Evolution of Cavitation Bubble in Tap Water by Continuous-Wave

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Evolution of cavitation bubble in tap water by continuous-wave laser focused on a metallic surface Nayoung Kim, Hyungmin Park, and Hyungrok Do Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b04083 • Publication Date (Web): 14 Feb 2019 Downloaded from http://pubs.acs.org on February 19, 2019

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Evolution of cavitation bubble in tap water by continuous-wave laser focused on a metallic surface Nayoung Kim,† Hyungmin Park,∗,†,‡ and Hyungrok Do†,‡ †Department of Mechanical & Aerospace Engineering, Seoul National University, Seoul 08826, Korea ‡Institute of Advanced Machines and Design, Seoul National University, Seoul 08826, Korea E-mail: [email protected]

Abstract As an example of photon-matter interaction, we experimentally investigate the temporal evolution of a millimeter-sized cavitation bubble, induced by focusing a continuouswave laser on a metallic plate in tap water. Our major interests are to understand the mechanism of bubble growth/shrinkage for a long time duration up to O(102 ) seconds and to draw the time-dependency relation of a bubble size, depending on the incident laser power. With the time passed after the laser with different power is focused, it is found that the phase change and/or transport of dissolved gas into the bubble play a dominant role in determining the bubble growth and shrinkage. Thus, we propose two stages in terms of time and three regimes depending on the incident energy, in which the evolutions of cavitation bubble in short and long time durations are distinctively identified. In regime I (lower incident power), the water nearby the focal point undergoes a phase change, resulting in an initial rapid growth of a bubble (first stage), but the convection flow due to locally heated surface causes the bubble to shrink at

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later times (second stage). As the laser power increases (regime III), more dissolved gas in the surrounding water enters the growing bubble and prevents the water phase from being absorbed into the bubble. Thus, the bubble growth is dominated by the dissolved gas. Between regimes I and III, there is a transitional regime II in which both the phase change of water and dissolved gas contribute to the bubble evolution. We further our understandings by developing the relations about the time-dependency of bubble size for each stage and regime, which agree well with the measured data. The scaling relations are also validated with different conditions of liquid such as degassed water and NaCl solution. While previous studies have mostly focused on the nanoand/or micro-sized bubble generation in a very short time (less than 1 second), we think that the present results will extend our knowledge on how to predict and control the size of laser-induced cavitation bubble for longer time duration.

INTRODUCTION Depending on the flow conditions, cavitation bubbles may show up in a liquid flow, and the growth and collapse dynamics of these bubbles significantly affect the flow characteristics or interact with the nearby solid surfaces, if any. Conventionally, the susceptibility of a cavitation is determined by the cavitation number, σ = (p − pv )/(0.5ρU 2 ); that is, its inception is encouraged when σ becomes smaller than a critical value. Here, p is the local pressure in the flow, pv is the vapor pressure of the fluid, ρ is fluid density, and U is the characteristic speed of the flow. The cavitation phenomenon has been vigorously investigated for locally accelerated high-speed flows, e.g., flow around a rotating blade in turbo-machinery. 1–3 On the other hand, the impact of a solid (or fluid) projectile through the free surface between immiscible fluids causes the deformation of interface, forming a cavity behind the projectile. 4,5 This kind of cavitation occurs even at a very low speed (U ) and thus it has been called as a low-speed cavitation, distinguished from the former one (high-speed cavitation). 4 While the dynamics of low-speed cavitation bubble has been understood through the inter-

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actions between inertia, surface tension, gravity, and viscosity of the fluid flow, there have been different attempts such as electrolysis, 6 electric spark, 7 and acoustic waves 8 to force the formation of cavitation bubbles for various engineering purposes. Among the above-mentioned methods, the laser-induced cavitation bubbles have been studied due to its advantage in terms of energy efficiency, controllability, fast response, and so on. 9 Basically, this approach originates from the concept of photon-matter interaction; when photons (i.e., light illumination with a high power) are focused onto a very small area, the highly concentrated energy effectively changes the material property (density, viscosity, and reactivity), phase, and the form of energy itself. 10 Since there is no mass (volume) transfer involved in delivering photons, the response time to achieve a targeted functionality is very short and the required hardware setup would be quite simple. As a source of photons, a pulsed or continuous-wave laser has been commonly used due to its superior collimated property, and the pulsed laser has been more popular because of its higher power density. 9 When a high-intensity pulsed laser is focused onto a certain material in water, the laser energy is locally absorbed by the material that is ablated in a very short time. Then, plasma is formed and its subsequent expansion results in the generation of a bubble. 11 Here, of particular interest is the bubble dynamics including a highly localized energy concentration, explosive vaporization, rebound (oscillation), jet formation, and shock wave, which occur quite fast at the speed of O(102 ) m/s. 9,12 As the plasma decays, its strong energy is transferred to the liquid to create a vapor phase, which undergoes a periodic growth and shrinkage until the collapse. During the evolution, the bubble shape is symmetric or non-symmetric depending on the wettability or temperature of the target surface. Since the initial driving force of bubble formation involves a very high pressure, the subsequent response such as rebounds has been theoretically modeled using Rayleigh-Plesset 13,14 or Gilmore 15 (compressibility effect considered) models (see Zhang et al. 9 for a review). While this phenomena has been related to the mechanical damage and surface erosion, 16 they are also considered to be a promising tool for fluid transport in microfluidic chip applications, surface cleaning, material process-

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ing (e.g., synthesis of nanoparticle colloids) in biology, chemistry, medical surgery, and so on. 9,17–19 Compared to the pulsed-laser applications, the bubble generation with a continuous-wave (CW) laser has been less investigated and there are a few studies found in the literature. 20–22 Although the energy density is lower than the pulsed laser, the continuous-wave laser is considered to be more useful in retaining the induced bubble for an elongated time. Zhang et al. 21 focused continuous-wave laser onto a chromium pad under various liquids and showed that the thermally induced bubbles can function as a micro-valve or pump in a micro-channel system. Zheng et al. 22 tried to locate a single vapor bubble in a micro-sandwiched water sheet by focusing a continuous laser on a silver film. They analyzed that the bubble size increases if the energy input by the laser is higher than the dissipated heat. When the laser power is balanced with the dissipation, the bubble size saturates at a constant value. On the other hand, the continuous-wave laser has been recently applied for a plasmonic (e.g., gold) nanoparticle heating (maximizing the heat generation with a relatively lower energy input without changing the property of a liquid), by which a micro-bubble is generated quite effectively. 23–27 These studies also reported that the physics behind a bubble formation could be analyzed more clearly with a continuous-wave laser focusing. As briefly introduced, many studies on the laser-induced cavitation bubble have been performed toward various practical applications, whether a pulsed or continuous-wave laser is used, and a substantial progress has been achieved. However, in the viewpoint of fundamental issue, the mechanism of formation and growth of laser-induced bubbles is not completely understood so far. This is related to the contributions of vapor (from phase change) and dissolved air (in the surrounding liquid) to the bubble growth. Zhang et al. 21 explained that the vaporization is dominant during the start-up, growth and saturation of the bubble. Baffou et al. 23 measured that a micro-bubble can last for several hundreds seconds and attributed it to the transport of dissolved air in the liquid. Very recently, Wang et al. 26 has suggested a quite convincing mechanism based on the experimental investigation on

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the growth of a micro-bubble above water-immersed Au plasmonic nanoparticle heated by a continuous-wave laser. They classified the increase of bubble size into two regimes of nucleation and growth phases where the contribution of vaporization and dissolved air is dominant, respectively. This was supported by the theoretical analysis such that the bubble radius (R) scales with time (t) as R ∼ t1/6 when the phase change governs the bubble growth and R ∼ t1/3 if the transfer of dissolved air is dominant, respectively. Considering the possible applications of laser-induced cavitation, however, previous studies have focused on the generation of micro- and/or nano-bubbles and their growth dynamics in a very short time duration of O(< 1) seconds. Thus, it is not clear whether the mechanisms suggested by previous studies hold for the generation and growth of a large (millimeter-scale) bubble, induced by a continuous-wave laser during a longer period of time. Also it is unknown how the bubble growth would change depending on the incident laser power. Therefore, in the present study, we experimentally measure the temporal evolution of a bubble resulting from focusing a continuous-wave laser on a steel plate in tap water, while varying the incident laser energy. Unlike the previous studies, we do not restrict the position or size of the bubble, and thus it is expected that we can obtain more general understanding on the growth dynamics of a continuous-wave laser induced bubble. In particular, we are interested in establishing the scaling relation between the bubble size and time, depending on the focused laser energy, which will be related to the driving force in bubble evolution. To support this, we also measure (visualize) the water temperature (fluid) near the growing bubble on the solid wall, which has not been performed in previous studies.

EXPERIMENTAL SETUP AND PROCEDURES Figure 1a shows the schematic diagram of the present experimental setup. As shown, a metallic (stainless steel, SUS304) plate (100 × 200 × 5 mm3 ) on which a laser-induced bubble would be produced is located vertically in the center of an acrylic tank (200×200×200 mm3 ).

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The tank is filled with tap water and no treatment has been done to remove the ions and dissolved gas, and we believe that the water would reach an air-equilibrated state because it has been left open to the ambient air more than one hour before each experiment. 24,26 We considered that tap water is closer to some practical applications such as industrial cleaning process and wastewater treatment. For example, the utilization of bubbles in water containing ions or gas is found in degradation of organic pollutants, water disinfection, cleaning and de-fouling of solid surfaces, 28 and the present results would be extended to these conditions. We focus a laser beam in the visible range (wavelength of 532 nm), generated with a continuous-wave laser (RayPower 5000, Dantec Dynamics) having the maximum power of 5 W, onto a stainless steel plate. For the considered wavelength of laser, the absorption coefficient of water is O(10−2 ) m−1 and the transmission rate of an acrylic plate (i.e., of tank wall) is above 90%. To concentrate the laser beam directly onto a small area on the plate, a plano-convex lens (diameter of 75 mm and focal length of f = 150 mm) is used. To vary the incident laser energy and examine its effect, the laser output power (Jf ) is controlled from 60 mW to 5 W, which is measured directly using a power meter (PM100D, Thorlabs) that utilizes a thermal power sensor (S425C, Thorlabs). The corresponding power density ranges from 5 × 103 to 4 × 105 W/cm2 (the spot diameter of a focused laser on the target is measured to be about 40 µm). On the other hand, to improve the absorption and emissivity of the focused laser, the stainless steel plate is coated with a jet-black paint (HiE-Coat 840CM, Aremco Products Inc.). The surface morphology has been measured with SEM before and after the paint coating, and it is found that the mean roughness (Ra ) is 4.0 µm and 6.5 µm, respectively, indicating that the coating itself does not affect the surface roughness. The surface has been examined after the laser focusing (bubble generation), and a dimple produced by damages has diameter of about 600 µm, as can be seen in figure 1b. Thus, after each set of experiment, we replace the plate with new one while keeping other conditions. Before the laser focusing, the water temperature is maintained at a room temperature, and we give a break (longer than 20 minutes) between each experiment, which is enough to

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recover the same initial temperature. To avoid the possible interference from the ablated matter, we also replace the tap water frequently. light diffuser

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steel plate light source

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Figure 1: (a) Experimental setup for bubble generation by focusing CW laser. A steel plate is placed in the middle of water tank, and a laser beam is focused on the plate. A plano-convex lens is used to make the laser beam diameter as small as possible. A bubble is generated at the focal point. (b) SEM image of damaged surface due to the laser ablation. (c) The result of image process to track the bubble surface. To further confirm the mechanism of bubble evolution with time and incident laser power, we additionally perform the experiments with different liquids. While keeping other conditions exactly same, we consider degassed water and NaCl solution as a working liquid. Degassed water is prepared by putting the whole tank with tap water in a vacuum chamber (gauge pressure is about −0.09 MPa) for over 48 hours. NaCl solution is made by adding sodium chloride (180 g) to distilled water (1.8% NaCl solution). The results are shown in figure 10. The generation and evolution of a bubble is captured with a high-speed camera (SpeedSense M310, Dantec Dynamics) at the rate of 100 fps (384 × 600 pixels) for maximum 180 seconds (to the instant when the bubble grows large enough to be detached from the surface and rises up due to the buoyancy) from the moment when the laser is turned on. The red-colored (wavelength of 675 nm) plane LED light is placed in the opposite side of the camera as a light source to produce the shadow images of a bubble. The camera is fitted with 7


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a 180 mm lens and orange filter (cut-off wavelength of 570 nm), to minimize the influence of the reflected laser on the optical measurement. Once the raw images for the evolving bubble are obtained, they are first binarized 29 to distinguish the area corresponding to the bubble whose equivalent radius, R, is calculated by assuming it as a circle (figure 1c). Indeed, we confirmed that the measured bubble shape does not deviate much from the spherical one (within 1%). With the current setup, the spatial resolution is 0.02 mm/pixel, so the bubble can be reliably measured when its radius is greater than 0.05 mm. Since the experiments are conducted in tap water without special treatment for purification, the repeatability of experiment might be slightly affected by the condition of water. Therefore, for each condition, more than 10 independent measurements are performed and averaged to obtain fully converged data for the bubble size. The uncertainty ranges (i.e., error bars) in the scattered plots shown below are determined in terms of the standard deviations. To support the analysis of bubble evolution, on the other hand, we additionally measure the water temperature and visualize the water flow around a growing bubble. First, a thermocouple (80pk-22, Fluke) is positioned as close as possible to the bubble to measure the temperature near the spot where the photons are concentrated, and the water temperature near the bubble surface is measured without interfering with the bubble growth. Second, we introduce Rhodamine-B particles into the water during the bubble formation, to visualize the surrounding water flow. Here, the quantitative evaluation of the velocity distributions (i.e., particle image velocimetry measurement) does not provide an accurate data due to the highly agitated particle images by the incident laser. Instead, we obtain the pathlines of the induced water flow by overlapping 50 instantaneous images (corresponding to the duration of 0.5 second), which has been used to visualize biological flows. 30

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Figure 2: Instantaneous bubble images generated by the CW laser with Jf of (a) 60 mW; (b) 260 mW; (c) 560 mW; (d) 4.8 W. Numbers in each figure denote the time (t) passed in seconds after the bubble generation is captured.

RESULTS AND DISCUSSIONS Global Picture of Bubble Growth Figure 2 shows the representative sequential images of evolving bubble with varying incident energy (Jf ) at the focal point. Here, the time t = 0 is designated as the instant when the bubble diameter exceeds 50 µm, that is when the bubble is distinguishable with the current setup. It is observed that the bubble shows up right after the photons are focused on the surface and the growth rate of cavitation bubble shows a different trend depending on Jf . When Jf is low, the bubble grows explosively initially (t < 3.0) but saturates early and then shrinks slowly even though the laser is still focused (figure 2a). As the incident energy increases, the bubble continues growing without shrinking, but the increase rate changes with Jf (figures 2b-d). For the high Jf ’s considered, the speed of bubble expansion at the initial stage is quite fast but becomes mild at later times (figures 2c, d), while the bubble size does not show a substantial change with time for the intermediate Jf (figure 2b). To quantify this observation in more detail, we plotted the temporal variation of equiv-

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t (s) Figure 3: Temporal variation of bubble radius (R) with Jf : ◦, 60 mW; , 120 mW; ♦, 260 mW; H, 560 mW; •, 960 mW; , 1.51 W; , 1.72 W; N, 2.30 W; H, 2.80 W; •, 3.21 W; , 3.75 W; , 4.28 W; N, 4.83 W. alent bubble radius (R) for all considered Jf ’s in figure 3. From the time-history of bubble radius, we can classify the energy dependency of bubble growth in time. Irrespective of the incident energy, the bubble size increases very fast at earlier times (i.e., t < 10), but the difference between Jf ’s shows up after the initial explosive growth is mitigated. Thus, in terms of the time duration passed after the focusing, we define two stages as the first (t . 10) and second (t & 10) stages, respectively. It is also possible to classify three regimes depending on the laser power (Jf ): in regime I (Jf ' 60 − 260 mW), the bubble tends to shrink at the second stage while it increases gradually in regime III (Jf & 960 mW). At the intermediate Jf ' 260 − 960 mW (regime II), the growing rate at the second stage is between those of regimes I and III. For each regime and stage, there are different driving forces to determine the growth behavior of a bubble, as discussed in the below.

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Figure 4: (a) The bubble growth at the first stage (t . 10): ◦, 60 mW; , 120 mW; ♦, 260 mW; H, 560 mW; •, 960 mW; N, 4.83 W. (b) Working mechanisms for lower and higher Jf ’s during the bubble generation at the first stage.

Bubble Growth at the First Stage: Phase Change of Water and Dissolved Gas We start with the first stage where the initial growth rates are quite fast for all three regimes. As shown in figure 4a, bubbles in the regime III grows slower than those in the regime I despite the higher energy input. This is because the dissolved gas in water moves through the bubble interface and interrupts the absorption of water vapor, when the laser power is high enough (regime III), as illustrated in figure 4b. In contrast, when the power is low (regime I), the temperature near the focal point rapidly increases in a short time, which results in the bubble generation due to the phase change of water. However, the increased temperature is not high enough and the volume of heated water is not larger than that of regime III, so the influence of the dissolved gas is small. With an increased laser energy, the surrounding water is also heated enough and the effect of dissolved gas becomes non-negligible; the gas particles populate below the bubble surface, preventing the transfer of water vapor into the bubble, so the growth rate of the bubble in regime III is slower than the lower Jf cases. In figure 4a, it is also interesting to see that the bubbles in regime II (e.g., Jf = 560 mW) become larger (at t > 6.0 at the first stage) than that of regime III (Jf = 960 mW). As we 11


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have classified, this range of power is thought to be transient such that both contributions of phase change of water and dissolved gas affect similarly to the bubble growth. Thus, the influx of gas into the bubble interface is less dominant than the regime III. For the same reason, the bubble radius for the case of Jf = 4.83 W (largest among considered) initially increases slower than those in the regime I (Jf = 60 − 260 mW). It is understood that the phase change of water is the major driving force for the bubble evolution in the regime I (lower power), which transitions to the dissolved gas in the regime III (higher power). At the intermediate power (regime II), both the phase change and dissolved gas contribute to the bubble growth. 0.4 0.3

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0.1 0.09 0.08 0.07 0.06 0.05 0.1

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Figure 5: The bubble growth in the regime I (◦, 60 mW; , 120 mW; ♦, 260 mW) at the first stage. The data are plotted on a logarithmic scale and the solid lines denote the curve-fitted predictions with equation 2, shown to confirm the validity of the scaling relation with time (t). Let us provide a closer look at the first stage of regime I (figure 5), where the bubble is thought to grow initially due to the phase change of water. This is supported by evaluating the Prandtl number (P r = ν/α; ν: kinematic viscosity, α: thermal diffusivity) that denotes whether the conduction or convection is dominant. For a water vapor at around 100 ◦ C, P r is calculated to be ∼ 0.01 (< 1.0), and this indicates that the conduction (thermal diffusion) is dominant. It is known that the vapor bubble (due to phase change) grows under two 12


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steps; inertia controlled (much more explosive) and thermal diffusion controlled ones. 31–33 Typically, the inertia controlled stage lasts only O(1) msec and the corresponding bubble size is O(10) µm. 31 Thus, we think that the present bubble captured at the first stage belongs to the thermal diffusion controlled condition, because the temporal and spatial resolutions of present study are not sufficient to capture the bubble initiation at the inertia-controlled stage. At the interface of a thermally growing bubble, on the other hand, the change of latent heat contained in the bubble is balanced by the heat flux at the bubble surface, which is expressed as below. 33

Lρv

d 4 3 πR = 4πR2 qr . dt 3

(1)

Here, L is the latent heat of water, ρv is the saturated vapor density at the saturation temperature (Tsat ) and qr is the heat flux at the bubble surface. If we assume that there is a thin thermal boundary layer on the bubble surface, the solution of Plesset & Zwick 34 can p be used and the bubble radius is obtained as R(t) = 2Ja 3Dl t/π, where the Jakob number Ja = ρl cpl |T∞ −Tsat |/(ρv L) denotes the ratio between the available heat in the liquid and the latent heat required for phase change (ρl : liquid density, cpl : liquid specific heat at constant pressure, T∞ : ambient temperature), and Dl is the liquid thermal diffusivity. Although it is difficult to obtain the temperature accurately, this result shows that the bubble size scales as R(t) ∼ t1/2 . Baltis & van der Geld 35 has also shown that the following approximation (equation 2) applies to the bubble growing on a heated wall.

R(t) = C1

p

t + C2 .

(2)

The constants C1 and C2 are empirically determined, and C2 can be ignored by assuming that the bubble is initiated from the thermal-controlled condition. In figure 5, it is shown that the present bubbles in the regime I tend to grow at the first stage with the time dependency of t1/2 , confirming that the major driving force of bubble growth is the phase change of water

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(thermal effect). It is also noted that the empirical constant C1 is an increasing function of Jf ; C1 increases from 0.17 to 0.21 as Jf increases from 60 mW to 260 mW. Next, we discuss the first stage of regimes II and III, in which the initial bubble growth rate is different from that of regime I (figure 4a). First, we hypothesized that this is because the main factor of bubble growth changes to the dissolved gas as the incident laser energy increases. Previously, Liu et al. 24 conducted an experiment to generate a bubble with a continuous-wave laser in water with and without dissolved gas. It is found that the timedependency of the bubble growth with dissolved gas condition is similar to the present results corresponding to the regime III. Here, the Schmidt number (Sc = ν/D, D: mass diffusivity), denoting the relative thickness of the hydrodynamic layer (momentum transfer) and masstransfer boundary layer is useful. That is, with the typical numbers of the regime III, Sc is estimated to be 0.002 (< 1.0), indicating that the diffusion of gas dominates the bubble evolution. As the incident energy becomes larger, on the other hand, it is also expected that a reaction due to the solid surface ablation occurs vigorously, involving the interaction between ions, atom clusters, particles, and a supercritical vapor in the liquid phase on the bubble surface. 9 Since no treatment has been applied to the present tap water, the increased water temperature (in regime III) is more likely to encourage the bubble growth through the reactions with ions and dissolved gas. Considering the reported range of environment for water splitting, 36 it may also occur from the present laser ablation. Although it is not feasible to distinguish with the present setup, the bubble growth through the reactions in the regime III would involve the influence of molecular hydrogen and oxygen formed from the water splitting. During this kind of reaction process occurring at the bubble surface, the number of moles of gas inside the bubble is balanced by the molar concentration of gas in the surrounding liquid. The molar flux to the bubble by reaction is defined as: 37,38 ∂c 1 dn =D , 4πR2 dt ∂r r=R

(3)

where c is the molar concentration of gas in the liquid, n is the number of moles of gas 14


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inside the bubble, and D is the diffusion coefficient of gas. Assuming the ideal gas condition, the state equation Pb V = nRg T is used (Pb : pressure inside the bubble, assumed to be constant, V : bubble volume, Rg : gas constant), and the left-hand side of equation 3 is expressed as (dn/dt)/(4πR2 ) = (dR/dt) · (Pb /(Rg T )). Here, pb is assumed to be constant considering that the change in bubble size does not affect the pressure balance across the bubble surface significantly, which has been adopted in elsewhere. 37,38 According to Cussler 39 and Fu & Pan, 38 right-hand side of equation 3 is further simplified as D(∂c/∂r) r=R = ks cs = km (c∞ − cs ), where ks is the first-order reaction rate, km is averaged mass-transfer coefficient from the liquid to the bubble interface, and cs is the molar concentration of the species at the bubble surface. Then, equation 3 becomes dR/dt = ((Rg T )/Pb ) · (ks c∞ D)/(D + ks R), by considering that the molar concentration under the steady assumption is expressed as cs = Dc∞ /(D + ks R). 37 With a proper initial condition for the bubble radius (R◦ ), it is integrated to express the radius of bubble growing mostly from the reaction at the interface, as a function of time: 37,38 0.5 0.4 0.3

R (mm)

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Figure 6: The bubble growth in the regime II (H, 560 mW) and regime III (•, 960 mW; H, 2.80 W; N, 4.83 W) at the first stage. The data are plotted on a logarithmic scale, and the solid lines denote the curve-fitted predictions with simplified equation 4, shown to confirm the validity of the scaling relation with time (t).

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D R(t) = − + ks

r

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D 2 2Rg T c∞ D t. + ks Pb

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As can be seen, this can be simplified as R(t) = C3 + (C4 + C5 t)1/2 . Here, three constants of C3 = −D/ks , C4 = (R◦ + D/ks )2 , and C5 = 2Rg T c∞ D/Pb contain the property of gas and liquid phases, and are thus empirically determined. In figure 6, we have shown that this relation fits quite well with the measured bubble radius in regimes II and III, indicating that the initial growth of bubble at these regimes are boosted by the reaction of dissolved gas in water. Among the empirical constants, C5 is an increasing function of incident energy (ranges from 0.0055 to 0.02 with increasing Jf ).

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Figure 7: (a) In the regime I (60 − 260 mW), the volume of heated water decreases after the bubble generation because the bubble blocks the heat absorption of a surrounding water, and the convection flow started from bubble formation causes a bubble shrinkage. (b) The bubble shrinkage in the regime I (◦, 60 mW; , 120 mW; ♦, 260 mW) at the second stage. Here, the solid lines denote the curve-fitted predictions with equation 8, shown to confirm the validity of the scaling relation with time (t). After the explosive growth of a bubble at the first stage (t . 10), the growth rate of bubble changes drastically depending on the regimes. For the regime I, the growing bubbles 16


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start to shrink down at t = t◦ ' 7.0 − 9.0 (this occurs earlier with increasing Jf ) (figure 3). As the bubble grows, it tends to prevent the direct focus of laser onto the surface (i.e., the volume of heated water decreases) and thus it retards the phase change of surrounding water (figure 7a). As the heat absorbed by the bubble decreases, it is expected that the water flow induced by the convection, which started from the bubble creation, would be responsible for the condensation into the liquid phase (i.e., phase change). Using the quasi-steady potential flow solution for a uniform flow around a sphere, the heat transfer (i.e., Nusselt number) to the bubble (with a phase change occurring at the interface) can be reasonably approximated as: 40,41

Nu =

h(2R) 4 1/2 2RUr 1/2 = , k π α

(5)

where h is the convective heat transfer coefficient, Ur is relative velocity between vapor and liquid, and α is the thermal diffusivity. Recently, Setoura et al. 25 has investigated the convection flow of liquid phase around a growing cavitation bubble induced on Au nanoparticles heated by a continuous-wave laser. They showed that the convection flow velocity gradually increases with increasing the bubble diameter. From their data, we have further found that the induced flow velocity scales as Ur ∼ (gR)1/2 . While the equation 1 should hold for the surface of thermally collapsing bubble, as well, the heat transfer is expressed as qr = h∆T and it becomes √ k 2R gR 1/2 dR = −∆T √ . Lρv dt α R π

(6)

This can be further integrated with an initial condition (R◦ ), and we obtain the expression for the bubble radius as:

R(t) =

R◦5/4

√ 5 ∆T · k 2 g 0.5 4/5 √ − t . 4 Lρv π α

(7)

In this formulation, including the property of gas and liquid phases, the temperature differ17


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ence (∆T ) across the bubble interface needs to be measured, which is quite difficult to be achieved with a higher accuracy. The equation 7 can be written as: h i4/5 R(t) = R◦5/4 − C6 t − t◦ .

(8)

Here, the empirical constant C6 is a decreasing function of Jf ; that is, as the incident energy increases, the decaying rate of bubble size decreases. In figure 7b, it is shown that the time-dependency of decaying bubble in the regime I is estimated quite well with equation 8, indicating that the phase change (condensation) at the bubble interface is the main driving force here. While the cases of Jf = 60 and 120 mW are well matched with our analysis, the case of Jf = 260 mW shows a relatively larger deviation as time progresses. This indicates that the dissolved gas in water becomes influential at this Jf . When dissolved gas moves into the bubble in a sub-cooled condition, the bubble first shrinks as the vapor near the bubble surface condenses. As a result, only gas component is left on the bubble surface, which prevents the condensation of additional vapor inside the bubble. 33 Although this gas component can diffuse to ambient water, its diffusion time scale is much slower compared to that of condensation. Therefore, the case of Jf = 260 mW is not completely explained by the condensation only and the decaying rate of bubble size is slower than the cases with lower Jf . Now, let’s move to the second stage of the regime III (and II). As explained above, at this regime, the bubble continues growing (without shrinking) but with a growth rate slower than that of the first stage (figure 3). To understand the detailed phenomenon at this condition, we have additionally measured the water temperature near the focal point and visualized the water flow around the bubble during its growth, for the case of Jf = 2.80 W (figure 8a). Interestingly, it is noted that the change rate of temperature varies according to the stages that were classified depending on the change in bubble radius; that is, the temperature rises sharply at t . 10 (first stage), and then gradually to be saturated at t & 10 (second stage). Since the temperature becomes relatively constant at the second stage, it is expected that 18


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Figure 8: (a) The water temperature near the growing bubble for Jf = 2.80 W. The insert images represent the pathlines of the surrounding flow field at the same instants. Pathlines are obtained by the method of Gilpin et al., 30 and each pathline is the motion of the particles for 0.5 second. The numbers in images indicate the time (s) from the bubble generation to the initiating time of the pathlines. (b) Comparison of temporal variation of the water temperature: ♦, Jf = 260 mW (regime I), H, 560 mW (regime II), and •, 3.21 W (regime III). the influx of gas into the bubble should be less than the first stage. In figure 8b, we have also compared the temporal variations of water temperature measured for Jf = 260 mW (regime I), 560 mW (regime II), and 3.21 W (regime III). As shown, the temperature rise in the regime III is much higher than the other regimes. For the regime I, the water temperature tends to decrease slightly at the second stage, supporting our explanation of bubble shrinkage due to the condensation, and temperature variation in the regime II shows a slow increase with time. Along the temporal change in the temperature, the corresponding pathlines of water flow induced by the growing bubble are shown together in figure 8a. At the first stage, the convection flow around the rapidly growing bubble shows up as a swirling pattern around it, which tends to disappear and is stabilized at the second stage. Setoura et al. 25 reported a similar convection flow around a micro-sized cavitation bubble induced by a continuouswave laser. They also explained that the outward velocity component of the convection flow saturates as the bubble size becomes larger than a critical value and the temperature difference across the bubble surface is maintained. As the bubble grows further in the second

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stage (e.g., t = 47.2 in the figure 8), on the other hand, water flow is locally attracted toward the bubble surface (indicated with a thick arrow) due to the bubble oscillation. In the second stage of regime III, the bubble oscillation can be seen when its radius exceeds a critical value. This seems to be an interaction between the laser beam and the bubble surface, which needs to be investigated in the future. Based on the changes in the temperature and liquid flow around a growing bubble, it is deduced that the amount of gas flux into the bubble would be constant at the second stage of regime III. Baltis & van der Geld 35 explained that the main mechanism of bubble growth on a heated wall in a saturated liquid flow is the heat absorption by the surrounding water rather than the direct heat transfer from the wall. In the present regime III, it is found that the dissolved gas in surrounding water heated by the incident laser comes into the bubble and makes the bubble growth, and the generation rate of gas product into the bubble is constant. Previously, Fu & Pan 38 defined this constant ratio (ng ) as ng = dn/dt, where n is the moles of gas product within the bubble. Considering that the pressure difference across the bubble interface (i.e., between the gas (Pb ) and liquid (Pl ) pressures) is governed by the Young-Laplace equation as Pb − Pl = 2σ/R, and assuming the ideal gas condition (Pb V = nRg T ), it is possible to drive the equation 9:

ng Rg T 4 dR = . Pl R2 + σR 3 dt 4π

(9)

By integrating this with an initial condition (R◦ ), we obtain the equation for R(t) as:

3

R(t) −

R◦3

3R T 2σ g 2 2 + R(t) − R◦ = ng t. Pl 4πPl

(10)

This equation can be rewritten as R(t) = [−4σ/Pl + 24/3 (4σ 2 /Pl2 )F (t)−1 + 22/3 F (t)]/6 where F (t) = [C7 +27C8 t+[−256σ 6 /Pl6 +(C7 +27C8 t)2 ]1/2 ]1/3 , C7 = −16σ 3 /Pl3 +27(2σR◦2 /Pl +R◦3 ), and C8 = 3ng Rg T /(4πPl ). 38 By comparing the order of magnitude, this is approximated as F (t) ' 21/3 (C7 + 27C8 t)1/3 and the bubble radius is expressed as:

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R(t) ' C8 t1/3 .

(11)

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Figure 9: The bubble growth in the regime II (H, 560 mW) and regime III (•, 960 mW; H, 2.80 W; N, 4.83 W) at the second stage. The data are plotted on a logarithmic scale, and the solid lines denote the curve-fitted predictions with equation 11, shown to confirm the validity of the scaling relation with time (t). In figure 9, we have shown that the temporal variation of bubble radius at the second stage of the regime III is scaled with time as t1/3 , indicating that the main mechanism in this regime is the constant transfer rate of dissolved gas into the bubble. The empirical constant (C8 ) increases from 0.03 to 0.15 as the incident energy increases. On the other hand, the case of Jf = 560 mW (regime II) is not completely fitted with the scaling relation of t1/3 . As we have mentioned above, this energy level belongs to the transition between regimes I and III, and the phase change of water also affects the bubble growth in addition to the dissolve gas. In summary, the bubble growth in the regime III is mainly related to the transfer of dissolved gas in surrounding water, but its temporal rate is initially proportional to t1/2 at the first stage and is reduced to t1/3 at the second stage. To further confirm the suggested mechanism of bubble evolution, the temporal change of bubble size in degassed water and 1.8% NaCl solution is measured and compared with result of tap water (figure 10). In the regime I (Jf = 260 mW), the bubble in degassed water grows 21


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Figure 10: The bubble growth in different liquids at the (a) first and (b) second stages. With degassed water: •, Jf = 260 mW; , 2.80 W and with 1.8% NaCl solution: , Jf = 260 mW; N, 2.80 W. For the comparison, the data with tap water (♦, Jf = 260 mW; O, 2.80 W) are shown together. Solid lines denote the curve-fitted predictions with equation 2 in (a) and equation 8 in (b) for the case of degassed water. Dashed lines denote the curvefitted predictions with equation 4 in (a) and equation 11 in (b) for the case of NaCl solution, shown to confirm the validity of the scaling relation with time (t). The data are plotted on a logarithmic scale. similar to the case of tap water at the first stage (t < 10) (figure 10a), and shrinks due to the condensation later (figure 10b). Because the dissolved gas was removed significantly, the bubble in degassed water shrinks more than that in tap water. With Jf = 2.8 W (regime III), on the other hand, the bubble in degassed water grows much faster than the case of tap water at the first stage. This implies that water vaporization occurs more vigorously in degassed water and the effect of dissolved gas (interruption of the water vapor absorption) is mitigated. At the second stage, the bubble in degassed water shrinks, which is opposite to the case of tap water, in which the bubble constantly grows due to the influence of dissolved gas. Moreover, it is found that the temporal bubble growth in degassed water is also predicted with scaling relations of R ∼ t1/2 and R ∼ −t4/5 for the first and second stages, respectively, confirming that the phase change of water dominates in the case of degassed water, while the dissolved gas becomes influential in the case of tap water (regime III). It is noted that the critical time to classify the first and second stages may change depending on the type of

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liquids. In NaCl solution, the bubble size at the first stage (with Jf = 260 mW) is small compared to other cases, indicating that the phase change of water is the main source of a bubble growth, rather than the dissolved gases or ions. In the regime III (Jf = 2.8 W), bubble growth at the first stage is faster than the tap water, but it becomes almost saturated at the second stage. As shown, the bubble growth at the first and second stages are well matched with the scaling relations of R ∼ t1/2 and R ∼ t1/3 , showing that the reaction with dissolved ions is the main driving force of a bubble growth in this liquid.

Departure of the Bubble from the Surface In the present study, the bubble growth is measured relatively for a long time, and in some conditions the bubble detaches from the surface and rises up due to the imbalance between surface tension and buoyancy. When it does not, the bubble moves slightly upward (departs from the original focal point), re-attaches to the surface, and stays there, which is attributed to the hydrophobicity of the present plate surface. For all cases considered, we have tracked the radius (Rf ) and instant (tf ) when the bubble leaves the plate (figure 11). For the regime I, the bubbles stay on the plate during the measurement, but the departure from the wall occurs for the regime III. In the regime II, both behaviors appear. As shown in the figure, the bubble size at the instant of departure increases with increasing Jf and becomes almost constant at larger Jf ’s. Similarly, Oguz & Prosperetti 42 showed that the volume of bubble that pinches off the end of gas-injecting needle is proportional to the gas flow rate supplied, while the bubble detachment time decreases with increasing the gas flow rate. For the present cases, it is also found that the bubble detaches from the wall earlier as the incident energy increases. Previously, Zeng et al. 43 suggested that the size of detached bubble from boiling is proportional to time as a simple power law of R(t) ' K · tn (K: growth constant), but the maximum bubble size achievable on the vertical wall in the present setup is limited by the force imbalance. 23


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Figure 11: The bubble radius (Rf ) when it departs from the wall and the time (tf ) from the bubble generation to the moment of detachment in the regime II (H, 560 mW) and regime III (•, 960 mW; , 1.51 W; , 1.72 W; N, 2.30 W; H, 2.80 W; •, 3.21 W; , 3.75 W; , 4.28 W; N, 4.83 W). Since the surface tension may affect the dynamics of a growing bubble, we have measured the contact angle between the bubble and vertical wall (figure 12). Limited by the spatial resolution of present setup, it was possible to measure the contact angle of a bubble when its equivalent radius (R) is larger than 0.1 mm. For the range of Jf considered, we found that the contact angles at upper and lower sides remain almost constant with time (figure 12a). This is expected from the fact that the bubble shape does not deviate significantly from the sphere during the evolution (figure 2). On the other hand, the base radius (Rb ), which is the radius of the interface between the vertical wall and bubble, increases gradually with time. In figure 12b, we have plotted the variation of time-averaged contact angles on upper (θ¯u ) and lower (θ¯l ) sides in terms of Jf , and the base radius at the instant of bubble departure (Rb,f ) is shown together. It is found that the contact angles and Rb,f tend to increase and become saturated as Jf increases in the regime III. This agrees with trend of bubble detachment time and size (figure 11).

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Figure 12: (a) Temporal variations of contact angles at the upper (◦, θu ) and lower (•, θl ) sides and base radius (H, Rb ) for the growing bubble in the regime III (Jf = 2.80 W). (b) Variation of time-averaged contact angles at upper (θ¯u , ) and lower (θ¯l , ) sides and the base radius at bubble departure (N, Rb,f ) with Jf .

CONCLUDING REMARKS In the present study, we have investigated the mechanism of laser-induced cavitation bubble evolution on a metallic surface in tap water. Unlike the previous studies that focused on the explosive growth and shrinkage of very small bubble with a pulsed laser, we use a continuous-wave laser to observe the behavior of a millimeter-sized bubble for longer time duration. We identified that the mechanism of bubble evolution (growth or shrinkage) is different depending on the incident energy. In the regime I (Jf = 60 − 260 mW), the surrounding water undergoes a phase change due to the focused laser, which generates a bubble in 2 − 3 seconds as R ∼ t1/2 . At later times, the convection flow is induced due to the locally heated surface, causing the bubble to shrink at the rate of R ∼ −t4/5 . As Jf increases to 960 mW−4.83 W (regime III), the temperature of surrounding water becomes much higher than that of regime I, so the dissolved gas is more likely to enter the growing bubble. When the gas component locates inside the bubble surface, it prevents the water phase from being absorbed into the bubble, so the bubble growth is dominated by dissolved gas rather than phase change of water. Therefore the bubble grows for a relatively longer time about 10 seconds as R ∼ t1/2 . After this stage, the temperature of surrounding water 25


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saturates with time and dissolved gas also comes into bubble at a constant rate, which results in the increase of bubble size further at the rate of R ∼ t1/3 . Between regimes I and III, there is a transitional regime II (Jf = 260 − 960 mW) in which both the phase change of water and dissolved gas contribute to the bubble evolution. These mechanisms of bubble evolution (and corresponding scaling relations with time) was further validated with different liquids, i.e., degassed water and NaCl solution. As the bubble size exceeds the limit imposed by the balance between adhesion force and buoyancy, the bubble detaches from the wall in the regimes II and III (in regime I, no departure was observed). As Jf increases, the departure time tends to decrease but the critical bubble size saturates at a constant value. For the best of our knowledge, this is the first experimental approach to measure the evolution of a millimeter-sized bubble for longer time duration, and identify its mechanism. We believe that the present results are useful to design a laser-induced cavitation system for various purposes.

Acknowledgement The authors thank the financial supports from the NRF (National Research Foundation) Programs (2016R1C1B2012775, 2017R1A4A1015523, 2016M2B2A9A02945068), funded by the Korea government (MSIP) via SNU-IAMD, and also the Institute of Engineering Research and Entrepreneurship at Seoul National University supported this work.

References (1) Arndt, R. E. Cavitation in fluid machinery and hydraulic structures. Annu. Rev. Fluid Mech. 1981, 13, 273–326. (2) Arndt, R. E. Cavitation in vortical flows. Annu. Rev. Fluid Mech. 2002, 34, 143–175.

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(3) Blake, J. R.; Gibson, D. C. Cavitation bubbles near boundaries. Annu. Rev. Fluid Mech. 1987, 19, 99–123. (4) Truscott, T. T.; Epps, B. P.; Belden, J. Water entry of projectiles. Annu. Rev. Fluid Mech. 2014, 46, 355–378. (5) Kim, N.; Park, H. Water entry of rounded cylindrical bodies with different aspect ratios and surface conditions. J. Fluid Mech. 2019, 863, 757–788. (6) Chung, S. K.; Zhao, Y.; Cho, S. K. On-chip creation and elimination of microbubbles for a micro-object manipulator. J. Micromech. Microeng. 2008, 18, 095009. (7) Poulain, S.; Guenoun, G.; Gart, S.; Crowe, W.; Jung, S. Particle motion induced by bubble cavitation. Phys. Rev. Lett. 2015, 114, 214501. (8) Shirota, M.; Sanada, T.; Sato, A.; Watanabe, M. Formation of a submillimeter bubble from an orifice using pulsed acoustic pressure waves in gas phase. Phys. Fluids 2008, 20, 043301. (9) Zhang, D.; Gökce, B.; Barcikowski, S. Laser synthesis and processing of colloids: fundamentals and applications. Chem. Rev. 2017, 117, 3990–4103. (10) Do, H.; Carter, C. Hydrocarbon fuel concentration measurement in reacting flows using short-gated emission spectra of laser induced plasma. Combust. Flame 2013, 160, 601– 609. (11) Vogel, A.; Lauterborni, W.; Timmi, R. Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary. J. Fluid Mech. 1989, 206, 299–338. (12) Lam, J.; Lombard, J.; Dujardin, C.; Ledoux, G.; Merabia, S.; Amans, D. Dynamical study of bubble expansion following laser ablation in liquids. Appl. Phys. Lett. 2016, 108, 074104. 27


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(13) Rayleigh, L. On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 1917, 34, 94–98. (14) Plesset, M. S. The dynamics of cavitation bubbles. ASME J. Appl. Mech. 1949, 16, 228–231. (15) Gilmore, F. R. The collapse and growth of a spherical bubble in a viscous compressible liquid. Calif. Inst. of Tech. Hydrodynamics Lab. Rep. 1952, 1–40. (16) Philipp, A.; Lauterborn, W. Cavitation erosion by single laser-produced bubbles. J. Fluid Mech. 1998, 361, 75–116. (17) Kabashin, A. V.; Meunier, M. Synthesis of colloidal nanoparticles during femtosecond laser ablation of gold in water. J. Appl. Phys. 2003, 94, 7941–7943. (18) Ohl, C. D.; Arora, M.; Dijkink, R.; Janve, V.; Lohse, D. Surface cleaning from laserinduced cavitation bubbles. Appl. Phys. Lett. 2006, 89, 074102. (19) Koukouvinis, P.; Strotos, G.; Zeng, Q.; Gonzalez-Avila, S. R.; Theodorakakos, A.; Gavaises, M.; Ohl, C.-D. Parametric investigations of the induced shear stress by a laser-generated bubble. Langmuir 2018, 34, 6428–6442. (20) Taylor, R. A.; Phelan, P. E.; Otanicar, T.; Adrian, R. J.; Prasher, R. S. Vapor generation in a nanoparticle liquid suspension using a focused, continuous laser. Appl. Phys. Lett. 2009, 95, 161907. (21) Zhang, K.; Jian, A.; Zhang, X.; Wang, Y.; Lib, Z.; Tam, H.-Y. Laser-induced thermal bubbles for microfluidic applications. Lab Chip 2011, 11, 1389–1395. (22) Zheng, Y. Z.; Wang, Y.; Liu, H.; Zhu, C.; Wang, S. M.; Cao, J. X.; Zhu, S. N. Size control of vapor bubbles on a silver film by a tuned CW laser. AIP Adv. 2012, 2, 022155.

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Graphical TOC Entry 1.0

R ~ t1/3

R ~ -t4/5

Regime I (Jf = 60-260 mW) R (mm)

Regime III (Jf = 960 mW-4.83 W)

Regime II (Jf = 260-960 mW)

R ~ t1/2 R ~ t1/2

0.1

first stage 0.1

1

second stage 10

100

t (s)

31


1000

Evolution of Cavitation Bubble in Tap Water by Continuous-Wave

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