The Pennsylvania State University. The Graduate School. College of Engineering CHARACTERIZING LASER INDUCED CAVITATION: EFFECTS OF AIR CONTENT,

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1 The Pennsylvania State University The Graduate School College of Engineering CHARACTERIZING LASER INDUCED CAVITATION: EFFECTS OF AIR CONTENT, BEAM ANGLE, AND LASER POWER A Thesis in Mechanical Engineering by Minna L. Ranjeva 2012 Minna L. Ranjeva Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2012

2 The thesis of Minna L. Ranjeva was reviewed and approved* by the following: Brian R. Elbing Associate Research Faculty Thesis Adviser Dan Haworth Professor of Mechanical Engineering PIC of MNE Graduate Programs Gary Settles Professor of Mechanical Engineering Karen A. Thole Professor of Mechanical Engineering Head of the Department of Mechanical Engineering *Signatures are on file in the Graduate School. ii

3 Abstract Laser-induced cavitation allows for cavitation bubbles to be systematically reproduced using a high power laser and focusing the laser beam to a point. This provides the opportunity to study the physics of the cavitation process under different circumstances in an experimental setting. Laser-induced cavitation has many applications. It has been used successfully to study cavitation near boundaries in an effort to understand the mechanisms of cavitation erosion. It has also found new applications in the world of medicine, as well as other areas. Previous work has largely focused on cavitation near a surface causing damage, but as new applications emerge, characterization of bubbles in a bulk fluid will be useful, permitting a high level of control over the bubble size, shape, and lifetime. With this in mind, laser-induced cavitation bubbles in a bulk fluid are characterized. The focusing angle of the lens, the air content of water, and the laser power are all varied to provide a comprehensive understanding of how these variables affect the bubbles development. Scaling for the bubble behavior is developed. iii

4 Table of Contents List of Tables.... vii List of Figures... viii 1 Introduction Background Physics General Laser-induced optical breakdown Plasma expansion and production of cavitation bubble Cavitation bubble growth and collapse Earlier work Recent attempts to characterize bubbles Newer applications of cavitation Laser cleaning Micro-pumps Lithotripsy Drug delivery Introduction summary Research Objectives Experimental Methods Test apparatus Water Tank Laser Optics Instrumentation Imaging setup Laser power Water dissolved gas content Test Matrix Measurement Uncertainty Camera Laser Lenses Pressure Air Content Experimental Results General trends and overview Repeatability Variation of bubble topology Bubble size Bubble size: sensitivity to beam angle iv

5 3.4.2 Bubble size: sensitivity to air content Bubble half-life Bubble half-life: sensitivity to beam angle Bubble half-life: sensitivity to air content Bubble diameter time history Scaling of Laser Induced Cavitation Scaling Comparison with non-spherical bubbles Vertical diameter Horizontal diameter Bubble half-life Behavior over time Error Propagation Limitations and future work Limitations Pulsed laser Equipment setup Assumptions in deriving scaling Future work Pressure Viscosity Particulate matter Air content Conclusions Appendix: Uncertainty Bibliography v

6 List of Tables Table 1 Distances between components in experimental set up in Figure Table 2 Lens specifications used to create bubbles Table 3 Average water-air content concentration (C) for each air content condition Table 4 standard deviation for air content concentration measurements Table 5 Measured quantities and their corresponding measurement uncertainty Table 6 Lowest laser pulse energy for which bubbles could be seen for each of the test conditions, E Table 7 Coefficients for second order polynomial best fit curves based on nondimensionalized lifetime profiles Table 8 Beam waist for lenses Table 9 Variables of interest used to derive scaling rules for spherical cavitation bubbles Table 10 Results of error propagation through calculations for nondimensional variables vi

7 List of Figures Figure 1 Experimental setup used to generate laser-induced cavitation bubbles. The laser beam is expanded and then focused through a lens. A camera was used to capture the cavitation bubbles. The dashed box in the side view represents the camera s nominal field-of-view Figure 2 This figure illustrates the relationship between beam divergence and angular spread. In this work, the convergence or focusing angle refers to the angular spread Figure 3 Snell s law applied to a ray path passing through air (n 1 =1.00), glass (n 2 =1.55) and water (n 3 =1.33). Increasing index of refraction bends the beam towards the axis perpendicular to the interface between the two mediums Figure 4 Energy per pulse as a function of attenuator setting for the laser used in the current study. The flash lamp was fixed at the maximum level Figure 5 Example of a bubble lifetime produced at relatively low laser power (7.3 mj per pulse) with the wide-angle lens configuration and intermediate air content level. Labelled data points correspond to labeled images at the top of the figure. In image A the bright white spot is produced from plasma generated by the focused laser beam, while the remaining images show the shadow produced from the backlighted bubble Figure 6 Example of a bubble lifetime produced at relatively high laser power (42 mj per pulse) with the wide-angle lens configuration and intermediate air content level. Labelled data points correspond to labeled images at the top of the figure. The growth, collapse and rebound of the bubble is apparent from the plot Figure 7 Comparison between low and high power bubble behavior. At lower pulse energies single, spherical bubbles are produced. At higher powers the bubble shape depends on the lens angle. The smaller angle lens produces one larger bubble formed from bubble coalesence. The wider angle lenses produce smaller, more elongated bubbles. In the figure SA, MA and WA refer to the small, medium and wide-angle lens configurations, respectively Figure 8 Comparing bubble diameter, there is reasonable agreement between data collected in different setups from different points in time. This indicates that comparing results between the two different setups is appropriate Figure 9 Narrow angle lens bubble patterns at high power (42 mj) in high air content water. Smaller bubbles formed along the path of the laser beam coalesce to form a single, larger, elliptical bubble Figure 10 Medium angle lens bubble patterns at high power (42 mj) in intermediate air content water. On the left is the bubble formation shortly after the laser pulse, on the right is the bubble formation at the time of maximum bubble diameter Figure 11 Wide-angle bubble patterns at high power. On the left hand side of (A), (B), and (C) is the bubble formation shortly after the laser pulse, and on the right hand side of (A), (B) or (C) are the bubble formations at the points of maximum bubble diameter. These images illustrate the variety of bubble patterns that can be formed Figure 12 Vertical bubble diameter as a function of laser energy per pulse for (A) low, (B) intermediate and (C) high air content conditions. The solid lines represent the best fit curves for each condition vii

8 Figure 13 Ratio of the horizontal to vertical bubble diameters plotted as a function of the laser pulse energy with (A) low, (B) intermediate and (C) high air content levels Figure 14 Vertical bubble diameter plotted versus the laser pulse energy for (a) narrow, (b) medium and (c) wide-angle lens configurations. Solid lines represent the best fit curves to the data Figure 15 Ratio of horizontal to vertical diameter plotted versus laser pulse energy for (a) narrow (b) medium and (c) wide beam angles Figure 16 Bubble half-life (time from laser pulse to achieve maximum bubble diameter) plotted versus the laser pulse energy with (a) low, (b) intermediate and (c) high or saturated air content levels Figure 17 Bubble half-life as a function of laser pulse energy with the (A) narrow, (B) medium and (C) wide-angle lens configuration Figure 18 Small angle, low air content lifetime curve Figure 19 Small angle, intermediate air content lifetime curve Figure 20 Small angle, saturated condition lifetime curve Figure 21 Medium angle lens, low air content lifetime curve Figure 22 Medium angle, intermediate air content lifetime curve Figure 23 Medium angle, saturated air content lifetime curve Figure 24 Wide-angle, low air content condition lifetime curve Figure 25 Wide-angle, intermediate air content lifetime curve Figure 26 Wide-angle, saturated lifetime curve Figure 27 Comparison of lifetime polynomial fit for each condition. SA/L stands for small angle, low air content. MA stands for medium angle, WA for wide-angle, I for intermediate air condition, H for high air content Figure 28 Single lifetime curve for nondimensionalized bubble diameter vs. time. This curve describes the bubble diameter s growth over time for t h 2. The different colors represent different laser energy ranges, while the shapes indicate the air content condition (squares are low air content, circles are intermediate, and triangles are the high air content condition) Figure 29 An illustration of the beam profile of a Gaussian beam near the focal point Figure 30 The scaled horizontal diameter (D h * ) is plotted versus the scaled vertical diameter (D v * ), holding Π 6 constant. This plot shows a linear relationship between Π 1 and Π 2 for the majority of bubbles. The outliers in this plot represent bubbles produced at high energies that do not maintain a spherical shape. These bubbles are indicated by open symbols and are not included when looking at the scaling relationships Figure 31 Relationship between t h */D v * and ΔE * shows a logarithmic relationship that appears to be only minimally affected by air content for spherical bubbles. The average ratio for each condition (lens, air content, laser power) is plotted Figure 32 Average th* versus Dv* for various ranges of ΔE*. The relationship appears to be linear Figure 33 The relationship between beam waist and E o appears to be linear Figure 34 Predicted D v * versus actual D v * when applying scaling to non-spherical bubbles. The solid line shows where the predicted and actual D v * values are equal. The scaling guidelines over predict the vertical diameter of the non-spherical bubbles viii

9 Figure 35 Predicted vertical diameter plotted against the actual vertical diameter when scaling relationships are applied to non-spherical bubbles. The black line indicates where the predicted and actual values are equal Figure 36 Predicted Dh* versus actual Dh* when applying scaling to non-spherical bubbles. The solid line shows where the predicted and actual Dh* values are equal. The horizontal bubble diameter appears to be predicted relatively well with the scaling relationships used here Figure 37 - Predicted horizontal diameter plotted against the actual horizontal diameter when scaling relationships are applied to non-spherical bubbles. The black line indicates where the predicted and actual values are equal Figure 38 Predicted t h * versus actual t h * when applying scaling to non-spherical bubbles. The solid line shows where the predicted and actual t h * values are equal. The scaling relationships used over predict the scaled half-life t h * for non-spherical bubbles Figure 39 Predicted half-life versus actual half-life for scaling relationships applied to nonspherical bubbles. The black line indicates where the predicted and actual values are equal Figure 40 Non-spherical bubble behavior over time. Each run represents the development of a single, non-spherical bubbles. The blue curve represents the curve in Figure 28, the generic lifetime curve obtained in chapter Figure 41 The ratio of horizontal to vertical diameter for non-spherical bubbles. This graph represents the average ratio of vertical to horizontal diameter for six non-spherical bubbles. This illustrates that non-spherical bubbles begin as more elliptical shapes and then become more spherical over time. It also shows the oscillation in size that nonspherical bubbles exhibit ix

10 1 Introduction 1.1 Background Cavitation is a phenomenon that occurs in nature when fluids develop areas of high speed or local pressure drops. These forces cause the rapid formation and then collapse of a cavity within a liquid, and this process is referred to as cavitation. Cavitation has traditionally been an area of interest in the scientific community due to its erosive effects on mechanical parts, such as propellers, and the fact that loud noise resulting from cavitation can cause an issue when vehicles desire to go undetected. Since people began to study cavitation for its erosive consequences, new techniques to both produce and record cavitation events have been developed. In the early stages of cavitation study, scientists had difficulty controlling the occurrence of cavitation events due to the statistical nature of this phenomenon in both space and time (Lauterborn & Bolle, 1975). Using a laser allows cavitation bubbles to be produced at a known location. Early research focused on cavitation events occurring near a boundary, since cavitation is well known for causing damage to propellers. More recently laser-induced cavitation has been used in a variety of medical applications such as lithroscopy (Kokaj et al., 2008). It is also being explored for use in other areas, for example laser cleaning of surfaces or micropump technologies (Song et al., 2004; Dijkink & Ohl, 2008). As more and more applications for laser-induced cavitation bubbles emerge, a greater understanding of how the environmental factors and controllable variables (such as laser power or beam angle) affect the growth and development of cavitation bubbles is needed. As much previous research has focused on the erosive consequences of cavitation bubble collapse, more information on bubble formation away from a boundary in an infinite medium, or how changes 1

11 in the properties of the fluids (such as air content or impurities) alter the size, shape, and lifetime of cavitation bubbles produced via laser could prove useful. With this in mind, this research focuses on the effects of laser power, water air content, and focusing lens angle. This information will be useful in controlling bubble production in various environments, and will provide particularly valuable knowledge as laser-induced cavitation bubbles are used in a variety of fields, including medicine. 1.2 Physics General Optical energy of the high-intensity laser pulse is converted into mechanical energy, allowing the formation and expansion of a plasma due to dielectric breakdown, propagation of a shock wave and growth of a cavitation bubble. The laser energy causes the temperature and pressure to increase at a point in space, producing plasma that expands rapidly. A cavitation bubble results, and when it reaches its maximum diameter it is nearly empty. Thus the cavitation bubble collapses due to the higher pressure outside its boundary. When the collapsing bubble reaches a given size it may rebound and the process repeats until there is insufficient energy for the bubble to rebound again. Bubble collapse in an infinite medium is symmetric, while bubble collapse near a boundary is asymmetrical. Near a rigid boundary a liquid jet develops that is directed towards the boundary, often causing damage. With a free surface as a boundary, the bubble migrates away from the boundary as it collapses (Gregoric, Petkovsek, & Mozina, 2007). Bubble dynamics near a surface have been of interest due to the erosive effects of cavitation, so the majority of research has focused on these conditions. 2

12 1.2.2 Laser-induced optical breakdown Laser-induced breakdown can work in two ways: laser-induced thermal breakdown and laser-induced optical breakdown. The first occurs due to continuous wave exposure or repetitively pulsed lasers at high power in materials that are opaque at the laser wavelength. The second mode, optical breakdown, occurs for short pulse durations between microseconds and femtoseconds. Optical breakdown will be the focus of this discussion, as the breakdown and resulting cavitation bubbles in this work are produced in water (transparent) with laser pulses in the nanosecond range. Optical breakdown produces plasma, or a gas of charged particles. Two mechanisms of breakdown exist, multiphoton absorption and cascade ionization. If a free electron already exists in the focal volume then photons from the laser pulse can be absorbed by the free electron, and this energy can be used to ionize a bound electron via a collision, resulting in two lower energy free electrons. This process repeats and leads to a cascade that results in breakdown and the formation of a plasma. The initial free electron(s) can be provided by impurities in the water sample. Multiphoton breakdown does not require a seed electron or particle collisions. In this case, each electron is ionized simultaneously by absorbing photons from the laser pulse. This type of breakdown does not require the presence of impurities and can occur in a pure medium. It is much faster than cascade ionization and can occur during shorter laser pulses. The irradiance threshold for multiphoton breakdown is much higher than that for cascade ionization, and therefore cascade ionization is much more common (Kennedy, Hammer, & Rockwell, 1997). Cascade ionization is assumed to be responsible for the breakdown and subsequent appearance of cavitation bubbles studied in this work, due to the presence of impurities in tap water and resulting lower irradiance threshold. 3

13 1.2.3 Plasma expansion and production of cavitation bubble Once breakdown occurs and plasma is formed the laser energy can cause the plasma to expand rapidly at supersonic velocities resulting in an acoustic emission as well as a shock wave and cavitation. Once the laser pulse is gone the plasma starts to cool. The plasma will cool by losing energy to shock wave emission, spectral emission, and thermal conduction into the bulk fluid. After significant cooling the plasma begins to decay through the process of electron-ion recombination. This whole process creates a cavitation bubble of vapor water at the breakdown site (Kennedy, Hammer, & Rockwell, 1997) Cavitation bubble growth and collapse The high temperature causes a bubble to form around the plasma volume and shock wave velocity causes the bubble to grow rapidly. The bubble continues to grow quickly as the shock wave detaches from the bubble due to the large pressure difference between the inside of the bubble and the surrounding medium. As the volume of the bubble increases, the pressure inside the bubble drops. Once the pressure reaches the saturated vapor pressure for the liquid the cavitation bubble reaches its maximum size. This is because the rate of evaporation of liquid into the bubble and the rate of condensation out of the bubble are equal for a brief moment in time. The saturated vapor pressure inside the bubble is then lower than the pressure of the surrounding liquid, resulting in the bubble starting to shrink. If there is enough energy in the bubble it can rebound due to the increasing temperature and pressure of the gas inside the bubble as it shrinks. The bubble can continue to oscillate in this manner until it finally collapses with no rebound (Kennedy, Hammer, & Rockwell, 1997). 4

14 1.3 Earlier work The use of lasers to induce cavitation bubbles (a process referred to as laser-induced cavitation or LIC) developed in the late 1960 s and through the 1970 s, with most experiments focusing on generating cavitation bubbles near a boundary to study the physics and erosion mechanisms of cavitation bubbles. At the helm of this research was Lauterborn, who coined the phrase optical cavitation to describe the phenomenon of producing cavitation bubbles using a laser. Lauterborn started in the early 1970 s, developing ways to study the growth and decay of cavitation bubbles near boundaries. In Lauterborn & Bolle (1975) some obstacles that previously had limited the understanding of laser-induced cavitation were overcome. A spherical cavitation bubble collapse near a solid surface could not be studied theoretically or experimentally until the early 1970 s. Numerical methods could not predict bubble behavior in final stages of collapse, while experimental investigations were encumbered by the fact that the appearance of cavitation bubbles in most situations is statistical in both space and time. While a few experiments in the 1960 s provided evidence of jet formation resulting in cavitation erosion, laser-produced cavitation bubbles were used starting in the early 1970 s to study cavitation under highly controlled conditions. They were able to gain an understanding of cavitation damage mechanisms for bubbles produced at varying distances from a brass plate and capture high speed images at a frame rate of up to 75,000 frames per second (fps). They compared their results to theoretical work on cavitation bubbles and damage (Plesset & Chapman, 1971), and saw good agreement between the experimental and theoretical work for γ = 1.5, where γ = h/r max, R max is the bubble s maximum radius and h is the distance from the bubble center to the boundary. Clearly, γ will influence the amount of damage that cavitation will cause to a surface. This was 5

15 one of the first opportunities to use experimental work to validate the theory proposed in Plesset & Chapman (1971) as methods to produce bubbles systematically were lacking (Lauterborn & Bolle, 1975). Interest in cavitation damage mechanisms continued, with many authors contributing to the body of knowledge on cavitation events occurring near a boundary. Authors also sought to understand how cavitation acted in the vicinity of different types of boundaries. Giovanneschi & Dufresne (1985) studied laser-induced cavitation and discussed to some extent how to control the bubble size and shape for reproducibility of results. Isolating a bubble was no longer an issue thanks to the development of laser-induced cavitation, but controlling the specific parameters of the bubbles generated via laser was still difficult. It is advised to use optics with a short focal length and a small ratio of f/d (focal length/diameter). The setup Giovanneschi and Dufresne used involved a Nd:YAG laser with wavelength of 1.06 µm. A beam of 7 mm diameter was expanded by a telescope assembly (diverging and converging lens) and the resulting beam had a diameter of 35 mm. This beam was then focused into water by a convex lens with focal length (f) of 50 mm in air, resulting in a f/d ratio of 1.9. Bubbles in an infinite medium as well as near a wall were photographed at a frame rate of fps. In an infinite medium it was found that a spherical bubble would remain spherical as it expands. Near a solid wall, an initially spherical bubble will grow spherically but deforms during the collapse phase, deforming more the closer the wall is to the bubble. The deformation can be seen as an additional disturbance along an axis perpendicular to the wall; thus the bubble becomes oval in a direction perpendicular to the wall, and this results in a jet directed at the wall as the bubble rebounds (Giovanneschi & Dufresne, 1985). 6

16 Lauterborn continued to delve into the area of laser-induced cavitation, and in Lauterborn & Philipp (1998) the specific damage mechanisms were investigated. At that point in time there had been some debate about specifically how cavitation bubbles cause damage to metal plates and solid boundaries. In order to achieve this, the authors used a Q-switched Nd:YAG laser and focusing optics to produce cavitation bubbles at known locations. They then varied the distance between the cavitation bubbles and a solid metal plate (99.999% pure aluminum due to its softness), and used a high-speed camera to track the bubble dynamics. One of the parameters they looked at was γ, which was varied between ~0 and 3. The high-speed camera recorded at two different frame rates: 56,500 frames/s for an overview, and one million frames/s for fast events such as jet formation or shock wave emission. After being exposed to cavitation bubbles, the metal sheets were analyzed for damage. High-speed camera images of the cavitation bubbles were observed and analyzed. When the bubbles reached their maximum bubble diameter the pressure inside the bubble was seen to be much lower than the ambient pressure and the bubbles began to collapse. The fact that a boundary exists on one side of the bubble (in the paper, the lower part of the bubble) caused retardation of radial water flow and therefore lower pressure than for the part of the bubble farther away from the wall (upper bubble wall). This caused the bubble to become elongated, and the center of the bubble moves toward the boundary during collapse. A liquid jet developed, directed toward the boundary, and the bubble became toroidal as the jet flows through the bubble. As γ is decreased the jet formed earlier in time, and for γ < 1 the jet hit the metal plate directly, with no deceleration from a water layer, which occurs at larger distances. The impact velocity of the jet on the boundary determines the damage capability. The smaller the distance between the bubble and the wall, the higher the jet velocity, and therefore the greater the 7

17 potential for damage. It was determined that the diameter of the damage area scaled with the maximum bubble radius. This work clarified that cavitation erosion is caused mostly by the collapse of a bubble in contact with a material, as there was some doubt as to the specific mechanism for cavitation damage (Philipp & Lauterborn, 1998). 1.4 Recent attempts to characterize bubbles As cavitation becomes widely used in new areas, complete characterization and understanding of the physics of cavitation is necessary. A lot of work has focused on characterizing the physics of cavitation near a boundary, but less information is available on laser-induced cavitation bubbles in a bulk liquid. Peel, Fang & Ahmad (2011) used two methods, pump-probe beam deflection (PBD) and high speed photography, to characterize cavitation bubbles induced in a bulk fluid (water) using a Nd:YAG laser with a wavelength of 1064 nm, pulse energy of 140 mj, pulse duration of 10 ns, and repetition rate of 1 Hz. In both cases, the focus of the study was on the bubble interface speed and bubble size, as well as the bubble lifetime. The laser pulse energy used in this paper is higher than energies used previously. At lower energies the relationship between laser pulse energy and bubble energy is linear. Using higher laser energies was desired to help determine if this linear trend continues at much higher laser energies. For the high-speed photography technique, a frame rate of fps was used. At this frame rate, the bubble s growth was tracked over time, with still images of the bubble every 20 µs. Cavitation bubbles were formed along the trajectory of the laser beam, with smaller bubbles initially forming as a result of multiple breakdown sites, and then merging to form single bubbles after a certain amount of time (~300 µs from the laser pulse trigger). The maximum bubble size was found to occur at about 320 µs, and the maximum bubble diameter was 8

18 approximately 2.20 mm. The total bubble lifetime was estimated to be approximately 280 µs (where the total image time is 480 µs, but the first bubble image is visible at 200 µs after the laser pulse). The authors compared their experimental results for the laser-induced cavitation bubbles with the Rayleigh equation, which is used to quantify cavitation in a bulk fluid based on the bubble wall velocity (i.e. how fast the radius of the bubble grows). Comparison between the experimental data and Rayleigh equation results was inconclusive, due to the fact that Rayleigh s equation assumes an incompressible liquid and the fact that in experiments the liquid density near the cavitation bubble will change (Peel, Fang, & Ahmad, 2011). This recent work illustrates that there is still much to learn about laser-induced cavitation bubbles and their behavior under different conditions. Scientists have also been discovering new ways of using cavitation in a positive way. While the majority of past research has focused on the erosion caused by cavitation events, future work should examine bubble dynamics under more varied and extreme conditions. 1.5 Newer applications of cavitation More recently, cavitation has been a topic of interest for many researchers, finding application in a wide variety of fields. It has been used in some biomedical applications, for surface cleaning, and in lab-on-a-chip technologies as just a few examples. Cavitation is proving to be a very versatile phenomenon with many uses, and while cavitation has traditionally been viewed as an undesirable phenomenon due to the noise and damage it produces, these newer applications aim to utilize cavitation in positive ways. For these newer applications, characterization is extremely important, as accurate characterization will allow people to control the size and effects of the cavitation process. This is particularly important in biomedical applications where unexpected results could cause damage to the human body. 9

19 1.5.1 Laser cleaning Laser-induced cavitation bubbles can be utilized in a process referred to as wet laser cleaning to remove particles from a substrate immersed in a liquid. When a high-power laser is focused into the liquid and optical breakdown occurs, a cavitation bubble is produced. The shock waves emitted as well as the liquid jet that develops during cavitation collapse produce high pressures (i.e. several gigapascals). It is also known that a cavitation bubble collapsing near a boundary (in this case the substrate) deforms and that a liquid jet is directed at the boundary. This phenomenon allows surfaces to be cleaned via laser-induced cavitation bubbles, which can prevent issues associated with other methods of laser cleaning. This wet laser cleaning method circumvents issues associated with a substrate absorbing laser irradiation, which can induce high temperatures that in turn can produce oxidization, melting, stress generation, and other changes to the physical and chemical properties of the substrate. To further facilitate substrate cleaning from the jets that result from cavitation bubble collapse, it is recommended that an organic solution be used to lower the viscosity and consequently increase the impact pressure on substrate contaminant particles. This will help increase the cleaning efficiency (Song et al., 2004) Micro-pumps Dijkink & Ohl (2008) used laser-induced cavitation bubbles to pump water through a small channel, applying LIC to lab-on-a-chip systems. Their cavitation-based technique is capable of pumping 4000 µm 3 in 75 µs. The cavitation bubble is induced above a boundary with a small opening that creates a channel. Because cavitation bubbles close to a rigid boundary form an asymmetrical jet, the jet forces water through the channel. If the jet did not occur as part of the cavitation process, the bubble expansion and collapse would allow water to first move into 10

20 the channel and then pull water out, resulting in an overall displacement of zero. The efficiency of the pump varied with cavitation bubble size and the distance between the bubble and the channel. One of the advantages of using a laser to create a pump is that no mechanical or electrical connections are needed for the pump itself (Dijkink & Ohl, 2008). This type of technology could utilize cavitation in a positive way for extremely small-scale systems Lithotripsy Lithotripsy is a process used to break down stones that form in the body. These stones are often referred to as calculi. Shock waves are used in lithotripsy to break up these stones. While there are four main types of lithotripsy, laser lithotripsy is best suited and most commonly used to break up bile duct stones and calculi in the ureter (tubes that transport urine from the kidney to the bladder). Laser energy is directed to a specific point using an optical fiber. Pulsed Nd:YAG lasers were considered as an option for breaking up these stones because they create shock waves that are ideal for disturbing stones. The drawback to using Nd:YAG lasers is that the fiber damage threshold depends on the irradiance, and transporting very short pulses places strict limitations on size of the fibers that can be used. While some special probes have been developed for use with Nd:YAG lasers, other types of lasers have also been investigated as alternatives (Kennedy, Hammer, & Rockwell, 1997). Nd:YAG lasers have been looking promising as a method of using laser lithotripsy to destroy stones. While research about this technology has been progressing, traditional surgeries have still been needed to remove the majority of the stones. This is largely due to a lack of understanding about the dynamics of the laser lithotripsy process. With improved understanding of bubble dynamics laser lithotripsy could provide a convenient, economical, and less painful technique than traditional surgeries (Kokaj, Marafi, & Mathew, 2008). 11

21 Recently, a new frequency-doubled, double-pulse Nd:YAG laser (FRDDY) has been developed and used to treat urinary stones. The frequency doubling means that wavelengths of both 532 and 1064 nm are used for the laser pulses, which allows for very high pulse intensity at a given point. The 532 nm wavelength light initiates the plasma formation and then the 1064 nm wavelength light heats the plasma causing first expansion and then contraction, fragmenting the stones in the body. The pulses are on the order of 1 µs, and therefore the surrounding tissues do not experience thermal damage from the laser pulses (Kim et al., 2008) Drug delivery Using cavitation bubbles has been proposed as a method for improving drug delivery to tumors and cancerous cells. The delivery of anti-cancer drugs from the bloodstream to cancer cells is inhibited by blood vessel walls, interstitial space, and cell membranes. Laser-induced cavitation could be used in specific locations to perforate tumor blood vessel walls and cancer cell membranes, and produce microconvection within interstitial spaces (Esenaliev et al., 2001). Dijkink et al. (2008) investigated the viability of cavitation-induced drug delivery. Epidermal HeLa cells were grown in a medium. Cell permeabilization was tracked by using a small fluorescent molecule (calcein) in the medium surrounding the cells. Apoptosis (cell death) was also studied using cell-staining dyes. Cavitation bubbles were induced at various distances from the cell boundary using a laser. The jet formed by cavitation bubble collapse near the boundary caused some cells to become suddenly detached and die. Below these detached cells another zone of cells was also impacted by the cavitation bubble jet resulting in large pores that caused apoptosis, and these cells died within a few hours. The next zone of cells was porated in such a way that drug delivery would be viable, and cells beyond this zone were unaffected by the cavitation event. The number and size of pores that could be generated for drug delivery are 12

22 related to the distance between the cavitation bubble and the cell boundary. This distance is characterized by the standoff distance γ, where γ = h/r max, where R max is the maximum bubble radius and h is the distance between the bubble center and the boundary. Decreasing γ resulted in more cells being detached, but an increase in the number of cells showing molecular uptake, indicating an increase in pore size and/or number (Dijkink et al., 2008). 1.6 Introduction summary Cavitation has been a topic of interest for over a hundred years. Initially considered an undesirable phenomenon due to its erosive effect and loud acoustic signature, it has in more recent years been utilized in a number of productive ways. The desire to study the physics of cavitation and isolate bubbles for observation resulted in the use of lasers to produce bubbles, a process referred to as laser-induced cavitation. While these bubbles initially allowed for controlled study of cavitation events near boundaries, other possibilities for their use soon emerged, and continue to be developed. Since many of the newer uses for laser-induced cavitation have only recently been developed or are in the early stages of investigation, bubble behavior under conditions not previously studied, such as much higher bubble energies, needs to be studied Research Objectives Based on the literature currently available, there is a wealth of knowledge about cavitation events near surfaces. However, less information is available on laser-induced cavitation bubbles in a bulk fluid and how to control the bubble dynamics. Therefore this research focuses on controlling bubble development through the air content of the bulk fluid, pulse energy used to generate bubbles, and the focusing angle of the lens used to produce bubbles. The combination of these elements will influence bubble size, shape, and temporal development. Understanding 13

23 the effects of each variable will shed light on how to produce bubbles with a desired size, shape or lifetime. This thesis presents the results of experiments done to reveal the effects of each variable, as well as scaling analysis to guide the selection of lens, laser power, and air content to produce bubbles with desired characteristics. 14

24 2 Experimental Methods 2.1 Test apparatus Water Tank Cavitation bubbles were produced in a tank using a focused laser beam. A laser beam passed through a beam expander, which was used to expand and collimate the laser. The laser beam diameter was expanded from 6 mm to the focusing lens diameter using a beam expander. The expanded beam was then directed through the focusing lens, forcing the laser light rays to converge at the focal point of the lens. The tank used was 0.30 m long, 0.15 m wide and 0.2 m tall. The tank was filled to 0.1 m with water, and the bubbles were formed at a depth of 0.05 m below the water surface. Figure 1 shows the distance between the components in the experimental setup. Here A is the distance between the beam expander outlet and the focusing lens, B is the distance between the focusing lens and the front wall of the tank, C is the distance between the cavitation bubbles and the camera, D is the distance between the focusing lens and the point where the cavitation bubble is produced, E is the distance between the cavitation bubble and the bottom of the tank, and F is the depth of water in the tank. The distances between the components for each test condition are given in Table 1. The lens angle referred to in this work as the convergence angle is often referred to as the angular spread. This is equal to twice the beam divergence, which is a term often used when discussing lasers (see Figure 2 for an illustration of each angle). 15

25 Figure 1 Experimental setup used to generate laser-induced cavitation bubbles. The laser beam is expanded and then focused through a lens. A camera was used to capture the cavitation bubbles. The dashed box in the side view represents the camera s nominal fieldof-view. 16

26 Table 1 Distances between components in experimental set up in Figure 1. Lens angle Air content A B C D E F (nominal) (ppm) (m) (m) (m) (m) (m) (m)

27 Figure 2 This figure illustrates the relationship between beam divergence and angular spread. In this work, the convergence or focusing angle refers to the angular spread. Table 2 Lens specifications used to create bubbles Lens angle Lens angle Focal length, Diameter, Ratio (nominal) (actual) f (mm) D (mm) (f/d) Laser Optics Cavitation bubbles were successfully produced in the tank of stagnant fluid (water) by focusing the beam of a Nd:YAG laser (Gemini PIV, New Wave Research) as shown in Figure 1. 18

28 The laser was operated at 532 nm wavelength with a nominal 6 mm diameter beam. The beam diameter was expanded using a beam expander (NT64-419, Edmund Optics), which was adjusted to produce a collimated beam at the diameter appropriate for the given focusing lens (see Table 1). This beam was then focused into the water tank with varying levels of air content with the use of three different focusing lenses (see Table 2). The laser was pulsed regularly at 15 Hz. The fact that the laser was pulsed regularly at 15 Hz may have introduced some scatter into the results of this experiment. Pulsing the laser at such a rate may cause the temperature around the beam focal point to increase relative to the bulk fluid temperature due to residual heating from earlier pulses. If single pulses were used instead of regular pulses, a larger separation between test samples would have been produced allowing the local fluid temperature to return to the bulk fluid temperature. This could have reduced the scatter in the results. The energy of each laser pulse could be varied by changing the flash lamp power and/or the laser attenuation. In the current study the laser flash lamp was fixed at the maximum power and the laser pulse power was varied with the attenuator setting. The lower end of the power range for the laser used was selected such that cavitation was barely audible to the human ear. The focusing angle of the lens can have a great impact on the bubble shape. In particular, a narrow focusing angle can result in the formation of multiple bubbles at one time along the laser path. A wider focusing angle, or cone, promotes the formation of a single bubble. The beam-focusing angle is a function of the laser beam initial diameter, the lens focal length and the optical path of the laser beam. To achieve a wider focusing angle the initial beam diameter should be maximized, which results in the limiting factor being the diameter of the focusing lens. The shorter the lens focal length the wider the resulting focusing angle. However, this also limits the distance between the lens and the cavitation bubble. The dependence on the optical path results in the beam angle being 19

29 sensitive to the fluid in which the bubble is being generated, which is due to Snell s law based on the refractive index of the medium. The beam angle in water for each lens was calculated using Snell s law (see Figure 3). Snell s law says that the angle of incidence of a ray on a boundary times the refractive index of the medium through which the light propagates is constant or n! sin θ! = n! sin θ!. Since the laser light travels first through air, then glass, and then water, three different materials must be accounted for, n! sin θ! = n! sin θ! = n! sin θ!. All of the indices of refraction (n 1, n 2 and n 3 ) are known. The initial angle of incidence θ 1 is calculated based on the known diameter and focal length of the lens, θ! = tan!!!!!, where D is the diameter of the lens and f is the focal length. From this information the angle in water, θ 3, can be determined. 20

30 Figure 3 Snell s law applied to a ray path passing through air (n 1 =1.00), glass (n 2 =1.55) and water (n 3 =1.33). Increasing index of refraction bends the beam towards the axis perpendicular to the interface between the two mediums. For this work, three lenses were used with focusing angles of approximately 20, 10 and 5 in water. These angles were chosen in order to explore the effects of using a relatively small, medium, and large focusing angle on bubble size and shape. The 20 lens had a diameter of 50 mm and focal length of 100 mm, providing a ratio of focal length to diameter of 2. This is comparable to previous work that has produced single, spherical bubbles. One such example is from the work of Giovanneschi and Dufresne (1985) who used a lens arrangement with a focal length to diameter ratio of 1.9. The small angle lens (22 mm diameter, 200 mm focal length) was selected due to previous experiments that demonstrated the appearance of multiple bubbles (Giovanneschi & Dufresne, 1985). The medium angle lens was selected so that the angle was 21

31 between the narrow and wide-angle, and a 50 mm diameter lens with 200 mm focal length was selected. 2.2 Instrumentation Imaging setup A high-speed video (HSV) camera (Memrecam GX-3, NAC) was used to capture images of the cavitation bubbles forming and collapsing in the water tank. The camera was mounted perpendicular to the laser beam path, looking into the tank. A filter was used on the camera to filter out the 532 nm wavelength light from the laser. A ring of halogen lights was mounted on the opposite side of the tank to backlight the images. A sheet of white paper was hung between the tank and the halogen light source to evenly diffuse the background light for the HSV images. The camera was connected to the computer via an Ethernet cable. Images were captured and the camera controlled via custom software (MEMRECAM GXLink). For lower power, images were acquired with a frame size of 64 x 64 pixels at a frame rate of 80,000 frames per second. At higher power (attenuator set at 200 and above) the image size was 96 x 64 pixels, and the frame rate was 75,092 fps. The larger frame size was needed at higher power as the bubbles tend to be larger, particularly in the horizontal direction as multiple bubbles merge together. The laser was pulsed at 15 Hz while the HSV captured images of the cavitation event. The maximum frame rate was dependent on the frame size (the smaller the frame size the higher the maximum frame rate). The frame rate needed to be sufficiently high to observe the cavitation event through its initial formation, growth and collapse. The final frame size was determined by slowly reducing the frame size such that the cavitation bubble filled as much of the frame as possible to observe it in the greatest detail while maintaining a sufficiently high frame rate. 22

32 In order to determine the bubble size, a target of known dimensions was placed in the tank and calibration images were acquired. The calibration target was a black sheet with white dots spaced 2.54 mm apart. The calibration image was used to determine the scale and therefore the bubble dimensions. The physical distance between dots in the target image is known. Using the measurement tool in the MEMRECAM GX Link software, the number of pixels between each dot can be measured. Therefore the pixels per millimeter could be determined. The bubbles were measured using the measuring tool to find the dimensions in terms of pixels, and the measurement was then multiplied by the value determined from the calibration image to convert the number of pixels to millimeters Laser power The laser energy per pulse is controlled by the flash lamp and the attenuator on the Gemini PIV Nd:YAG laser. Increasing either the flash lamp or the attenuator level can increase the laser pulse energy. For this work, the flashlamp was set to the maximum value and held constant and the attenuator was adjusted to vary the power. The laser energy per pulse in mj was extrapolated from existing information on the maximum energy per pulse of the laser and the attenuation curve associated with the laser. The maximum laser power was determined to be 129 mj, based on calibration information corresponding to the specific Gemini PIV laser used in this experiment. The attenuation curve was acquired from the New Wave Research website. The attenuation curve indicates the percent of the maximum energy that is reached with each attenuation step of 100, where the attenuator can be set from 0 to Combining these two pieces of information, the curve shown in Figure 4 was computed. 23

33 Energy per pulse (mj) A1enuator se5ng Figure 4 Energy per pulse as a function of attenuator setting for the laser used in the current study. The flash lamp was fixed at the maximum level Water dissolved gas content Felix & Ellis (1971) used a laser to induce cavitation in tap water, deionized water, and methyl alcohol. This work demonstrated that impurities in a liquid increase the number of hot spots where plasma can form in the liquid. Similarly, the amount of air dissolved in the water can also potentially affect the size and shape of the bubble. More air provides more nucleation sites for cavitation bubbles and therefore the bubble size and shape may be affected at a given laser power level. More nucleation sites may result in multiple bubbles being produced and bubbles being formed at a lower laser power. The air content of the bulk fluid was measured using a Van Slyke apparatus. A 10 ml sample of the bulk fluid with unknown air content was tested in the Van Slyke apparatus to measure the air content. First, a vacuum is applied to the sample and the sample is agitated for 4 24

34 minutes to separate the dissolved air in the original sample from the water. The vacuum was produced by varying the height of a volume of mercury relative to the sample. The water and gas are then forced into a 2 cm 3 volume cavity. Now the air occupies a known volume at a given pressure (measured from height of the mercury) and temperature (measured with a thermometer). The ideal gas law is used to determine the volume at a standard temperature, which is then used to determine the air content of the sample (Carl, 1977). The water air content is presented in units of parts-per-million (ppm), which was defined in terms of mass parts. In this work, the water air content concentrations are referred to herein by their nominal values (10, 15 and 20 ppm). The average measured values for each condition are provided in Table 3. The de-aerated (low air content) water was obtained by using a vacuum. A large tank was filled with tap water. A vacuum was pulled on the tank and several hours elapsed. After several hours water was drained from the bottom of the tank. Water taken directly from the tap was used for the high air content condition. The intermediate air content condition was achieved by leaving the deaerated water overnight. Table 3 Average water-air content concentration (C) for each air content condition Air content condition C (nominal) (ppm) Average C (actual) (ppm) Low Intermediate High

35 2.3 Test Matrix The objective of the current study was to characterize laser-induced cavitation bubbles. It was assumed that the cavitation bubble s formation, growth and collapse is dependent upon the optical arrangement (e.g. laser power, beam focusing angle) and bulk fluid properties (e.g. fluid density, temperature, dissolved gas content, turbidity and pressure). In the current study the laser beam focusing angle, laser pulse energy, and bulk liquid air content were varied. The pressure was held constant at slightly above atmospheric pressure (cavitation bubble location was approximately 50 mm below the tank free-surface), the bulk fluid temperature was held constant at room temperature (approximately 25 C) and the bulk fluid used was tap water (density = 997 kg/m 3 ). The test matrix varied the beam focusing angle from 5 to 20, the laser pulse energy varied between 0 and 42 mj/pulse and the water air-content was varied between 10 and 20 ppm. Future work will expand upon the current study to assess the influence of pressure, bulk fluid density and distance from a solid surface. 2.4 Measurement Uncertainty All measurements involve a degree of uncertainty that contributes to error and limits the degree of accuracy of the results. In this section, the measurement uncertainty associated with each component of the experimental set up is discussed, and the effect that this uncertainty has on the final results of the analysis will be touched on in Chapter Camera The camera setup involved uncertainty in both space and time. The spatial uncertainty was due to the way in which the bubble diameters were measured from the images produced by the camera. For each frame, the left, right, top and bottom of the bubble were identified visually using the human eye, and then the measurement tool was used to determine the distance between 26

36 the left and right or top and bottom of the bubble. The measurement uncertainty for the bubble length is 4 pixels (±2 pixels from the measured diameter). Based on the setup with the calibration image that resulted in the greatest number of millimeters per pixel, the diameter measurements for the cavitation bubbles have an uncertainty of ±0.158 mm. The temporal uncertainty has two parts, the temporal resolution and the exposure time. In this case, the exposure was set equal to the time between frames. Therefore the maximum possible uncertainty is associated with the temporal resolution, which is the frame rate ±½ of the time between frames. With a frame rate of 75,092 fps, half a frame is equivalent to µs Laser The laser provides another source of uncertainty. Each pulse can have slightly different energies even at the same attenuator and flash lamp settings, resulting in bubbles that are produced at slightly different energies. Residual heating in the area where cavitation is produced could also cause bubbles to be produced at different energy levels even when the laser settings are kept the same. Due to the way in which the energy pulse versus attenuator setting curve (Figure 4) was obtained, this work assumes a measurement uncertainty for the laser pulse energy of ±10%. For the highest laser pulse energy used, 42 mj, the pulse energy would be 42 ± 4.2 mj Lenses The lens-focusing angle was calculated via Snell s law, which assumes an ideal lens. For these calculations the diameter and focal length of the lenses were used. Since the lenses are not ideal lenses there will be some distortion towards the outer edges of the lenses, and therefore the diameter is assumed to have an uncertainty of about 10%. The manufacturer (Edmund Optics) specified focal length tolerance for the 10 and 20 lenses is ±1%. The focal length tolerance for the 5 lens is assumed to also be ±1%. 27

37 2.4.4 Pressure The experimental uncertainty in the pressure is a function of how accurately the distance from the surface of the water to the point of cavitation was measured. This distance was measured using a tape measure and evaluated using the human eye. It is estimated that this distance has an uncertainty of ±5 mm, which corresponds to ±49 Pa Air Content The uncertainty in the air content measurements was estimated by comparing multiple water samples taken from the same source. The standard deviations for the three different air content conditions were calculated and are presented in Table 4. The standard deviation for each condition is converted into a percentage, and the average percentage (12%) is used as the uncertainty for all three conditions. Table 5 summarizes the uncertainty associated with each measured quantity. Table 4 standard deviation for air content concentration measurements Nominal air content (ppm) Standard deviation

38 Table 5 Measured quantities and their corresponding measurement uncertainty Quantity Bubble diameter D v, D h Uncertainty ±0.158 mm Frame rate ±6.7 µs Laser pulse energy Lens diameter Lens focal length Pressure Air content ±10% (or ±4.2 mj max) ±5% (or ±2.5 mm max) ±1% (or ±2 mm max) ±49 Pa ±12% (average) 29

39 3 Experimental Results 3.1 General trends and overview A few general trends can be seen in the cavitation bubbles generated under the different conditions from the test matrix. Below the trends will be listed in a qualitative sense, and the specific trends will be discussed in more depth throughout the rest of the chapter. 1. Increasing the power increases the bubble size 2. Increasing the power increases the bubble lifetime 3. Lower power produces more spherical bubbles 4. Increasing the power produces more bubbles at a time 5. Increasing the focusing angle of the lens decreases the bubble size 6. Increasing the focusing angle decreases the bubble lifetime 7. Increasing the focusing angle produces more spherical bubbles 8. Smaller focusing angles allow bubbles to be produced at lower power While the bubbles produced under the different conditions exhibited different maximum sizes and a range of shapes from spherical to elliptical, they all follow a somewhat similar development from the point of inception when the laser pulse appears at the focal point (denoted as time t = 0 for each bubble), and then collapsing until the bubble is no longer visible. Figure 5 and Figure 6 show the bubble size versus time for a bubble produced at relatively low and high laser energy per pulse, respectively. Please note that the images of the bubbles have been edited to enhance visibility of the bubble formations. Both figures were produced using the wide-angle lens configuration in water with the intermediate air content level. The first, run 211, was produced at a power of 7.3 mj, and the second, run 205, was produced with a laser power of 42 mj. These runs were selected to demonstrate how the profiles of the bubble lifetime change with 30

40 increasing power and show the general trends in bubble behavior. The white spot in Figure 5a shows the plasma that is formed by the laser light, and the rest of the frames illustrate the bubble s behavior over time. At lower powers, the bubbles produced tend to be relatively smaller, singular, spherical and have a shorter lifetime. They do not rebound or oscillate in size (i.e. the bubble forms, grows, collapses, and then is no longer observed). The wide-angle lens produced the smallest bubbles, so a bubble produced at 7.3 mj with the small angle lens configuration would be significantly larger than the bubble produced at the same power with the wide-angle lens configuration, and may have multiple bubbles present. Figure 5 would be more indicative of bubbles produced at very low powers for the small angle lens (around 2 to 5 mj). Figure 6 shows the temporal development of a bubble produced at the highest laser energy used in this experiment (42 mj). Compared to Figure 5 it illustrates a few key differences in bubble behavior. Clearly, the bubble lifetime is longer (about 300 µs compared with around 65 µs) and the bubble size has increased, nearly doubling. The appearance of multiple bubbles and the way they merge together to form larger, oblong bubbles is a trend at high powers. Another interesting feature is that the bubble has two peaks in bubble diameter, with the first peak occurring at 66 µs with a bubble diameter of 1.25 mm, and a second peak occurring at 187 µs with a diameter of 1.17 mm. This is a significant difference between bubbles generated at higher versus lower power. The higher power bubbles tend to rebound and oscillate while the lower power bubbles simply collapse. 31

41 Figure 5 Example of a bubble lifetime produced at relatively low laser power (7.3 mj per pulse) with the wide-angle lens configuration and intermediate air content level. Labelled data points correspond to labeled images at the top of the figure. In image A the bright white spot is produced from plasma generated by the focused laser beam, while the remaining images show the shadow produced from the backlighted bubble. 32

42 Figure 6 Example of a bubble lifetime produced at relatively high laser power (42 mj per pulse) with the wide-angle lens configuration and intermediate air content level. Labelled data points correspond to labeled images at the top of the figure. The growth, collapse and rebound of the bubble is apparent from the plot. Figure 7 compares how bubble generation and growth differ for bubbles produced by all three lens configurations at the upper and lower bounds of the laser pulse energy range tested. Although the figure shows bubbles produced under different air content conditions, the comparison of these bubbles is appropriate since it is shown subsequently that the results have negligible sensitivity to the air content levels. In Figure 7 the run number is listed and the lens condition is indicated by SA, MA or WA standing for small angle, medium angle, and wide- 33

43 angle, respectively. For low levels of power, all three lenses created single, spherical bubbles, as can be seen in Figure 7 A, B, and C. The bubbles produced by the small angle lens at high powers produce noticeably different shapes from bubbles produced by the medium and wideangle lens. At 42 mj, all three lenses form a string of multiple bubbles along the path of the laser beam, as illustrated in Figure 7 Da, Ea, and Fa. The bubbles produced by the small angle lens coalesce and form a single larger bubble, which continues to grow outward in the vertical direction. The medium and wide-angle lenses both produce a significant number of smaller bubbles along the beam path (see Figure 7 D, E and F). Some of these combine to form larger bubbles, while others grow as single bubbles. Figure 7 Db, Eb, and Fb show what the bubble configurations look like at the time of maximum diameter. This results in a combination of individual bubbles and longer bubbles that are two or three times the length of the single bubbles in the horizontal direction, but are similar in diameter in the vertical direction. These trends are discussed further in the following sections. 34

44 Figure 7 Comparison between low and high power bubble behavior. At lower pulse energies single, spherical bubbles are produced. At higher powers the bubble shape depends on the lens angle. The smaller angle lens produces one larger bubble formed from bubble coalesence. The wider angle lenses produce smaller, more elongated bubbles. In the figure SA, MA and WA refer to the small, medium and wide-angle lens configurations, respectively. 3.2 Repeatability The bubble diameter was measured using the measurement tool available in the MEMRECAM software. The measurements were made by clicking on the left and right-most 35

45 points of the bubble for the horizontal diameter and the top and bottom of the bubble for the vertical diameter. The distance between the two points was then given in pixels, which was then converted to millimeters using the calibration images. The time from frame to frame (in µs) was determined based on the camera frame rate. When tracking the bubble diameter over time, it was decided that the vertical diameter, and not the horizontal diameter, would be tracked. The vertical diameter was selected due to the variability in the horizontal diameter and formation of multiple bubbles that coalesce along the beam axis (horizontal direction). Since bubbles at higher power sometimes coalesced into a larger bubble that was longer in the horizontal direction but sometimes formed many individual bubbles, the vertical diameter was determined to be a more reliable measure of bubble growth. However, comparison between the vertical and horizontal bubble dimensions is provided subsequently. Whether many individual bubbles formed along the path of the laser beam or one large bubble developed, the vertical bubble diameters were in the same range. Due to the availability of the laser, these data were collected in two phases, thus requiring that the equipment be set up twice. Some differences in the distance between elements in the experiment resulted, most notably the distance between the camera and the tank wall, though other distances had some variation. Ideally all the data would have been collected at once, but comparison of the two phases allows for an assessment of the repeatability of the experiment. The narrow angle lens, intermediate air content condition at laser energy per pulse ranging from 20 to 50 mj was repeated in both phases of testing. This was done to make sure that comparisons could be made across the data sets collected at different points in time. The results for maximum vertical diameter versus laser power are shown in Figure 8. The blue points represent values obtained in the first phase, and the red squares indicate values obtained in the second phase. 36

46 Generally the two data sets overlap adequately. The average percent difference between data collected in February and March was calculated to be about 7%, with values in March being on average 7% lower than in February. There appears to be an outlier in the February data, where a bubble had a diameter of ~1.8 mm when produced with a pulse energy of 42 mj. The cause for this outlier is unknown, but excluding it from the calculation the average percent difference between data collected in February versus March drops to just 5%. The results support comparison between bubbles that are produced in different experimental setups. The small difference in bubble sizes between the two data sets allows conclusions about the effects of the parameters being tested to be drawn Ver7cal diameter (mm) first set (Feb) second set (Mar) Pulse energy (mj) Figure 8 Comparing bubble diameter, there is reasonable agreement between data collected in different setups from different points in time. This indicates that comparing results between the two different setups is appropriate. 37

47 3.3 Variation of bubble topology When bubbles are generated near the minimum energy required to produce visible cavitation, the cavitation bubbles that form are single, spherical bubbles for all the test conditions. At higher power, the bubbles behave differently based on the lens used to generate the bubbles. In fact, even for bubbles generated with the same lens configuration, there can be pulse-to-pulse variation in the bubble generation, growth, and collapse. This is particularly notable for the medium and wide-angle lens configurations. The bubbles produced at the highest energy, 42 mj, with the narrow angle lens configuration showed minimal pulse-to-pulse variation. Figure 9 shows 5 different runs, and what the bubble(s) looked like at the point of maximum vertical diameter. For all five runs, the laser pulse produces around 5 small bubbles. These bubbles then coalesce into a single larger bubble that grows in the vertical direction. While the bubble in Ah does not manage to form a bubble as uniform in vertical diameter as the other runs, it still follows the general trend of the bubbles coming together to form a single, elliptical bubble. 38

48 Figure 9 Narrow angle lens bubble patterns at high power (42 mj) in high air content water. Smaller bubbles formed along the path of the laser beam coalesce to form a single, larger, elliptical bubble. As the laser-focusing angle became wider, the bubble behavior exhibited greater variety and became less predictable. Figure 10 and Figure 11 show the bubble development at 42 mj for the medium and wide-angle lens configurations, respectively. Figure 11 also shows the bubbles produced using the wide-angle lens under all three air content conditions. For each run, the bubbles are shown shortly after the laser pulse and then at the point of maximum diameter. This 39

49 is done to illustrate how the bubbles change from individual bubbles into other configurations over time. For all of the runs, many small bubbles are initially generated along the path of the laser beam. Over time, the bubbles grow in different ways. A couple of different behaviors are observed: 1. The individual bubbles that are produced initially may continue to expand as individual bubbles, as demonstrated in Figure 10 f and h, as well as Figure 11 Af and Bh. 2. The bubbles may coalesce to form one very long bubble, which is illustrated in Figure 10 j as well as Figure 11 Ad, Af and Cj. 3. Some of the bubbles may coalesce while others grow as individual bubbles, as in Figure 10 b, and Figure 11 Ah, Aj, Bj and Cg. The resulting bubbles may be smaller, as in Figure 10 h, or larger, as in Figure 10 j. The variety of behaviors causes difficulty in quantifying the bubble time history, especially when multiple bubbles coalesce during the lifetime. 40

50 Figure 10 Medium angle lens bubble patterns at high power (42 mj) in intermediate air content water. On the left is the bubble formation shortly after the laser pulse, on the right is the bubble formation at the time of maximum bubble diameter. 41

51 Figure 11 Wide-angle bubble patterns at high power. On the left hand side of (A), (B), and (C) is the bubble formation shortly after the laser pulse, and on the right hand side of (A), (B) or (C) are the bubble formations at the points of maximum bubble diameter. These images illustrate the variety of bubble patterns that can be formed. 3.4 Bubble size Bubble size: sensitivity to beam angle The sensitivity of the bubble diameter to beam angle was investigated by plotting the bubble diameter versus laser energy for each lens angle configuration while holding the air content constant. Bubbles produced by the three different lens angles produced bubbles of different sizes. As mentioned earlier, the small angle lens produced larger bubbles at lower 42