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Abstract
This paper aims to explain when the vaporization or thermal decomposition prevails during laser-induced bubble growth and how they influence bubble morphology. Bubbles were generated by irradiating a 304 stainless steel plate submerged in degassed water using millisecond lasers with a pulse width of 0.4 ms and powers of 1.6 kW and 3.2 kW, respectively. The dynamic evolution of bubbles was recorded by a high-speed camera. Moreover, the numerical models were developed to obtain a vaporization model and a decomposition model by incorporating the source terms due to the vaporization and decomposition mass fluxes into the governing equations, respectively. The simulated dynamic bubble evolution is consistent with the experimental results. When the laser power is 1.6 kW, a thin-layer bubble is formed, which gradually shrinks and eventually disappears after the laser stops irradiating. When the laser power is 3.2 kW, a spherical bubble is formed, and its volume decreases significantly after the laser stops irradiating. Subsequently, it remains relatively stable during the observation period. The fundamental reason for the difference between the bubble morphologies obtained from the vaporization model and the decomposition model lies in the presence of a condensation zone in the gas phase. When water vaporization or thermal decomposition dominates, the temperatures obtained from the models align with the decomposition ratios at varying temperatures reported in the literature. Our findings are significant for understanding the dynamic behavior of bubbles, with implications for various laser processing underwater.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Laser irradiation underwater has drawn much attention in recent years due to its extensive applications, such as underwater laser processing [1,2], laser shock peening [3,4], laser cleaning [5], synthesis of nanomaterials [6,7] and material transport [8,9]. Within these applications, the formation of bubbles is an inevitable phenomenon that can significantly impact the processing results. For instance, bubbles can hinder the surface accuracy and processing efficiency [2,10], or they can serve as a mask to aid in the laser processing of composite structures spanning from millimeter to nanoscale [11]. Better control of the dynamic evolution of underwater bubbles induced by laser is necessary for optimizing these applications. The dynamic evolution is a complex phenomenon that involves multiple mechanisms, such as plasma recombination [12], physical changes in phases [13], and diffusion of dissolved gases [13,14].
In the case of high-energy short-pulse and ultrafast lasers, water molecules can be broken down to form plasma because of the extremely high peak power. The resultant bubbles from this phenomenon are commonly referred to as photo-induced bubbles (PIBs). The progression of PIBs usually involves violent oscillations. During the oscillations, most of the gas content is vapor [15,16], which is the combined effects of water evaporation and water vapor condensation. In contrast to phase change, plasma recombination results in the formation of new substances, namely H2 and O2 [12,17]. Plasma can be produced in two processes. Firstly, the water absorbs the energy of the high-energy laser pulse. Secondly, the bubbles rapidly collapse. The power density needs to be high enough in the first process. Therefore, the laser pulses can be femtosecond [18], picosecond [19], and nanosecond [12,20] pulses. The second process requires the generation of high temperature and pressure during the collapse of bubbles. This process can be overlooked for femtosecond lasers due to the small size of the formed bubbles and the gentle nature of the bubble collapse process [12]. Although the gases produced through plasma recombination are at a low percentage [12], the non-condensable nature of these gases can mitigate the bubble collapse [15].
In contrast, continuous lasers with relatively lower peak power tend to induce the formation of thermally-induced bubbles (TIBs). This process is typically divided into two stages [13,14,21]. In the initial stage, bubble formation is stimulated by the vaporization of water. During the subsequent growth stage, bubble expansion is governed by the diffusion of dissolved gases in water. The significant difference of the dissolved gas content between TIBs and PIBs is understandable because the timescale of gas diffusion is on the order of seconds (O(s)), which is much higher than the growth time of PIBs, on the order of milliseconds (O(ms)) [15]. In Peng’s investigation of laser-induced bubbles in ultrapure water with 5 ns pulses, the proportion of H2 and O2 at the maximum size of the bubble fluctuates between 1.2% and 1.3%. However, the concentration of dissolved air is significantly lower by two orders of magnitude, rendering the diffusion of dissolved gases negligible [12]. Wang et al. employed a continuous laser to irradiate the sample for a maximum of 5 seconds. They found that the relationship between the size of the bubble and time can be described by the equation $\textrm{R}(\textrm{t} )\propto {\textrm{t}^{1/3}}$ in air-equilibrated water. While the bubble size remains constant in degassed water [21]. The same relationship for the formation of millimeter-scale bubbles in tap water is also confirmed in the case of continuous laser irradiation over an extended period [14].
Much research has been done on the plasma recombination, changes in phase, and diffusion of dissolved gases, but inadequate consideration has been given to the role of thermal decomposition of water, either for TIBs or PIBs. Thermal decomposition of water occurs under high-temperature conditions [22–24]. Therefore, it can be ignored for individual short pulses and ultrafast lasers. However, when a series of consecutive laser pulses irradiate the surface of a sample, it is still possible to elevate the temperature high [25–27] enough for the thermal decomposition of water to occur. High temperatures can be achieved when the laser power is high enough for continuous laser. Kim et al. pointed out that bubble growth incorporates the influence of hydrogen and oxygen generated from water decomposition under higher power continuous lasers. However, it was not feasible to distinguish this effect from water vaporization and diffusion of dissolved gases in their experiments [14]. In summary, the contribution of thermal decomposition to the dynamic evolution of bubbles remains unclear. Therefore, it is crucial to examine the role of thermal decomposition in the evolution of thermally-induced bubbles.
The aim of this paper is to investigate the different roles of vaporization and thermal decomposition in the dynamic evolution of TIBs, and to elucidate the conditions governing the two different mechanisms. In order to minimize the diffusion time of dissolved gases and ensure an adequate thermal diffusion time for the generation of TIBs, this study utilizes long-pulsed millisecond lasers, in contrast to the use of short pulses and ultrafast lasers which typically produce PIBs. By varying the laser power, we explore the dynamic evolution of bubbles dominated by vaporization and those dominated by thermal decomposition. Unlike previous studies that have relied on numerical fitting of experimental data to estimate the combined contributions of water vapor and dissolved gases [14,21], our research establishes a numerical model that integrates phase change effects into the momentum, mass, and energy equations. Different mass source terms are employed to separately evaluate the impacts of phase change and thermal decomposition on bubble evolution. The findings of our study are significant for understanding the dynamic behavior of laser-induced bubbles, with implications for various laser processing underwater.
2. Experimental methods
The schematic of the experimental setup is illustrated in Fig. 1. The experiment employed a Nd:YAG millisecond laser (GSI JK 300D) with a wavelength of 1064 nm and a peak power of 16 kW. The pulse width was set to 0.4ms and the power was adjusted to 10% (1.6 kW) and 20% (3.2 kW) of the peak power. A 304 stainless steel sheet (20 mm × 20 mm × 2 mm) was fixed on the base in the water tank. The sample surface was polished using sandpaper up to a 3000 grit, and then subjected to ultrasonic cleaning using acetone solution. The surface reflectance was measured employing a UV-Visible spectrophotometer (UV-3600) at the wavelength of 1064 nm, yielding a value of 65.8%. The water tank was filled with deionized water and then boiled for 30 minutes to minimize dissolved air in the water. After cooling to room temperature (20 °C), the tank was fixed in the XY plane.
The laser was delivered via a 300 µm diameter optical fiber to a laser head fixed along the z-axis. The laser beam passed through a collimating lens with a focal length of 200 mm, a total internal reflection prism, and a focusing lens with a focal length of 160 mm, all within the laser head. It then passed through a 3 mm thick quartz glass window positioned on the water tank and converged at point O in the water. The thickness of the water layer between the quartz glass window and the sample was set to 10 mm. In order to produce both water decomposition-dominated bubbles and vaporization-dominated bubbles, it was necessary to vary the laser power density within a narrow range. Therefore, certain amount of defocus, denoted as H (set to 3 mm), was required for the sample surface.
The dynamic evolution of bubbles was recorded by a high-speed imaging system. This system comprised a 300W LED white light source with adjustable brightness, a high-speed camera (Optronis, CP80-3-M-540), and a PC host with a frame grabber (AS-FBD-4XCXP6-2PE8). The camera recorded frames at a speed of 20,000 frames per second, with a resolution of 192 × 200 pixels. Due to the limited proportion of the relevant results in the images, the pictures were cropped to 100 × 100 pixels, resulting in a cropped field of view size of 2 mm × 2 mm.
3. Numerical simulation model
3.1 Physical process description and formulation
Upon exposure to the laser, the surface of the sample begins heating. In addition, the water in contact with the sample surface undergoes either vaporization or thermal breakdown. As gas accumulates, bubbles begin to grow. On the gas-liquid interface away from the sample surface, water vapor releases heat and condenses. Hence, the motion of the gas-liquid interface requires the consideration of both bubble dynamics and changes in the gas-liquid state. We utilized the phase-field method to convert the problem of interface movement into the task of solving the phase-field variable on a stationary grid. This allowed us to obtain interface information indirectly. The gas-liquid state change was addressed by integrating source terms into the governing equations. In the experiment, the laser energy was intentionally set to a lower peak power to ensure that the bubbles grow gradually rather than explosively. Therefore, the incompressible Navier-Stokes equations were employed to simplify the calculations.
The dynamic evolution pattern of bubbles in both cases is determined by modelling the phase transition and the thermal decomposition of water. The detailed description of the governing equations in this study refers to the bubble growth during saturation boiling [28,29]. The main improvement over existing studies lies in the modification of the mass flux to make it applicable to the thermal decomposition of water.
3.2 Assumptions
To facilitate the numerical simulation and modelling of the bubble evolution induced by laser irradiation, certain assumptions were made to simplify the complexity of the system. The key assumptions include:
- 1. The influence of bubbles on the laser power density irradiated on the sample surface is ignored.
- 2. The reflectance of the sample surface remains constant during the laser pulse irradiation.
- 3. The temperature increase caused by the direct absorption of laser energy by water is neglected, since only one pulse is applied.
- 4. It is assumed that water decomposes directly after vaporization in the thermal decomposition model.
- 5. The high-speed gas molecules passing through the gas-liquid interface are ignored.
3.3 Solution domain, boundary, and initial conditions
A two-dimensional axisymmetric model was employed, due to the symmetry of the entire process. Figure 2(a) displays the boundary conditions, mesh and computational domain, comprising the fluid domain (depicted in green and representing water) and the solid domain (depicted in gray and representing 304 stainless steel). To prevent the boundary conditions from influencing the calculation results, the computational domain was expanded to its maximum size (fluid domain: 6 mm × 6 mm; solid domain: 6 mm × 2 mm). To enhance computational accuracy and minimize computational cost, a refined quadrilateral mesh (mesh size: 20 um) was selectively applied to regions where the gas-liquid interface may cross (green region in the refinement area: 1 mm × 1 mm) and to the regions with a significant temperature gradient in the sample (grey region in the refinement area: 1 mm × 0.4 mm). In contrast, a coarsened triangular grid was employed for the remaining areas. The refined grid areas are also the regions shown in the magnified image of the results. Considering the symmetry of the solution domain, only half of the axisymmetric domain along the r-axis is modelled, with the symmetry axis being the Z axis.
Fig. 2. (a) Boundary conditions, mesh of refinement area and computational domain; (b) Power density on the surface of the sample.
The contact angle, measured using a contact angle goniometer (SINDIN SDC-350H), is determined to be 1.24 radians. The surface emissivity is specified as 0.2 [30]. The power density on the sample surface under different laser power conditions is shown in Fig. 2(b). Due to the different transmission properties of laser in water and air, this study utilizes geometric optics simulation to compute the power density. Details of the simulation methodology can be found in Supplement 1.
In the fluid domain, the initial velocity is 0 m/s, and the relative pressure with respect to standard atmospheric pressure (101,325 Pa) is 0 Pa. The initial temperature of both water and the sample is 293.15 K. Point O was set as a point-wise constraint for the gas phase, serving a role equivalent to a gas pocket. These initial conditions were defined to represent the stationary state of the fluid and sample before the laser pulse, with the gas phase constraint at point O acting as a starting point for the evolution of the gas-liquid interface.
3.4 Physical properties
The phase field variable $\phi $ characterizes the two-phase system consisting of gas and liquid during the process of bubble growth. A value of $\phi = 1$ represents the liquid phase, while $\phi ={-} 1$ indicates the gas phase. The transition at the gas-liquid interfaces is depicted by a diffusion region, where the phase field variable $\phi $ transitions from -1 to 1. Thus, the thermal properties of the fluid domain can be expressed as a function of the volume fractions of the two phases:
Material properties used in the numerical model can be found in Supplement 1. The volume fractions of the liquid and gas phases are defined as the functions of phase field variable $\phi $:
3.5 Governing equations
To account for the mass changes occurring at the gas-liquid interface due to phase transition and the thermal decomposition of water, it is necessary to define the mass flux at this interface. The expression for mass flux varies depending on whether water undergoes phase change or thermal decomposition. Phase change encompasses both vaporization and condensation, constituting a bidirectional process. Conversely, thermal decomposition solely involves the transition from the liquid phase to the gas phase, making it a one-way process.
The mass flux expression for the phase transition of water can be written as follows [28]:
Where C (m/s) should be large enough to maintain the interface temperature equal to the saturation temperature. This expression is the mass flux expression for saturated bubble boiling. When the temperature of the region exceeds the saturation temperature, $\dot{m} > 0$, indicating vaporization. Conversely, when the temperature of the region is below the saturation temperature, $\dot{m} < 0$, indicating condensation. Therefore, it can depict a bidirectional process. After incorporating this expression into the governing equations, the model is referred to as the vaporization model.The mass flux expression for the phase transition of water is modified to apply to the thermal decomposition of water:
For two-phase flow with no phase change at the gas-liquid interface, the governing equation describing interfacial dynamics is the fourth-order Cahn-Hilliard equation [29,31]:
To account for the influence of the water-gas phase transition or the thermal decomposition of water on bubble evolution, the source term $- \dot{m}\delta \left( {\frac{{{V_{f,g}}}}{{{\rho_g}}} + \frac{{{V_{f,l}}}}{{{\rho_l}}}} \right)$ should be incorporated into the Cahn-Hilliard equations:
Momentum equation (N-S equation):
The continuity equation for incompressible fluids is $\nabla \cdot {\mathbf u} = 0$. Nevertheless, within the vicinity of the gas-liquid interface, there can occur a transfer of mass resulting in different velocities on either side of the interface. In order to address this specific case, it is necessary to include a source term $\dot{m}\delta \left( {\frac{1}{{{\rho_v}}} - \frac{1}{{{\rho_l}}}} \right)$ in the continuity equation:
Energy equation:
The mass flux at the interface is also reflected in the source term of the energy conservation equation, denoted as $Q ={-} \dot{m}\delta L$. In the case of water decomposition, $L = \frac{{\mathrm{\Delta }{H_f}}}{{{M_w}}}$, represents the latent heat of water decomposition. The standard molar enthalpy of formation for water, denoted as ${H_f}$, is -285.8 kJ/mol. Additionally, the molar mass of water, represented as ${M_w}$, is 0.018 kg/mol. In the case of water phase change, L is 2256.54 kJ/kg, calculated based on the enthalpy formula from Ref. [32].
When $\dot{m} > 0$, indicating a transition from liquid to gas, Q acts as a heat sink. Conversely, when $\dot{m} < 0$, indicating a transition from gas to liquid, Q acts as a heat source. The equation for energy conservation, considering phase transitions at the interface, can be expressed as:
4. Results and discussion
4.1 Model applicability verification
Laser powers of 1.6 kW and 3.2 kW are substituted into the vaporization and decomposition models, correspondingly. This can be accomplished based on the assumption that the bubble growth is predominantly governed by the vaporization and thermal decomposition under the conditions of 1.6 kW and 3.2 kW, respectively.
The occurrence of thermal decomposition of water requires the Gibbs free energy ($\mathrm{\Delta }G = \mathrm{\Delta }{H_f} - T\mathrm{\Delta }S < 0$) to be negative. Based on this equation, the calculation suggests that the temperature should exceed 1750 K. With increasing temperature, the proportion of thermal decomposition rises [22]. However, the decomposition rate is only 1 percent at 2000 K, increasing to 36 percent at 3000 K. At 3500 K, the decomposition rate reaches 77 percent [23]. Therefore, to verify if the conditions are satisfied, it is imperative to assess the maximum temperature of the specimen, which typically occurs at the center point (i.e., point O in Fig. 2). This temperature serves as the criterion for determining model suitability. Figure 3 illustrates the temperature variation at point O over time.
Fig. 3. Temporal temperature variation curve of the laser spot’s center point on the specimen surface. The black line represents the temperature curve with 1.6 kW incorporated into the vaporization model; the red line corresponds to the temperature curve with 3.2 kW integrated into the decomposition model. Points A, B, C, and D represent the intersection points of these two curves with the thermal decomposition temperature of water.
Upon the initiation of laser irradiation (at 0 ms), the surface temperature of the sample rapidly increases. As peak power increases, the temperature rise rate also increases.
Under the condition of 1.6 kW, the temperature at the center of the laser spot (point O) experiences the following variations. The temperature gradually increases to 1750 K (point A in Fig. 3) at 0.29 ms. When the laser ceases irradiation at 0.4 ms, the maximum temperature of 1934 K is reached. Then, the temperature decreases gradually to 1750 K at 0.41 ms (point B in Fig. 3). Consequently, the time span between points A and B during which the temperature surpasses 1750 K is 0.12 ms. This suggests that the temperature at point O remains predominantly below the decomposition temperature throughout the majority of the bubble growth period. Thus, vaporization predominantly drives bubble growth, with thermal decomposition contributes insignificantly. This satisfies the prerequisite conditions for the vaporization model.
Under the condition of 3.2 kW, the temperature at point O experiences the following variations. At 0.07 ms, the temperature gradually increases to 1750 K (point C in Fig. 3). At 0.4 ms, the laser stops irradiating, and the maximum temperature of 3390 K is reached. Then the temperature decreases gradually to 1750 K at 0.68 ms (point D in Fig. 3). Consequently, the time span between points C and D during which the temperature exceeds 1750 K spans 0.61 ms. This indicates that the temperature at point O is above the decomposition temperature throughout the majority of the bubble growth period. Consequently, thermal decomposition plays a significant role in the bubble growth process. Under the condition of the highest temperature of 3390 K, the decomposition proportion is less than 77% [23]. In theoretical modelling, it is assumed that the gasified water will decompose completely. Consequently, the theoretically estimated amount of decomposed gas is more than the actual amount of gas present in the bubble's steady state.
4.2 Thin-layer bubble evolution process
Figure 4(a) illustrates the dynamic evolution of a thin-layer bubble formed on the surface of the sample under the condition of 1.6 kW. The images in the figure are chosen from a sequence (see Visualization 1) captured by a high-speed camera at critical instants.
Fig. 4. (a) Dynamic evolution sequence of thin-layer bubble under 1.6 kW. (b) Detailed temperature distribution on the surface of the sample at different times and locations.
During the laser irradiation period (0-0.4 ms), a dark thin layer develops on the surface of the sample (marked by the red dashed box at 0.1 ms). Simultaneously, flocculent clusters are released from the thin layer. The formation of these clusters could be attributed to the intrusion of high-temperature gas into the water, causing the creation of microbubbles or unevenly heated water masses. This leads to the refractive index change, causing light scattering from the background light source.
After the termination of the laser pulse, flocculated clusters continue to be released from the thin layer for a period of time (0.4-1 ms). The reason for this phenomenon is that the sample acts as a heat source, leading to the evaporation of water and the creation of gas molecules with a significant velocity. These gas molecules are capable of permeating the gas-liquid boundary. Simultaneously, the surface temperature of the sample gradually decreases. Until 1 ms, the velocity of the vaporized water molecules becomes inadequate to break through the gas-liquid interface, leading to a noticeable cessation in the release of flocculent clusters from the thin layer. After that, flocculent clusters in water gradually become lighter and eventually vanish due to the decreasing temperature and gas dissolution. Only a few black particles left, as circled in the red dashed line area at 5 ms in Fig. 4(a). These black particles are non-condensing bubbles formed through the thermal decomposition of water, as explained in Section 4.1.
The release of flocculent clusters is closely related to the surface temperature of the sample. The temperature distribution on the sample surface at different times is shown in Fig. 4(b). At 1 ms, the highest temperature point on the sample surface, located at the center of the laser spot, reaches 852 K. Therefore, it can be inferred that the release of flocculent clusters requires the sample temperature to be higher than 852 K. The cyan-filled region corresponds to the area on the sample surface where the temperature is high enough to facilitate the release of flocculent clusters during the time interval of 0.4-1 ms. For instance, at 0.5 ms, the portion of the temperature distribution curve on the sample surface that intersects with the cyan-filled region is segment MN. Therefore, point N represents the boundary for whether flocculent clusters can be released, and its corresponding x-coordinate is approximately 0.3 mm. From Fig. 4(a) at 0.5 ms, it can be seen that the radius of the region where flocculent clusters are released from the sample surface is approximately 0.35 mm. Hence, the experimental and simulation results are roughly consistent. Furthermore, the temperature curves at different times also indicate that as the distance from the laser center decreases, the sample temperature increases. This clarifies the reasons behind the increased intensity and greater distance traveled by the flocculent clusters released from the center in Fig. 4(a). Conversely, flocculent clusters released from the periphery are found in close proximity to the thin layer.
The radius of the thin layer is related to the region on the surface of the sample where the temperature surpasses the saturation temperature. The inset of Fig. 4(b) displays the specific radius at various time intervals. It decreases by PQ (0.075 mm) from 0.4 ms to 1 ms, followed by an additional reduction of QR (0.167 mm) from 1 ms to 5 ms. At 7 ms, the temperature across the entire sample surface drops below the saturation point. This process is also evident in Fig. 4(a). The radius of the thin layer remains relatively stable until 1 ms. Then it experiences a significant decline and ultimately vanishes entirely by 7 ms.
Under the condition of 1.6 kW, the simulated results of the dynamic evolution of thin-layer bubbles are shown in Fig. 5(a). During the period of laser irradiation(0-0.4 ms), the bubble undergoes a transformation from a hemispherical to a thin-layer shape. Figure 5(b) displays more precise time intervals, ranging from 0 to 0.2 ms. At 0.02 ms, the bubble in the fluid domain occupies only a small fraction of the space contained by the saturation temperature line. The liquid phase between the saturation temperature line and the gas-liquid interface is superheated water. As a result, the superheated water quickly turns into vapor, leading to a rapid expansion of the bubble. The saturation temperature line is continuously expanding, and the gas-liquid interface is catching up with it at an accelerated pace. Beyond 0.04 ms, certain regions even surpass the saturation temperature line. The gas phase situated between the saturation temperature line and the gas-liquid interface consists of supercooled vapor. This portion of vapor is on the verge of liquefaction and is situated near the top of the bubble. As a result, the rate of upward expansion of the bubble decreases, leading to its transition from a spherical to a flattened shape. By 0.18 ms, the bubble achieves full stabilization, forming a thin layer.
Fig. 5. (a) Simulation results of the dynamic evolution of thin-layer bubble under 1.6 kW. (b) Time steps refined within the interval of 0-0.18 ms. The red region in the figure represents the gas phase. The blue region represents the liquid phase. The magenta line corresponds to the isothermal line of the saturation temperature.
Nevertheless, the experimental results do not provide any evidence that the bubble undergoes a transformation from a hemispherical to a thin-layer shape. This limitation arises from the constraints imposed by the model. In reality, the vaporization process initiates not only from the central point where the initial gas pocket is situated. Due to the high laser power density, the sample surface within the laser irradiation area rapidly attains the vaporization temperature, rendering the entire region a potential seed for bubble formation. However, constraints were implemented during the model setup to restrict the onset of vaporization only from the gas-liquid interface at the center of the laser spot. As a result, a significant portion of superheated water at 0.02 ms remains unable to vaporize, leading to the observed hemispherical over-shooting at 0.1 ms.
The simulated results of the thin-layer bubble after 0.2 ms represent the outcome following the rectification of model method errors, and the shape is consistent with experimental results.
At 0.4 ms, the cessation of the laser heat source initiates the gradual shrinkage of the thin-layer bubble. However, significant shrinkage in size is not observed until 1 ms. From 1 ms to 5 ms, the radius of the region covered by the thin-layer bubble experiences a notable decrease. By 7 ms, the thin-layer bubble vanishes entirely. Combining the experimental results presented in Fig. 4, it becomes evident that the observed black thin layer in the experiment represents a thin-layer bubble covered by microbubbles or unevenly heated water.
The model fails to simulate the high-temperature gas breakthrough across the gas-liquid interface into the water. This results in an oversight regarding the enhanced cooling effect of the released flocculent clusters. Moreover, the model overlooks the scattering effects of flocculent clusters and bubbles on the laser, potentially causing simulated temperature to exceed the actual values.
4.3 Spherical bubble evolution process
Figure 6 illustrates the dynamic evolution of a spherical bubble forming on the surface of the sample under the condition of 3.2 kW. The images in the figure are selected from a sequence (see Visualization 2) captured by a high-speed camera. In contrast to the behavior observed at 1.6 kW, where a thin black layer forms and eventually disappears, here the bubble undergoes a transition from a thin layer to a hemispherical shape. Ultimately, the hemispherical bubble persists throughout the entire observed duration.
After 0.1 ms of laser irradiation, a black thin layer emerges on the surface of the sample, resembling the thin layer observed under the condition of 1.6 kW. However, subsequent phenomena on the sample surface differ from those at 1.6 kW. From 0.1 ms to 0.4 ms, the middle of the thin layer gradually protrudes, forming a hemispherical shape. From 0.5 ms to 4 ms, the contact angle between the hemispherical bubble and the sample oscillates, reaching its maximum at 4 ms. Concurrently, a significant cessation of flocculent clusters release from the thin layer occurs. At 9 ms, the flocculent clusters present in the water become virtually indiscernible. Beyond 9 ms, the black thin layer on the sample surface gradually diminishes in size, disappearing completely by 21 ms. The bubble undergoes a substantial decrease in size from 4 ms to 9 ms, and subsequently maintains a relatively stable volume until the experiment's maximum observation time of 1 s. As discussed in Section 4.1, the bubble is composed not only of hydrogen and oxygen generated from water decomposition but also contains a portion of water vapor. Therefore, the volume reduction is the combined result of water vapor condensation and the decrease in gas temperature. The coexistence of both the spherical bubble and the black thin layer suggests that the observed black thin layer is not simply a thin-layer bubble, but is more likely to be flocculent clusters or discontinuous thin-layer bubbles enveloped by flocculent clusters.
Under the condition of 3.2 kW, the simulated results of the dynamic evolution of spherical bubble are shown in Fig. 7(a). During the laser irradiation period (0-0.4 ms), the bubble grows rapidly, with the fastest growth rate observed between 0-0.1 ms. Within this temporal interval, a more detailed time step refinement is shown in Fig. 7(b). At 0.01 ms, the phenomenon is similar to that observed at 0.02 ms in the vaporization model. At 0.02 ms, certain region of the gas-liquid interface even exceeds the saturation temperature line. The period is considerably shorter than that (0.04 ms) observed in the vaporization model. In the gas region, the portion located between the saturation temperature line and the gas-liquid interface appears in the same position as observed at 1.6 kW, i.e., still at the top of the bubble. However, the assumption here is that water vaporizes and then decomposes directly. Consequently, condensation is not possible in this area, despite the temperature being lower than the saturation temperature. The reason for the excessive portion of superheated water at 0.01 ms, which is similar to that discussed in Section 4.2, is attributed to the point-constrained gas pocket.
Fig. 7. (a) Simulation results of the dynamic evolution of spherical gas bubbles under 3.2 kW; (b) Time steps refined within the interval of 0.01-0.05 ms. The red region in the figure represents the gas phase. The blue region represents the liquid phase. The magenta line corresponds to the isothermal line of the saturation temperature.
Within the time range of 0.1 ms to 0.4 ms, the bubble's shape experiences instability and deviates significantly from a hemispherical shape. The absence of gas condensation in this model indicates that the deviation is not caused by liquefaction at the interface. Hence, the concave shape observed in the time range between 0.2 ms and 0.4 ms may be a result of the fluid's inertia. This will be further demonstrated in section 4.4.
Visualizing the actual variations in the size of the bubble is difficult due to its oscillating nature. Consequently, a volume integral is conducted on the gas phase area, as depicted in Fig. 8. It is apparent that the bubble volume experiences a quick increase within the initial 2.5 ms, followed by a period of stabilization. The expansion of the bubble is non-linear, characterized by an initial rapid growth followed by a steady decline in the growth rate. This trend continues until approximately 2.5 ms when the bubble reaches its maximum size. Subsequently, the size remains rather stable, with occasional fluctuations (see Visualization 3). Beyond 0.4 ms, the bubble continues to expand despite the cessation of the laser heat source. This expansion is attributed to the presence of a liquid-phase zone that remains between the saturation temperature line and the gas-liquid interface on the sample surface.
During the rapid expansion of the bubble volume (0-1 ms), a close alignment is observed between the saturation temperature line and the gas-liquid interface (Fig. 7(a)). This time period coincides with the highest intensity release of flocculent clusters observed in the experimental results. In the stage when the bubble volume increases slowly or even remains constant (after 2 ms), the saturation temperature line quickly contracts away from the gas-liquid interface until it eventually disappears (Fig. 7(a)).
It should be acknowledged that the results obtained from the decomposed model are consistent with experimental results only in terms of trends such as bubble growth, oscillation, and maintenance. However, there are significant discrepancies in bubble volume between the experimental and simulation results. The model assumes that all vaporized water undergoes direct decomposition, while in reality, only a portion of the vaporized water is decomposed, leaving the remainder in the form of water vapor. Additionally, the model's expression for mass flux at the gas-liquid interface prevents water vapor condensation, even at the position where the temperature is below saturation. This discrepancy was evidenced by the observed shrinkage of the bubble during the time period from 4ms to 9ms in the experiment. Consequently, these factors contribute to the bubble volume in the final result obtained by simulation being larger than that observed in the experiment.
4.4 Phase transition at the gas-liquid interface
Figure 9 displays the velocity fields of the thin-layer and spherical gas bubbles, as well as the heat source from the phase transition at the gas-liquid interface, at 0.2 ms. At the three-phase contact point (gas/liquid/solid), water absorbs heat due to vaporization or decomposition, resulting in a negative heat source in this region.
Fig. 9. Velocity field and phase-change heat source of (a) thin-layer bubble and (b) spherical bubble at 0.2 ms. The magenta line represents the gas-liquid interface. Streamlines and arrow plots depict the velocity fields. Cloud maps represent the phase-change heat source.
The thin-layer gas bubble is depicted in Fig. 9(a). The streamlines converge near the gas-liquid interface, away from the surface of the sample. Moreover, the velocity directions on both sides of the gas-liquid interface are opposite to each other. This phenomenon occurs because bubble growth is controlled by water vaporization, resulting in water vapor condensing as a result of subcooling, and hence, a positive heat source in this area. In contrast, the spherical gas bubble shown in Fig. 9(b) exhibits a phenomenon different from that in Fig. 9(a). The streamlines do not converge near the gas-liquid interface, and the velocity directions on both sides of the gas-liquid interface are identical. In addition, the temperature at the interface is below the saturation temperature (see Fig. 7(a)). However, the heat source in this region is zero. This means there is no phase change in this region. Consequently, the mass flux expression provided in this paper not only guarantees the condensation of water vapor produced by vaporization when below the saturation temperature but also ensures that gases produced by thermal decomposition will not condense even under conditions below the saturation temperature. It should be noted that a vortex exists in the central region of the bubble, resulting in the interface curving downward. This also supports the inference in Section 4.3 that the reason for the concave shape of the bubble is due to the effect of fluid inertia.
Although the mass flux expression in Refs. [29,28] is the same as that in the vaporization model, the simulated bubble morphologies differ. Instead, the bubble shape in the literature corresponds to that in the decomposition model. This discrepancy arises from the difference in the initial temperature settings of water. Their study was conducted at the saturation temperature, whereas our study maintained room temperature. In the case of the vaporization model, water vapor condenses in the subcooled region, which is located inside the gas-liquid interface away from the three-phase point. The condensation results in the formation of thin-layer bubbles. Conversely, there is an absence of a subcooled region inside the gas-liquid interface in their research. In the case of the decomposition model, although the temperature of the gas phase may be lower than the saturation temperature, condensation cannot occur in this portion of the gas. Hence, the common reason for the formation of spherical bubbles is the absence of a condensation zone within the bubbles. If such a region exists, thin-layer bubbles may form.
Furthermore, this observation further validates the inference made in literature [21] that bubble growth can be divided into two stages. The first stage is explained as being dominated by vaporization, while the diffusion of dissolved gas predominates in the second stage. According to the findings our study, if bubble growth continues to be explained as primarily driven by vaporization in the second stage, then the size of the bubble would be limited by the condensation of water vapor at the gas-liquid interface. In this scenario, the size of the bubble would be constrained. Therefore, according to existing literature, the second stage of bubble growth is interpreted as being primarily driven by the diffusion of dissolved gas. The spherical shape of the vaporization-dominated bubble observed in the literature during the first stage is attributed to the small area irradiated by the laser.
5. Conclusion
The results confirm the validity of vaporization and decomposition models in explaining bubble growth under specific conditions, with temperature thresholds delineating the dominance of vaporization or thermal decomposition in bubble dynamics. In the context of 1.6 kW, the formation of thin-layer bubbles manifests distinct characteristics, including flocculent cluster release and temperature-dependent morphology changes. Additionally, spherical bubbles formed at 3.2 kW exhibit rapid growth, size reduction, and subsequent stabilization, reflecting a combined influence of vaporization and decomposition processes. Analysis of velocity fields and heat sources at the gas-liquid interface offers insights into phase transitions during bubble evolution. Differences in bubble morphology are attributed to the presence or absence of a condensation zone in the gas phase. These findings enhance our understanding of bubble formation mechanisms, with implications for applications such as laser-induced bubble generation and material processing. Future research may focus on refining computational models and experimental techniques to capture the complexities of bubble evolution more accurately, advancing various technological and scientific endeavors reliant on bubble dynamics.
Nomenclature
$C$ | constant in the mass flux |
${C_p}$ | specific heat capacity |
$d$ | smooth interval for the Heaviside function |
$G$ | Gibbs free energy |
${H_f}$ | standard molar enthalpy of formation |
$k$ | thermal conductivity |
$L$ | latent heat |
$\dot{m}$ | mass flux |
${M_w}$ | molecular weight of water |
$p$ | pressure |
$Q$ | heat source |
$r$ | radius from spot center |
$S$ | standard molar entropy |
$t$ | time |
$T$ | temperature |
${V_f}$ | volume fraction |
${{\boldsymbol F}_{\textrm{st}}}$ | surface tension |
${g}$ | gravity acceleration |
${\boldsymbol I}$ | unit matrix |
${\boldsymbol u}$ | velocity field |
$\gamma $ | mobility |
$\delta $ | interface smoothing function |
${\varepsilon _{pf}}$ | thickness of the diffuse interface |
$\lambda $ | mixing energy density |
$\mu $ | viscosity coefficient |
$\rho $ | density |
$\phi $ | phase field variable |
$\psi $ | phase field help variable |
Funding
National Key Research and Development Program of China (2021YFF0500200); National Natural Science Foundation of China (52175432, 61927814, U20A20290).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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