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Exploring the Dynamics of Optical Thermocavitation Bubbles Using Planar

Laser-Induced Fluorescence

Vicente Robles Advisor: Dwight Whitaker

Department of Physics and Astronomy Pomona College

Thesis submitted to:

Pomona College In partial fulfillment for the degree of

Bachelor of Arts in Physics 2016

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Abstract While hydrodynamic cavitation has been investigated by engineers for over a century in hopes of suppressing damages such as propeller failure and hydraulic instabilities, little literature exists on cavitation induced by optical components. Recent studies investigate the controlled generation of optical thermocavitation and its potential beneficial applications. A review of the theory of cavitation bubbles is presented here followed by a full description of an experimental non-intrusive method for measuring the temperature of optical thermocavitation bubbles. The experiments were completed in the University of California Riverside.

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Acknowledgements

Much thanks is sent to my thesis advisors: Dr. Whitaker and Dr. Hudgings, who provided me with guidance on this work. Thank you to my mentors and laboratory group: Dr. Aguilar, Dr. Banks, Dr. Felipe-Devia, and Ismael Martinez for a being great scientists and for encouraging me to pursue higher education. Thank you to my friends and girlfriend for keeping me sane and special thanks to my sisters: Cristina and Cynthia and to my padres: Vicente and Gloria, gracias por su gran apoyo.

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Table of Contents

1. Introduction

1.1. Background 1.1.1. Hydrodynamic cavitation 1.1.2. Acoustic cavitation 1.1.3. Particle cavitation 1.1.4. Optical cavitation

1.2. Project Motivation

2. Fluid Dynamics

2.1. Continuous and Pulsed Lasers 2.2. Dynamics 2.3. Cavitation Number 2.4. Rayleigh-Plesset Equation 2.5. Fluorescence 2.6. PLIF

3. Experimental Methods

3.1. Experimental Setup 3.2. Procedure

3.2.1. Absorption Spectrum 3.2.2. Temperature Calibration Curve

4. Results

4.1. Boundary Layer 4.2. Thermal Lensing

5. Conclusion

5.1. Closing Discussion 5.2. Future Work

6. Appendixes

6.1. Appendix A: Derivation of 6.2. Appendix B : Circuit for trigger and Arduino code

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Chapter 1

Introduction Imagine living your crab life peacefully in Deep Ocean. You wake up for a walk and go about your day. Before you know it, BANG! You are dead and now the mantis shrimp’s breakfast. The mantis shrimp holds the record for the fastest punch in the animal kingdom. This sea creature uses its two club-like appendages to strike its prey with an acceleration faster than a .22 caliber bullet [1]. The punch velocity is so fast that it causes water to quickly vaporize and form vapor bubbles. These bubbles collapse and release shockwaves that emit large amounts of heat and light killing prey almost instantly. This effect is called cavitation. Cavitation, in its simplest definition, is the formation of a vapor bubble in a fluid followed by the emission of high-pressure shockwaves. This varies from boiling in that it is a much more explosive, and instantaneous process. Cavitation also involves superheating a parcel of liquid (rather than a larger volume) far beyond its boiling point. [2] This phenomenon is present in environments outside of mantis shrimp punching and has been a problem for engineers in various fields, causing material breakdown, erosion, vibrations and other unfavorable outcomes. The word “cavitation” was coined in 1895 by naval architecture R.E. Froude. [3] Cavitation occurs when there is a rapid decrease in pressure and a cavity forms in the liquid. This is often most commonly induced by a sudden change in velocity of a fluid. During this condition, a vapor bubble is formed and grows until a surrounding high pressure field causes the bubble to burst and release a high energy shockwave. [3] There are various methods in which cavitation can be induced, these methods are characterized into the following: tension and energy deposit [4]. Tension

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cavitation is induced by pressure variations that occur in the fluid. This category can be further split into two types of cavitation: hydrodynamic and acoustic cavitation. On the other hand, optical thermocavitation and particle cavitation are formed through energy deposition.

1.1. Background

1.1.1. Hydrodynamic Cavitation

Hydrodynamic cavitation is the most commonly thought of cavitation process. This type of cavitation is induced by the flowing of a liquid which presents a pressure gradient. This type of cavitation was first observed by naval engineers who witnessed significant wear in propellers in the form of dents on the metal blades. Soon it was noted that the creation and implosion of bubbles near the metal surface was the cause of the surface fatigue. The bubbles were formed due to low pressure regions which occurred in high velocity areas. This relationship between velocity and pressure can be expressed with Bernoulli’s equation as shown in chapter 2. Hydrodynamic cavitation has historically been an issue for machines and components such as hydraulic turbines, pumps and blades. The presence of cavitation in these types of flow systems presents negative effects such as noise and erosion which lead to a reduction in performance quality overtime. As such a powerful phenomenon, applications can benefit from the energy that is released. Two examples of nature utilizing and taking advantage of this are the mantis shrimp described above and the pistol shrimp. Similar to the mantis shrimp, the pistol shrimp utilizes cavitation to obliterate its prey. Figure 1 on the right shows the pistol shrimp’s claw which is snapped shut in a matter of

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Figure 1: Timed frames of pistol shrimp “shooting” a cavitation bubble from its claw [5].

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microseconds. The quick acceleration of the surrounding liquid causes the local pressure to drop and the water to vaporize due to a lower boiling point. This creates a cavitation bubble.

1.1.2. Acoustic Cavitation Acoustic cavitation, like hydrodynamic cavitation, is produced by pressure differentiations present in fluid flow. This change in pressure arises due to incident sound waves in the ultrasound frequency range of 22 KHz to 1 MHz [4]. Microscopic gas bubbles result from the conversion of kinetic energy from vibrations to the heating of the liquid. The bubbles quickly grow during rarefaction half-cycles of the applied longitudinal wave. This growth is due a term known as rectified diffusion which is mass transfer in the form of gas into the bubble. When the bubbles reach a critical diameter, they quickly collapse [4]. Often times, there is an emission of energy in the form of photons during the collapsing phase. This is called sonoluminescence.

1.1.3. Particle Cavitation

Particle cavitation is the formation of bubbles through rapid-heating caused by ionized particles such as neutrinos. The medium through which the charged particle passes, quickly absorbs energy that is present from a leftover ionized trail. Boiling in the liquid will occur due to a thermal shock and cavities will form [4].

1.1.4. Optical Cavitation Optical cavitation, similar to particle cavitation, is induced through the deposition of energy into liquid. The formation of a vapor bubble occurs by focusing a laser into an absorptive liquid. Optical cavitation occurs when a laser superheats an absorptive liquid and creates a vapor bubble. When the vapor bubble collapses, energy is emitted in the form of an acoustic shockwave [4]. Optical cavitation includes two types: thermocavitation and ionocavitation. The distinction comes from the method in which the liquid is heated. Optical thermocavitation, as opposed to ionocavitation, is described by a process where the laser directly superheats the liquid to a critical temperature beyond its boiling point. Continuous wave (CW)

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lasers produce this as opposed to pulsed wave lasers which carry high energy density per pulse. The use of pulsed lasers ionize the liquid into plasma which then becomes the source of heating for surrounding liquid. Rastopov and Sukhodolsky induced optical thermocavitation with continuous wave (CW) lasers in the 1990s as a way to study fluid composition [1, 2]. The use of low-power CW lasers for inducing cavitation has paved the way for many applications because of their simplicity and low cost. 20 years after Rastopov and Sukhodolsky observed CW cavitation, Ramirez-San-Juan, et al produced cavitation using a CW laser focused into a saturated solution of copper nitrate [3]. Their research investigated the relationship between cavitation frequency and laser power. Increasing laser power correlates to an increase in the frequency of cavitation events. This project builds off of their findings and aims to expand on CW laser induced cavitation for thermal management applications.

1.2. Project Motivation

The study of cavitation has evolved from learning how to prevent an undesirable, damaging phenomenon to developing methods of inducing cavitation for beneficial applications. Examples of these applications are in the fields of biomedicine and fluid controls such as Laser-Assisted Surface Cooling Enhancement (LASCE) and Skin Poration by Optical Cavitation (SPOC). LASCE and SPOC are applications being developed in Dr. Aguilar’s laboratory. SPOC is a drug delivery method that seeks to benefit from the energy released upon the collapsing of a cavitation bubble and using it to porate skin temporarily in order to have direct access for drug delivery. LASCE aims to achieve cooling a targeted region by taking advantage of the convection and induced mixing that occurs during the collapsing phase of a vapor bubble. As the bubble pushes heated liquid away from the site of cavitation, cold liquid travels inward toward the site of cavitation. Figure 1 shows this dispersal of hot liquid after cavitation.

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Figure 2: Still frames showing collapse of cavitation bubble. Markings indicate scale of 1 mm. 1) Maximum diameter 2) collapse 3) ejection of hot fluid.

To advance these applications, the effects of CW laser-induced cavitation on its surroundings must be understood. A non-intrusive technique called was Planar Laser-Induced Fluorescence (PLIF) was developed to measure the temperature field around a cavitation bubble. Further improvement of PLIF will not only advance the progress of LASCE, but will also open doors to applications in the fields where controlled cavitation may be beneficial such as biomedicine, fluid controls, and microfluidics. Before advancing towards these applications, there are additional cavitation dynamics to be explored. Certain applications may be sensitive to thermal and acoustic damage; research is needed to mitigate these side effects. The effects of multiple cavitation events in sequence must also be explored. It is very difficult to precisely control the frequency of cavitation events. Depending on conditions, Dr. Aguilar’s laboratory has recorded frequency of bubble formation up to 150 Hz. As the number of vapor bubbles formed increases, the likelihood of interference between each event also increases. Literature on the effects of multiple bubbles is scarce, which makes it difficult to gauge the impact each successive event has on the process. If scientists were able to know the fluidic effects corresponding to bubble frequency, then they will be able to advance and optimize efficiency of applications such as LASCE.

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In addition to exploring the number of bubbles that optimizes LASCE, the shockwave phase of the vapor bubbles will also be studied. By understanding the factors that contribute to the magnitude of the energy, conditions can be altered to minimize damaging effects. Understanding this will also help in determining the appropriate number of bubbles that can produce the best cooling for purposes of LASCE. Researching these topics will not only help improve Dr. Aguilar’s experiments, but it will also be applicable to other cavitation types and their impacts on various equipment such as damage on watercraft propellers produced by hydrodynamic cavitation. Ultimately, the objective of this study is to deeply examine the fluid mechanics occurring in these events. Future work will be done to further answer the following questions: 1) what factors determine energy output and how can they be avoided and; 2) how do the interactions of multiple cavitation events in sequence look like. By understanding these areas and incorporating PLIF, applications proposed in Dr. Aguilar’s University of California Riverside laboratories such as Laser-Assisted Surface Cooling Enhancement and Skin Poration by Optical Cavitation can be executed. Chapter 1 builds background and presents types of cavitation (hydrodynamic, acoustic, particle and optical) as well as the project description. Chapter 2 will introduce the fluid dynamics behind the formation of cavitation events and the Rayleigh-Plesset equation which governs a bubbles’ growth and collapse. The experiments completed at the University of California Riverside laboratory, will be presented in Chapter 3. This will include the optical setup used along with experiments. Chapter 4 discusses the preliminary results achieved during the summer of 2015 and the events that were produced while inducing OTC and their effects on the system. Finally, Chapter 5 concludes the thesis with discussion on future work.

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Chapter 2 Bubble Dynamics and PLIF To understand the process of cavitation, it is necessary to have an overview of fluid mechanics. This chapter briefly describes the evolution and stages of a cavitation bubble’s lifetime and provides fundamental background and definitions of terms needed to understand the dynamics of cavitation.

Continuous and Pulsed Lasers As described in Chapter 1, optical cavitation can be achieved through different types of lasers: continuous wave and pulsed lasers. Pulsed lasers operate with a beam power that comes in pulse durations of time ranges from microseconds to milliseconds. The distinguishing feature of the pulsed laser is the ability to rapidly release high energy with power outputs peaking up to megawatts. Continuous wave (CW) lasers on the other hand operate at stable average continuous beam powers much lower than pulsed lasers. Although inducing cavitation with pulsed lasers is achieved more commonly, the experiments presented in this project are done so with a CW laser. Lower operating costs along with lower energy densities and average power outputs make CW favorable for use with patients in biomedical applications. Optical cavitation is the rapid process of vaporization of a liquid due to optical energy. The process creates a bubble whose eruption emits a powerful acoustic shockwave. The life of an optical cavitation bubble can be further investigated in five stages: irradiation, nucleation, growth, collapse and rebound [5]. Each period develops differently for CW and pulsed lasers.

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Irradiation is the period for which absorption of optical energy occurs. For a CW laser, this period occurs throughout the cavitation process with a decrease in irradiation as the bubble grows in diameter. For a pulsed laser, irradiation occurs only when the laser is active. Previous studies have shown that irradiation with a pulsed laser excites the liquid so intensely that the atomic level is affected. The liquid molecules release electrons and form plasma which continues to super heat the surrounding liquid even after, a process that CW lasers do not produce [6]. Nucleation is the breaking down of the liquid’s molecules which allows for energy to lead to vaporization. The bubble begins to grow and sees sizes of microns for pulsed lasers and diameters up to 5 mm for CW lasers. Higher laser power correlates to smaller and faster formation of bubbles [7]. The bubbles collapses as soon as the pressure within the bubble falls short of the local pressure outside. Lauterborn and Bolle experimentally observed the collapse shapes of a cavitation bubble near a solid boundary [6]. Figure 3 depicts the general shapes the scientists observed. It is significant to note that the surface of the bubble furthest from the boundary collapses quicker and produces a polar jet.

The quick formation of this shape causes the surrounding liquid to be pulled into the site of cavitation and produce mixing and convection, cooling the area.

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Figure 2.1: Bubble collapse near solid boundary based on results from L and Bolle.

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This is where the basis of the LASCE project stands; with the hypothesis that accurate cooling can be obtained by controlling the properties of the bubbles. The rebound period includes the formation of powerful acoustic waves and secondary waves of bubbles [4].The emitted energy is what makes cavitation an interesting phenomenon to study. The strong shockwave has previously produced negative damages but researchers are looking for cases in which a controlled effect can create beneficial outcomes. To achieve regulated outcomes, it is necessary to understand the underlying fluid mechanics occurring in cavitation events.

Dynamics In general, fluid mechanics is the study of fluids in interaction with other fluids or solids. Fluid mechanics can be further split into three branches: gas dynamics, aerodynamics and hydrodynamics. The cavitation process investigated in this thesis falls under hydrodynamics which is the study of motion of fluids. Fluids can be distinguished from solids by applying a shear stress. The definition of shear stress is a force per unit area acting tangent to the area. Under the influence of shear stress, fluids deform continuously while solids reach a critical angle and stop deforming, eventually breaking. A fluid that deforms uniformly is said to be a Newtonian fluid while a non-uniform, continuous deformation describes a non-Newtonian fluid. This thesis focuses on cavitation bubbles in a Newtonian fluid. A fluid can be further split into a liquid and gas depending on the density properties. For the purposes of this thesis, a liquid will be assumed to be incompressible. An incompressible fluid is one which density does not vary with time. Another term worth describing is viscosity, which can be defined as internal cohesive forces between molecule collisions in fluids. There are two general degrees in which viscosity can be used to describe liquids: viscous and inviscid. First, a viscous flow is one in which the friction forces are significant while an inviscid flow is when the forces are negligible. In fluid mechanics, Bernoulli’s equation can be used in the cases of inviscid and incompressible fluids. The equation shows the relationship between pressure and velocity and elevation.

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! + 12 !!

! + !"ℎ = !"#$%&#% P is the pressure, ! is density of the fluid, V is its velocity, and g and h are the gravitational acceleration and elevation respectively. Regions of flow with high velocity are thus present in low pressure regions which runs with the possibility of cavitation occurring. This is because lower pressure correlates to a lower boiling temperature and a phase change occurs if the pressure of the liquid drops lower than the vapor pressure. Vapor pressure is defined as the pressure exerted by the vapor when in “equilibrium” [7]. At a given temperature, the vapor and liquid are in equilibrium when the exiting evaporation rate equals the condensation rate. This is equivalent to the saturation pressure, which can be described as the pressure at which a phase change occurs at a given temperature.

In fluid dynamics there are two points of views to analyze motion: Lagrangian and Eulerian. The Lagrangian point of view entails following the individual particles of the fluid throughout the whole process while the Eulerian point of view is composed of an open system or a fixed control volume through which energy and mass can flow through and be analyzed. Cavitation bubbles are described in the Eulerian point of view.

Cavitation Number

In engineering and the sciences, many equations are used to describe and calculate events. In order for scientists to correctly evaluate and compare solutions across fields, it is important to use similar factors to measure up against. Standardizing methods of measurement and making equations be independent of parameters and variables is an excellent method vastly used in fluid mechanics. Such equations are called dimensionless which means exactly that, the yielded values are without dimensions. One of these important dimensionless parameter is the cavitation number which is used in measuring the degree of development of cavitation.

!! = !!!! − !!!Δ!

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!! !is noted as a reference pressure taken far from the site. !! is the vapor pressure. Ρ is the density of the liquid, which is assumed incompressible meaning that the density is constant. Because cavitation occurs when fluid pressure drops below the vapor pressure, a high cavitation number will denote a non-cavitation region. [8]. When a fluid suddenly drops below the vapor pressure, cavitation will occur because lower pressures equate to lower boiling points and the liquid will quickly evaporate. This evaporation can be due to a few methods, the two more common ones being 1) an increase in fluid velocity flow which causes the pressure to decrease and evaporation to occur, and 2) an increase in temperature which instantly superheats the liquid. The cavitation number is most often used to describe hydrodynamic cavitation thus we use the Rayleigh-Plesset equation to describe optical cavitation.

Rayleigh-Plesset Equation

The study known as bubble dynamics began with physicist Lord Rayleigh who was investigating the damaged caused by cavitation on ship propellers. His work has since been refined and provides an ordinary differential equation known as the Rayleigh-Plesset equation. This equation can be used to model cavitation bubbles through their collapsing phase and describe the relationship between a bubbles size evolution and pressure.

! !!!!"! +

32!"!"

!= 1! [ !! − !!!(!) +!!!! !

!!!

!!− !2!!!

− 4!!

!"!" ]

R is the bubble radius as shown in figure X. the driving term !! − !!!(!) shows up in a similar way as in the cavitation number. This term determines the evolution of the bubble size. The second term on the right hand side, contributes calculation of non-condensable gas in the bubble. The third and fourth terms contribute the surface tension and the dynamic viscosity. [8]

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The second order differential equation can be derived from the conservation of mass and conservation of momentum equations. There are many assumptions made such as spherical symmetry, making the equation fairly inaccurate. Scientists are building computational models that can more accurately describe the cavitation collapse. The derivation for the equation presented here can be followed in Appendix A.

To simplify the equation, we can assume the following:

• Fluid is measured as an incompressible liquid which means that the density stays constant with time.

• Flow is considered inviscid which means that the viscous forces are negligible.

After these assumptions the Rayleigh-Plesset equation simplifies to:

! !!!!"! +

32!"!"

!= !! − !!! !

!

This simplified equation can be integrated twice to fin the collapse time based on the bubble’s maximum diameter:

! = 0.915!!"#!

!! − !!!.!

The bubble energy can also be pulled from the Rayleigh-Plesset equation. This energy is a potential energy that is determined by pressure differences from inside and outside the bubble. This value also depends on the maximum bubble size.

! = 43!!"#

! (!! − !!)

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Figure 2.2: Energy levels for a nucleus with spin quantum number ½. Frequencies with energy magnitudes of ∆! = ћ!! are needed to induce a transition from one state to another.

The potential energy of the bubble is what determines the magnitude of the shockwave. This powerful shockwave, if controlled or mitigated, can provide beneficial outcomes for applications. For example, enhancing the shockwave’s impact for skin poration can ensure enough strength to penetrate only through the desired layer.

Fluorescence Fluorescence, in a general definition is the emission of electromagnetic radiation with wavelengths in the range of visible light. Fluorescence is a branch of photoluminescence which is the generation of photons by exciting molecules with radiation. Essentially, the process can be described in three steps, 1) absorption, 2) relaxation and 3) emission. First, nuclear spin states absorb energy and jump energy states as shown in Figure 4. The electrons then vibrate in the exited energy states and later fall to the ground state. While the electrons transition from their current energy level the lowest state, they emit photons with an energy equal to: ∆! = ћ!!.

Planar Laser Induced Fluorescence

Planar Laser-Induced Fluorescence (PLIF) is an optical technique often used for quantitative measurements for velocity, concentration and temperature. Here we discuss the method in context of temperature measurements. This is because it provides a non-intrusive method of measuring the temperature field of

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cavitation bubbles. The setup used is discussed in the following chapter. It is composed for an illuminating laser and optical components such as mirrors and lenses to produce a sheet of light. This sheet is used as a source of energy which is absorbed by the medium in which cavitation occurs. The absorption causes the solution to fluorescence with certain magnitudes. The strength of the fluorescence is related to the temperature of the solution.

In PLIF, a laser is used to excite a tracer dye such as fluorescein or rhodamine. The tracer absorbs the energy and spontaneously re-emits photons as fluorescence. The laser used must have power within the absorption band of the dye used. CW lasers in the range of 480 nm and 515 nm are most commonly used in experiments. Additionally, rhodamine B along with other rhodamine dyes are most commonly used as tracers because they are water soluble and are thus less likely to interfere with solution properties [2].

In order to achieve the planar part of the name, a light source incident to the solution must be a plane. To achieve this, a cylindrical lens is used. Another approach is using a rapidly rotating mirror to scan the area multiple times.

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Chapter 3

Experimental Methods

While cavitation has long been viewed as an undesirable, damaging

phenomenon, scientists have explored applications of cavitation in the biomedical and fluid control fields. Optical thermocavitation is a process in which a laser is focused into an absorptive liquid, causing it to superheat. This leads to the creation, growth and collapse of a vapor bubble.

Applications such as laser-assisted surface cooling enhancement and skin poration by optical cavitation are being developed in Dr. Aguilar’s laboratory in the University of California Riverside. The former seeks to achieve cooling through natural convection and induced mixing while the latter is a drug delivery method that works by puncturing the outer layer of skin. To explore the dynamics of bubble formation and its effects on surroundings, a technique was developed to measure the temperature field around a cavitation bubble. The non-intrusive technique is called Planar Laser-Induced Fluorescence. This chapter will describe the experimental setup and method completed to achieve the results presented in Chapter 4.

Experimental Setup

Conventional temperature sensors such as resistant temperature detectors are prone to damage from shock waves and also interfere with flow during the cavitation process. We have developed Planar Laser-Induced Fluorescence (PLIF), a non-intrusive method of measuring the temperature field around cavitation bubbles. This is critical to the execution of LASCE. Figure 3.1 illustrates

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the experimental setup of PLIF with the optical elements and the laser paths shown.

A glass cuvette holding an absorptive aqueous solution of copper nitrate (CuNO4, 24% by mass in water) and Rhodamine-B (100mL water to 0.01grams of Rhodamine-B) sits on an adjustable table with resolution movement of 1 micron. An 810 nm diode laser is focused into the copper nitrate aqueous solution. The CW laser provides an uninterrupted beam of light powered by a variable board of 0-30 watts. The copper nitrate mixture was chosen as the absorptive solution due to its high absorption coefficient at the pump laser of a wavelength of 810 nm [3]. The 810 nm light is passed through a focusing lens with a focal distance of 25.4 mm and is absorbed by the copper nitrate, leading to cavitation. The pump laser is also used to trigger the camera by directing part of the ray with a dichroic mirror into a photodiode (DET10A Si Biased Detector) which is connected to an Arduino that outputs a signal to the camera. The Arduino circuit and code are presented in Appendix B.

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Figure 3.1: Planar Laser-Induced Fluorescence experimental diagram. The probe laser is directed coaxially to the cavitation-inducing pump laser, and induces fluorescence in the Rhodamine-B. The high-speed camera records a short video used for image analysis.

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At the same time, a 440 nm laser coaxial to the pump laser passes through a cylindrical lens and induces fluorescence in the Rhodamine. The cylindrical lens turns the laser output from a symmetric beam to a sheet of light which allows for imaging analysis on a single plane. The fluorescence is measured by a high speed video camera (Miro, M310) at 2000 frames per second and a resolution of 1280 x 800 pixels. The HS camera utilizes two filters limiting the light that passes through to only yellow, the fluorescence color. The fluorescent intensity of the Rhodamine depends on temperature as shown in Graph 3.2; thus, measuring the fluorescence allows temperature to be determined.

Procedures

To implement PLIF as a technique to measure the temperature field of a vapor bubble, it was necessary to verify that the solution was not influencing the cavitation process. Secondly, a calibration curve relating various temperatures and the fluorescence intensities had to be developed.

Absorption Spectrum

First, the absorption coefficients of the solution of copper nitrate, Rhodamine-B and water were found. Graph 1 shows the absorption coefficients (α) vs six different wavelengths (405 nm, 440 nm, 520 nm, 543 nm, 638 nm and 810 nm) where 810 nm is the wavelength of the pump laser and 440 nm is the wavelength of the PLIF laser. Each laser was operated with different voltage magnitudes due to the fact that some were absorbed more than others. This inconsistency in current and voltage can be ignored as the absorption coefficients are independent of voltage and are only affected by distance and

Wavelength (nm)

Current Limit (mA)

Voltage (V)

405 200 4

440 1600 5.5

520 200 5.5

534 200 4

638 900 5

810 --- ---

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properties of the medium the beam travels through. The table on the right shows the limiting current for each laser to keep them from burning out. The coefficients were found by setting up the respective wavelength diode laser in a heatsink and aiming the light through a glass cuvette and into a Newport Model 1815 C power meter. Neutral density filters with values of 1.0, 0.6 and 0.3 were mounted on the detector to protect it from high intensities. These filters decrease the intensity of the incident light by a certain percentage. The power meter was set with the appropriate calibration factor and two measurements were made at each wavelength. The first value recorded was the power reading with an empty cuvette and the second value recorded was the power reading with the solution. The setup is shown in Figure 3.2 with a top view and front view.

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Figure 3.2: Top image shows a top view of the power meter setup. Bottom image presents a front view of power meter setup.

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Beer’s Law was then used to calculate the absorption coefficient:

! = !− !! !"

!!!

,

where ! and !! are the power readings with the absorptive solution and without respectively. d is the distance traveled by the laser through the solution; the dimensions of the cuvette provide a 1cm path. It is important to note that the absorption of the PLIF laser is several magnitudes less than the 810 nm pump laser. The absorption coefficient of the pump laser is about 9 and the absorption coefficient of the 440 nm probe laser is less than 1. Since every increment of ! is a tenfold increase in absorption, the pump laser is 10! times more absorbent.

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Graph 3.1: Absorption coefficient of the solution at 6 different wavelengths.

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Temperature Calibration Curve

To correlate the fluorescence of the vapor bubble to the temperature at a certain point, a temperature calibration curve was developed. The solution was stirred and heated on a hot plate. Two concentrations of Rhodamine-B were used, the first with 2 drop per 10 mL of copper nitrate solution and the second with 5 drops to the same volume. The temperature was increased in increments of 10°! from 25°! to 75°!, and a video of 100 frames was captured. ImageJ, an image processing and analysis software was used to analyze the stack of 100 frames

and calculate the average intensity (RGB-pixel average) over the entire spatial field of the camera at each temperature. It is difficult to see the intensity differences in a still image with the bare eye, thus Figure 5 is an image of a collapsing bubble that shows a spectrum of fluorescent intensities. This figure includes green and red refractions from the pump laser guide light and the probe laser which contributes artificial fluorescence. This was later avoided by including a long and a short pass filter with the wavelengths of 550 nm and 650 nm respectively [5].

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Figure 3.3: PLIF image capture by camera of cavitation event

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A linear relationship between the temperature and intensity was found for both concentrations. Collaborators from Mexico have computationally determined that the lasers heat up the solution up to 250°C or higher before cavitation

occurs.

Currently, the assumption that rhodamine fluorescence follows a linear trend is made. This is an approximation that other research groups have made, but extrapolating to such far temperatures may produce less accurate measurements.

PLIF, as a method to measure the temperature field of a cavitation bubble, is very accurate as the high fluorescence allows for a camera frame rate of 2000 fps. The technique is truly only limited by the image noise that arises when measuring the fluorescence intensity. Small fluctuations in color of pixels is presented during analyzing a cavitation video which is divided into a stack of

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Graph 2: Average fluorescence vs temperature for two concentrations. One drop of Rhodamine-B measured 36.8 µL in volume.

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still images. The settings of the high speed video presents artificial noise which cannot be fixed by longer exposure times. For this reason, the cell size used during image analysis was varied to determine which amount provided more accurate results. A single stack can be analyzed with different cell sizes which is determined by the size of elements used to divide an image in a video of 300 frames was analyzed in order to show the increase in noise with higher number of cells used. Figure 3.4 depicts how the images are divided into cells. The number of cells can be controlled based on user input and the program measures the average RGB intensity of each cell and cycles through the stack in order to record a chronological evolution of the temperature. The average RGB values correlate to the temperature of the liquid.

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Figure'3.4:'Still'images'showing'fluorescence'of'rhodamine'B.'Normal'image'on'the'left'and'still'image'on'the'right'with'cells'overlapping.'

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Graph 3 shows the relationship of pixel noise (measured in standard deviation of fluorescence intensity) to the number of cells in the analysis. A lower noise without sacrificing resolution is ideal. The increase in noise level between 256 cells and 1024 cells is minimal, but the image analysis algorithm takes days to deliver thus a cell size between those values is favored.

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Graph 3: Standard deviation vs number of cells analyzed.

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Chapter 4

Results

Image analysis was conducted on 300 stacked images for cavitation induced at 5 watts. The stack was recorded at 2000 fps, giving 500µs per frame; or not enough to analyze bubbles with lifetimes of half of that. Nevertheless, the main intent of PLIF was to make temperature measurements upon collapse of bubbles and the evolution of the solution’s behavior after that. Future work will be aimed at fixing that time resolution.

The mixing phase occurs for about 150 ms after the collapse of the bubble. Hot liquid is ejected from the site of cavitation and induces convection, which has shown to significantly reduce the temperature and heat collected during bubble growth.

While using PLIF has been demonstrated effective for analyzing temperatures, it is not ideal for visualizing the phases or effects occurring during cavitation. Using a 520 nm laser for luminescence allows us to see the phases of a cavitation bubble. Figure 4.1 shows temperature measurements 0 ms, 5 ms and 30 ms upon collapse of the bubble. The images are from top to bottom: the phase contrast achieved by using the 520 nm laser, PLIF image taken from camera with cells overlaid and the temperature contour map created by image analysis and the information from the calibration curve.

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Thermal Lensing and Boundary Layer

A previous study focusing on measuring cavitation frequency has noted the existence of a thermal lensing effect causing the cavitation events to occur near the cuvette wall [5]. This seems to hold regardless of the position of the laser’s focal point. Ongoing work is being completed to further understand the degree of this effect.

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Figure 4.1: Mixing phase upon start, 5 ms and 30 ms. From top to bottom, the images are phase contrast, PLIF and contour temperature map.

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Due to the PLIF setup only allowing video capture of fluorescence – a relatively dim source of illumination, a separate setup was used to have a more direct visual of the cavitation. A 520 nm laser pointed directly at the camera was used as an illumination light source. This setup allows for the thermal lens to be seen as well as the growth of the thermal boundary layer, but does not provide for quantitative temperature measurement.

Thermal lensing is when the index of refraction of a medium changes due to a change in temperature. The boundary layer is a plane of surrounding liquid that is affected by the laser and flows upward continuously.

Adjusting the focal point of the pump laser within the liquid does not shift the site of cavitation. This can be attributed to the heating of the liquid and creation of a thermal lensing effect. Current experimentation is being carried to measure the degree of this phenomenon. The beam size of the pump laser is measured at different distances from the 25.4 mm focusing lens. A long pass filter of 750 nm must be used to block the red guide beam and only capture the 810 nm pump laser. Recording measurements at increments of fractions of millimeters will allow the diffraction and converging point due to the thermal lensing be observed. Phantom Control Camera is a video analysis software that allows the measurements of the beam size.

Figure 4.2 shows a thermal lens along with a dark shadow which depicts a boundary layer. A layer of surrounding liquid is affected by the pump laser and flows upward continuously.

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Figure 4.2: Still frames showing induced thermal lensing and thermal boundary layer growth near cuvette wall. From left to right: no heating, laser on, heated liquid.

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Chapter 5

Conclusion

This project serves to enable thermal characterization of cavitation bubbles, a necessity for LASCE and other applications. Natural convection and mixing occurs upon collapse of a cavitation bubble and thermal studies are needed to analyze the degree to these effects. Conventional temperature probes are prone to damage and are not sensitive enough to measure the temperatures. Thus PLIF was developed, a non-intrusive technique. Planar laser induced fluorescence was used to make accurate quantitative temperature measures for the cavitation irradiation, and mixing after collapse. PLIF uses Rhodamine-B in an aqueous copper nitrate (CuNO4, 24% by mass in water) solution. Rhodamine-B fluoresces when exposed to a 440 nm wavelength laser. We developed a calibration curve relating the measured intensity with temperature. First, the fluorescence intensity was measured against temperature in increments of 10℃ from 25℃ to 75℃, and a linear relationship was found. The fluorescent intensity decreases by approximately 10% for each interval. Second, the optimal concentration of Rhodamine-B in the solution was determined. At room temperature, we found that as the concentration went from 2 droplets of Rhodamine-B to 5 droplets per 10 mL of aqueous CuNO4, the average fluorescence increased from 37.1 (RGB-pixel average) to 86.6.

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Phase contrast image analysis shows temperature changes and flows induced by cavitation bubbles. Laser heating produces a thermal boundary layer near the wall of the cuvette. The ejection of fluid upon the collapse of the cavitation bubble forces mixing and cooling at the site of cavitation.

Before advancing towards applications of LASCE, there are additional cavitation dynamics to be explored. The ratio of energy to induce cavitation needs to be minimized to enhance cooling effectiveness. Certain applications may be sensitive to thermal and acoustic damage; research is needed to mitigate these side effects. Further development of this technique will open doors to further applications in biomedicine, fluid controls, cooling, microfluidics, and nanomaterials.

Future work includes improving the optical setup to allow for simultaneous use of PLIF and Spatial Transmission Modulation (STM), a technique to measure

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Figure 3: Collapse of cavitation bubble 1) Before laser is on 2) Maximum diameter of

bubble 3) Dissipation of heated liquid.

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cavitation frequency. This adjustment will allow the measurement of frequency, size and temperature cavitation bubbles all at once. The team will also investigate the effects of different absorptive solutions such as a carbon-nanotube and methanol mixture because the degradation rate of the current solution could be improved.

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Bibliography

[1] Patek, S.N. and Caldwell, R.L. Extreme impact and cavitation forces of a biological hammer: strike forces of the peacock mantis shrimp Odontodactylus scyllarus. The Journal of Experimental Biology 208 (2005).

[2] Ramirez-San-Juan, J.C., et al. Cavitation induced by continuous wave lasers. 2007. [3] Kim. Ki-Han, Chahine. Georges, Franc. Jean-Pierre, Karimi. Ayat. Advanced

Experimental and Numerical Tecniques for Cavitation Erosion Prediction. Springer Dordrecht Heidelberg New York London. 2014

[4] Shah. Y. T., Pandit A.B., Moholkar V. S.. Cavitation Reaction Engineering. Springer Science and Business Media New York. 1999.

[5] D. Banks, M. Daniels, G. Aguilar. “Recent Advances in Optical Thermocavitation.” [6] University of Twente. The Physics of the Snapping.

http://stilton.tnw.utwente.nl/shrimp. 2000. [7] S. F. Rastopov and A. T. Sukhodolsky, “Cluster nucleation in the process of CW

laser induced thermocavitation,” Phys.Lett. A 149, 229 (1990). [8] S. F. Rastopov and A. T. Sukhodolsky, “Sound generation by thermocavitation

induced CW-laser in solutions,” Proc. SPIE1440, 127 (1991). [9] J. P. Padilla-Martinez, C. Berrospe-Rodriguez, G. Aguilar, J. C. Ramirez-San-Juan,

and R. Ramos-Garcia, Physics of Fluids (2014). [10] D. Banks, M. Daniels, C. Ajawara, and G. Aguilar., Frequency and Bubble Size in

CW Optical Cavitation, in ILASS Americas 27th Annual Conference on Liquid Atomization and Spray Systems, Raleigh, NC, May 2015

[11] Y. A. Cengel, J. M. Cimbala, Fluid Mechanics Fundamentals and Applications Third Edition, McGraw-Hill New York, 2014.

[12] D. Banks, “Enhanced Cooling for High Heat Flux Applications Using Droplet Impact and Optical Cavitation”, University of California August 2015

[13] Boulais, E., R. Lachaine and M. Meunier (2012). "Plasma Mediated off-Resonance Plasmonic Enhanced Ultrafast Laser-Induced Nanocavitation." Nano letters.

[14] Ld’ Agostino, M. V. Salvetti, Fluid Dynamics of Cavitation and Cavitating TurboPumps. SpringerWien NewYork, 2007.

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Appendix A:

Derivation of Rayleigh-Plesset Equation

The second order differential equation can be derived from the conservation of mass and conservation of momentum equations. We begin with the mass conservation equation, also known as the continuity equation for a control volume

0 = ! !"!" !" + ! !! ⋅ !!!!"!

!"!!"

The first term is the time rate change of mass through the control group while the second term is the net mass flow rate through the control surface. The surface integral can be further split into two parts, one for the inlet flow stream and the second for the outlet flow stream. These two parts can be written in terms of mass flow rate.

!"!" !" = ! !!"

!!" − ! !!"#

The left hand side volume integral which describes the rate of change of mass in the control volume can be rewritten with infinitesimally small volume of Cartesian coordinates for simplification:

!"!" !" = !

!"!"

!!" !!"!!"!!"

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The right hand side of equation X with the net mass flow rate is Taylor expanded at each component for both the inlets and outlets from the control volume. After further simplification, the continuity equation becomes:

!"!" + ∇ ! ⋅ (!!)

We model cavitation bubbles as spheres and call the bubble radius R(t), the velocity U and pressure P are functions of time and r, the radial distance from the origin.

We can thus use the continuity equation in spherical coordinates:

!"!" +

1!!!"!!!!" + 1

! sin !!"# sin !

!" + ! 1! sin !

!"#!" = 0

Figure 3: Figure showing geometry of bubble from fundamentals of cavitation book

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We can simplify this equation by making assumptions that will remove certain terms. We begin by assuming that the liquid is incompressible thus making density independent of time. Next we can assume that the bubble is symmetrically spherical which means that velocity and pressure vectors only depend on the distance r and not !!or !. The equation is then simplified to:

1!! !

!!" ! !

!! !, ! = 0

Solving the differential equation and applying the no-slip boundary (velocity of liquid at boundary of bubble is same as rate of growth of bubble’s radius) condition yields an expression for the velocity:

! !, ! = !!

! !"!"

Then using the incompressible Navier-Stokes equation, a non-linear partial differential equation describing motion of parcel of liquid, where ! is the

dynamic viscosity and ! is the velocity of the fluid

! !!!" = !−∇! + !!! + !∇!!!

We can expand into spherical coordinates and by symmetrical spherical geometries we can cancel all partial derivatives of !!and ! giving us:

− 1!!" !, !!" = !!"!" + ! !"!! !!

After substituting equation y into equation z and integrating from R to infinity, we get the Rayleigh-Plesset equation.

! !!!!"! +

32!"!"

!= 1! [ !! − !!!(!) +!!!! !

!!!

!!− !2!!!

− 4!!

!"!" ]

Which, after assumptions are made can be simplified to equation t. First, the fluid is measured as an incompressible liquid which means that the density stays constant with time. Secondly, the flow is considered inviscid which means that the viscous forces are negligible. Even after making these assumptions, the

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equation doesn’t accurately describe model for hemispherical bubbles near solid boundaries because thermal differences are neglected even though optical cavitation operates through a large thermal difference.

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Appendix B:

Circuit Schematic and Arduino Code

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