbles. In this paper, only one hemispherical bubble appeared on the superhydrophobic surface after the step, and no violent rupture occurred. The comparison of the two experiments once again showed that the bubble generation in this experiment was not caused by hydraulic cavitation.
In fact, studies have shown that the occurrence of cavitation is not entirely dependent on pressure but also related to other factors. By means of a free-energy lattice Boltzmann simulation, G. Kähler et al. [
24] found that the viscous stress, interfacial contributions to the local pressure, and the Laplace pressure are also relevant to the opening of a vapor cavity. In addition, G. Kahler et al. studied the formation process of the steam cavity below the corner of the bag wall when the fluid flows through the obstacle. This process is similar to the bubble formation process in this paper. In Reference [
11] and this article, the pressure at the surface drops to a certain value, and the gas core at the wall evolves into a cavity over time. The exact shape and direction of the cavity growth depends on the pressure distribution in the channel. However, the difference is that the pressure near the wall in Reference [
24] is lower than the equilibrium vapor pressure, and the gas in the cavity is steam. In this paper, the pressure at the wall is much higher than the equilibrium vapor pressure. The gas in the cavity comes from super hydrophobic surface and dissolved gases in the water. G. Falcucci et al. [
25] also present direct evidence of flow-induced incipient cavitation through the lattice Boltzmann method. Therefore, in order to explore the causes of bubbles from the perspective of numerical simulation, a meso-micro method is required, such as the Lattice Boltzmann Method (LBM), which may be involved in future research.
According to the numerical simulation and experimental results, it is found that superhydrophobic surfaces and the backward-facing step provide the material basis and dynamic conditions for the occurrence of this phenomenon. The study of Brennan [
20] (p. 16) shows that cavitation nuclei with a certain number and can stably exist in liquid, which poses the material conditions for liquid to form cavitation. And hydrophobic surfaces can lead to heterogeneous nucleation and greatly suppress the tensile strength of liquid. The stable bubble nucleon mechanism hypothesis proposed by Harvey [
26,
27] suggests that the undissolved gas nuclei can stably exist in hydrophobic solid fractures because, in such cases, the surface tension will play a role in reducing pressure, so that the gas is not forced to dissolve and remains to be gas phase instead.
In the superhydrophobic surface of this experiment, there is a fabricated micro-nano structure (
Figure 5), which provides material conditions for the generation of pseudo-cavitation. On the surface with these micro-nano structures, superhydrophobic coatings are also sprayed, so hydrophobic cracks are formed on the superhydrophobic surface and stable gas nuclei are found in the cracks, as shown in
Figure 12. The generation of local low pressure in the liquid is the dynamic feature for this phenomenon. Due to the negative pressure downstream of the backward-facing step flow (
Figure 11), the dissolved gas in the liquid continuously precipitates and gathers to the negative pressure area, and further diffuses into the tiny gas nuclei in the micro-nano structure on the superhydrophobic surface to make the bubbles continuously larger, forming a stable large bubble on the superhydrophobic surface. Thus, this phenomenon of bubble growth caused by the diffusion of dissolved gas in the liquid into the bubble through the mass transport of the bubble wall is named pseudo-cavitation, which can be categorized as non-phase-change cavitation [
28] (pp. 7–10).
3.3. Evolution of Bubbles over Time
Figure 13 show the whole process of bubble emergence, growth, oscillation, detachment, and splitting at the same Reynolds number as time changes, which can be defined as a bubble cycle. In a bubble cycle, firstly, the gas nucleus is generated in the micro-nano structure cracks on the superhydrophobic surface, as shown in growth process in
Figure 13. Then, under the action of negative pressure, the non-condensable gas in the water precipitates and diffuses into the tiny gas nucleus between the cracks, resulting in the continuous growth of bubbles, as shown in
Figure 13. During the growth process, the bubbles continuously oscillate and deform on the surface, and the frequency of oscillation is very high, which increases the disturbance of the flow field. After a period of development, the bubble volume reached the maximum. In the small Reynolds number stage (Re < 4000), bubbles adhere to the micro-nano structure superhydrophobic surface stably. With the increase of Reynolds number, bubbles detached from the wall. Because of the separation vortex in the recirculating flow region, the bubbles firstly move to the left and then separate along the streamline trajectory of the separation vortex. As shown in
Figure 13, the bubble leaves gas nucleus in its original position after detachment, creating conditions for bubble regrowth. After the bubbles are detached, they are torn in the liquid and split. Then, bubbles grow again on the surface, and the next bubble cycle begins. In a bubble cycle, the detachment and splitting of the bubbles are very fast, occurring in the last second, and the bubbles are growing and oscillating at other times.
3.4. Effect of Reynolds Number on Bubble Position and Size
The pressure distribution in the flow field at different Reynolds numbers can be obtained from the numerical simulation results. The pressure distribution not only affects the position of bubble formation but also affects the growth of gas nuclei.
Figure 14 shows the pressure distribution on the superhydrophobic surface downstream of the backward-facing step at different Reynolds numbers. As shown in
Figure 14, with the change of position, the pressure on the surface decreases first and then increases. There is a minimum pressure value at a certain point, where the tensile strength of the liquid is the weakest in the liquid. The gas nucleus attached to this position on the superhydrophobic surface expands gradually under the negative pressure, tearing the liquid and growing into large bubbles.
As shown in
Figure 14, on the superhydrophobic surface downstream of the backward-facing step, the minimum pressure gradually decreases with the increase of Reynolds number. The position of the lowest pressure point shows the following law with the change of Reynolds number. When the Reynolds number increases from 2300 to 6000, the position of the lowest pressure on the surface gradually moves away from the backward-facing step. When the Reynolds number increases from 6000 to 9000, the position of the minimum pressure on the surface is fixed at
x/h = 1.176 and does not change. With the Reynolds number increasing from 9000 to 11000, the position of the lowest pressure on the surface is gradually away from the step. In the simulation results, the trend of the position of the lowest pressure point on the superhydrophobic surface with the Reynolds number provides the underlying reason for the trend of the bubble emerging position.
It is found through experiments that, besides the fact that the gas nuclei at the lowest pressure point on the superhydrophobic surface can grow into bubbles, the gas nuclei in other low-pressure regions near this point may also develop into bubbles, as shown in
Figure 15. However, the bubbles generated in the low-pressure region near the lowest pressure point are not stable, which will quickly approach the bubbles at the lowest pressure point under the driving force of pressure difference. Finally, the bubbles merge into a bubble at the lowest pressure point with large volume.
Figure 16 shows the change of the bubble centroid position (
Center-X) with Reynolds number in the experiment. It is found that the bubble position does not change significantly and does not show certain regularity. This is due to the small size of the experimental pipe, the small range of variation of the bubble position, and the fact that the measured data of the bubble center-of-mass position is an average value, resulting in the inability to accurately measure the variation pattern of the bubble position in the experiment. Meanwhile,
Figure 16 indicates the variation of the equivalent volume diameter (
de) of bubbles in the backward-facing step flow field at different Reynolds numbers. When the Reynolds number increases from 2300 to 4000, the average equivalent volume diameter of bubbles increases rapidly from 2.82 mm to 3.13 mm. When Reynolds number increases from 4000 to 7000, the average equivalent volume diameter of bubbles decreases from 3.13 mm to 2.70 mm, and the change rate is slow. When the Reynolds number increases from 7000 to 11,000, the average equivalent volume diameter of the bubble decreases sharply from 2.70 mm to 1.28 mm, and the bubble volume decreases rapidly.
As shown in
Figure 17, the flow field and the distribution of bubble behind the step are shown. Qi et al. [
29] found that, when 2000 < Re < 3500, the length
of the recirculating flow region increases with the increase of Reynolds number, and when Re > 3500, the length
of the recirculating flow region is independent of Reynolds number and tends to a stable value. Therefore, in this experiment, when 2300 < Re < 4000, with the increase of Reynolds number, the length of the recirculating flow region
also increases, and the separation line changes from separation line II to separation line I. Influenced by the height of the separation line, the maximum volume of the bubble under the corresponding Reynolds number becomes larger with the increase of Reynolds number. When Re > 4000, with the increase of Reynolds number, the length
of the recirculating flow region no longer changes, and the position of the separation line no longer changes, but the reflux velocity of the recirculating flow region is increasing, and the impact on the bubble is getting bigger and bigger, which leads to the maximum volume of the bubble formed at the corresponding Reynolds number getting smaller and smaller.
3.5. Effect of Reynolds Number on Bubble Oscillation Amplitude and Shape
The deformation of bubbles is studied by the aspect ratio
E analysis, as shown in
Figure 18. When the bubble volume no longer increases at each Reynolds number, the data of bubble aspect ratio varying with time is selected for analysis. It can be seen from
Figure 18 that, when the Reynolds number is 2300, the disturbance of water flow is small, and the aspect ratio of bubbles is about 0.77 and remains almost unchanged, indicating that the oscillation amplitude of bubbles is small. When the Reynolds number increases, the flow disturbance becomes larger, and the aspect ratio curve of bubbles begins to oscillate. With the increase of Reynolds number, the oscillation amplitude of the bubble aspect ratio curve increases, showing that, with the increase of Reynolds number, the oscillation amplitude of the bubble due to the influence of water flow disturbance increases, and its deformation rate also increases. When the Reynolds number is 11,000, the volume of the bubble is small, so the oscillation amplitude is less affected by the flow disturbance. It can be seen from
Figure 18 that the aspect ratio change under this condition is relatively small.
When the Reynolds number is between 2300 and 7000, the aspect ratio varies from 0.65 to 1, indicating that the bubble shape is close to spherical cap shape at this stage. When Reynolds number is between 8000~10,000, the aspect ratio decreases, the height of the bubble is 0.3~0.6 times of the width, and the shape of the bubble is close to elliptical cap shape. When the Reynolds number is 11,000, the aspect ratio of the bubble further decreases, indicating that the bubble is flatter. It can be directly seen from
Figure 19.
3.6. Effect of Reynolds Number on Bubble Detachment and Splitting
Bubble detachment also follows a certain regularity with the change of Reynolds number, which can be divided into two regions according to the trend shown in
Figure 20. For the region without detachment phenomenon (Reynolds number between 2300~5000), the bubbles stably adhere to the superhydrophobic surface downstream of the step, and there is no bubble detachment and splitting. For the region with detachment phenomenon (Reynolds number between 5000~11,000), when the Reynolds number is 5000, the bubbles begin to detach, split, and grow again, with an average bubble cycle of 315 s. When the Reynolds number further increases from 5000 to 6000, the bubble period is getting smaller and smaller, and the reduction rate is fast. Then, when the Reynolds number is between 6000 and 11,000, with the increase of Reynolds number, the frequency of bubbles from the wall is getting faster and faster, and the bubble period is gradually decreasing, while the reduction rate is slower.
Figure 20 shows the variation of bubble splitting position with Reynolds number. It can be seen from the figure that the position range of bubble splitting is
x/h = 1.3~3.6. With the Reynolds number increasing from 5000 to 7000, the bubble splitting position is closer to the step. When the Reynolds number increases from 7000 to 10,000, the splitting position of the bubble is basically unchanged and stable at
x/h = 1.5.
By extracting the bubble centroid position, the trajectory of the bubble from detaching the surface to before splitting is obtained, as shown in
Figure 21. According to the statistical results of the bubbles from the surface to the splitting and the experimental observations after the bubbles splitting, bubble trajectory I and bubble trajectory II in
Figure 22 can be drawn.
Figure 22 is the typical flow structure of backward-facing step flow. The flow field downstream of the step can be divided into separation region, reattachment region, and redevelopment region along the flow direction. The flow field downstream of the step can be divided into corner vortex region, recirculating flow region, shear layer region, and mainstream region along the vertical direction [
30].
It can be seen from
Figure 13 that, when bubbles split, multiple bubbles will be split from the separated large bubbles, and the reason for its split can be explained by combining
Figure 21 and
Figure 22. As shown in
Figure 22, after the bubble departs from the surface, it firstly moves along the trajectory of the separation vortex in the recirculating flow region, then passes through the partition line of the recirculating flow region and the shear layer region along the bubble trajectory I, and moves from the recirculating flow region to the shear layer region, and, finally, moves downstream. Another possible is the bubble moves along the bubble trajectory II from the recirculating flow region through the separation line to the shear layer region, and then through the shear layer boundary to the mainstream region. When bubbles pass through the separation line or the shear layer boundary, the bubbles are split into multiple bubbles by the separation line or the shear layer boundary due to the different fluid velocities in each region. When the Reynolds number is between 5000~7000, the volume of the detached bubble is larger, and the buoyancy force is greater, so the trajectory of the detached bubble is bubble trajectory II. And, when the bubble splits, the larger bubble moves along the bubble trajectory II and the smaller bubble moves along the bubble trajectory I. When the Reynolds number is between 7000~11,000, the volume of the detached bubble is smaller, and the buoyancy force is smaller, so the trajectory of the detached bubble is bubble trajectory I.