Mechanism of sonoluminescence
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Sonoluminescence
Sonoluminescence
Sonoluminescence is the emission of short bursts of light from imploding bubbles in a liquid when excited by sound.-History:The effect was first discovered at the University of Cologne in 1934 as a result of work on sonar. H. Frenzel and H. Schultes put an ultrasound transducer in a tank of...

 is a phenomenon that occurs when a small gas bubble is acoustically suspended and periodically driven in a liquid solution at ultrasonic frequencies, resulting in bubble collapse, cavitation
Cavitation
Cavitation is the formation and then immediate implosion of cavities in a liquidi.e. small liquid-free zones that are the consequence of forces acting upon the liquid...

, and light emission. The thermal energy that is released from the bubble collapse is so great that it can cause weak light emission. The mechanism of the light emission remains uncertain, but some of the current theories, which are categorized under either thermal or electrical processes, are Bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

 radiation, argon rectification hypothesis., and hot spot. People are beginning to lean more towards thermally processes because temperatures have consistently been proven with different methods of spectral analysis. In order to understand the light emission mechanism, it is important to know what is happening in the bubble's interior and at the bubble's surface.

Current Competing Theories

Prior to the early 1990s, the studies on different chemical and physical variables of sonoluminescence were all conducted using multi-bubble sonoluminescence (MBSL). This was a problem since all of the theories and bubble dynamics were based on single bubble sonoluminescence (SBSL) and researchers believed that the bubble oscillations of neighboring bubbles could affect each other. Single bubble sonoluminescence wasn't achieved until the early 1990s and allowed the study of the effects of various parameters on a single cavitating bubble. After many of the early theories were disproved, the remaining plausible theories can be classified into two different processes: electrical and thermal.

Single-Bubble Sonoluminescence (SBSL)

SBSL emits more light than MBSL due to fewer interactions between neighboring bubbles. Another advantage for SBSL is that a single bubble collapses without being affected by other surrounding bubbles, allowing more accurate studies on acoustic cavitation and sonoluminescence theories. Some exotic theories have been made, for example from Schwinger in 1992 who hinted the dynamical Casimir effect
Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, like capacitors placed a few micrometers apart, without any external electromagnetic field...

 as a potential photon-emission process. Several theories say that the location of light emission is in the liquid instead of inside the bubble. Other SBSL theories explain, that the emission of photons due to the high temperatures in the bubble are analogical to the hot spot theories of MBSL. Regarding the thermal emission a large variety of different processes are prevalent. Because temperatures are increasing from several hundred to many thousand kelvin during collapse, the processes can be molecular recombination, collision-induced emission, molecular emission, excimers, atomic recombination, radiative attachments of ions, neutral and ion Bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

, or emission from confined electrons in voids. Which of these theories applies depends on accurate measurements and calculations of the temperature inside the bubble.

Multi-Bubble Sonoluminescence (MBSL)

Unlike single-bubble sonoluminescence, multi-bubble sonoluminescence is the creation of many oscillating and collapsing bubbles. Typically in MBSL, the light emission from each individual bubble is weaker than in SBSL because the neighboring bubbles can interact and affect each other. Because each neighboring bubble can interact with each other, it can make it more difficult to produce accurate studies and to characterize the properties of the collapsing bubble.

Bubble Interior

One of the greatest obstacles in sonoluminescence research has been trying to obtain measurements of the interior of the bubble. Most measurements, like temperature and pressure, are indirectly measured using models and bubble dynamics.

Temperature

Some of the developed theories about the mechanism of SBSL result in prognoses for the peak temperature from 6000 K to 20,000 K. What they all have in common is, a) the interior of the bubble heats up and becomes at least as hot as that measured for MBSL, b) water vapor is the main temperature-limiting factor and c) the averaged temperature over the bubble does not rise higher than 10,000 K.

Bubble Dynamics

These equations were made using five major assumptions, with four of them being common to all the equations:
  1. The bubble remains spherical
  2. The bubble contents obey the ideal gas law
    Ideal gas law
    The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...

  3. The internal pressure remains uniform throughout the bubble
  4. No evaporation
    Evaporation
    Evaporation is a type of vaporization of a liquid that occurs only on the surface of a liquid. The other type of vaporization is boiling, which, instead, occurs on the entire mass of the liquid....

     or condensation
    Condensation
    Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....

     occurs inside the bubble

The fifth assumption, which changes between each formulation, pertains to the thermodynamic behavior of the liquid surrounding the bubble. These assumptions severely limit the models when the pulsations are large and the wall velocities reach the speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....

.

Keller-Miksis Formulation

The Keller-Miksis formulation is an equation derived for the large, radial oscillations of a bubble trapped in a sound field. When the frequency of the sound field approaches the natural frequency of the bubble, it will result in large amplitude oscillations. The Keller-Miksis equation takes into account the viscosity, surface tension, incident sound wave, and acoustic radiation coming from the bubble, which was previously unaccounted for in Lauterborn's calculations. Lauterborn solved the equation that Plesset, et al. modified from Rayleigh's original analysis of large oscillating bubbles. Keller and Miksis obtained the following formula:



where is the radius of the bubble, the dots indicate first and second time derivatives, is the density of the liquid, is the speed of sound through the liquid, is the pressure on the liquid side of the bubble's interface, is time, and is the time-delayed driving pressure.

Prosperetti Formulation

Prosperetti found a way to accurately determine the internal pressure of the bubble using the following equation.



where is the temperature, is the thermal conductivity of the gas, and is the radial distance.

Flynn's Formulation

This formulation allows the study of the motions and the effects of heat conduction, shear viscosity, compressibility, and surface tension on small cavitation bubbles in liquids that are set into motion by an acoustic pressure field. The effect of vapor pressure on the cavitation bubble can also be determined using the interfacial temperature. The formulation is specifically designed to describe the motion of a bubble that expands to a maximum radius and then violently collapses or contracts. This set of equations was solved using an improved Euler method.



where is the radius of the bubble, the dots indicate first and second time derivatives, is the density of the liquid, is the speed of sound through the liquid, is the pressure on the liquid side of the bubble's interface, is time, and is the driving pressure.

Rayleigh-Presset Equation

The theory of bubble dynamics was started in 1917 by Lord Rayleigh during his work with the Royal Navy to investigate cavitation damage on ship propellers. Over several decades his work was refined and developed by Milton Plesset, Andrea Prosperetti
Andrea Prosperetti
Andrea Prosperetti is the Charles A. Miller Jr. Distinguished Professor of Mechanical Engineering at the Johns Hopkins University and the Berkhoff Professor of Applied Physics at the University of Twente in the Netherlands. He is known for his work in the field of multiphase flows including bubble...

, and others. The Rayleigh-Presset Equation is:



where is the bubble radius, is the second order derivative of the bubble radius with respect to time, is the first order derivative of the bubble radius with respect to time, is the density of the liquid, is the pressure in the gas (which is assumed to be uniform), is the background static pressure, is the sinusoidal driving pressure, is the viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 of the liquid, and is the surface tension
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...

 of the gas-liquid interface.

Bubble Surface

The surface of a collapsing bubble like those seen in both SBSL and MBSL serves as a boundary layer between the liquid and vapor phases of the solution.

Generation

MBSL has been observed in many different solutions under a variety of conditions. Unfortunately it is more difficult to study as the bubble cloud is uneven and can contain a wide range of pressures and temperatures. SBSL is easier to study due to the predictable nature of the bubble. This bubble is sustained in a standing acoustic wave of moderate pressure, approximately 1.5 atm. Since cavitation does not normally occur at these pressures the bubble may be seeded through several techniques:
  1. Transient boiling through short current pulse in nichrome wire.
  2. A small jet of water perturbs the surface to introduce air bubbles.
  3. A rapidly formed vapor cavity via focused laser pulse.

The standing acoustic wave, which contains pressure antinodes at the center of the containment vessel, causes the bubbles to quickly coalesce into a single radially oscillating bubble.

Collapse

Once a single bubble is stabilized in the pressure antinode of the standing wave, it can be made to emit pulses of light by driving the bubble into highly nonlinear oscillations. This is done by the increasing pressure of the acoustic wave to disrupt the steady, linear growth of the bubble which cause the bubble to collapse in a runaway reaction that only reverts due to the high pressures inside the bubble at its minimum radius.

Afterbounces

The collapsed bubble expands due to high internal pressure and experiences a deminishing effect until the high pressure antinode returns to the center of the vessel. The bubble continues to occupy more or less the same space due to the acoustic radiation force, the Bjerkens force, and the buoyancy
Buoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...

 force of the bubble.

Surface Chemistry

The effect that different chemicals present in solution have to the velocity of the collapsing bubble has recently been studied. Nonvolatile liquids such as sulfuric and phosphoric acid
Phosphoric acid
Phosphoric acid, also known as orthophosphoric acid or phosphoric acid, is a mineral acid having the chemical formula H3PO4. Orthophosphoric acid molecules can combine with themselves to form a variety of compounds which are also referred to as phosphoric acids, but in a more general way...

 have been shown to produce flashes of light several nanoseconds in duration with a much slower bubble wall velocity, and producing several thousand-fold greater light emission. This effect is probably masked in SBSL in aqueous solutions by the absorption of light by water molecules and contaminants.

Surface Tension

It can be inferred from these results that the difference in surface tension between these different compounds is the source of different spectra emitted and the time scales in which emission occur.

Light Emission

The inertia of a collapsing bubble generates high pressures and temperatures capable of ionizing a small fraction of the noble gas within the volume of the bubble. This small fraction of ionized gas is transparent and allows for volume emission to be detected. Free electrons from the ionized noble gas begin to interact with other neutral atoms causing thermal bremsstrahlung
Bremsstrahlung
Bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is...

 radiation. Surface emission emits a more intense flash of light with a longer duration and is dependent on wavelength. Experimental data suggest that only volume emission occurs in the case of sonoluminescence. As the sound wave reaches a low energy trough the bubble expands and electrons are able to recombine with free ions and halt light emission. Light pulse time is dependent on the ionization energy
Ionization energy
The ionization energy of a chemical species, i.e. an atom or molecule, is the energy required to remove an electron from the species to a practically infinite distance. Large atoms or molecules have a low ionization energy, while small molecules tend to have higher ionization energies.The property...

 of the noble gas with argon having a light pulse of 160 picoseconds.
Radiance Relative Brightness
Bright
Semi-bright
Dim
Very Dim
Extremely Dim

Solution Type Average Max. Radiance
Xenon in Water
Krypton in Water
Argon in Water
Neon in Water
Helium in Water
in Water

Electrical Processes

In 1937 the explanations for the light emission have been with the favoritism through electrical discharges. The first ideas have been about the charge separation in cavitation bubbles, which have been seen as spherical capacitors with charges at the center and the wall.
At the collapse, the capacitance decreases and voltage increases until electric breakdown occurs. A further suggestion was a charge separation by enhancing charge fluctuations on the bubble wall, however, a breakdown should take place during the expansion phase of the bubble dynamics.
These discharge theories have to assume that the emitting bubble undergoes an asymmetric collapse, because a symmetric charge distribution cannot radiate light.

Thermal Processes

Because the bubble collapse occurs within microseconds, the hot spot theory states that the thermal energy results from an adiabatic bubble collapse. In 1950 it was assumed that the bubble internal temperatures were as high as 10,000 K at the collapse of a spherical symmetric bubble. In the 1990s, sonoluminescence spectra were used by Suslick
Kenneth S. Suslick
Kenneth S. Suslick is the Marvin T. Schmidt Professor of Chemistry, Professor of Materials Science & Engineering, and Professor of the Beckman Institute for Advanced Science & Engineering at the University of Illinois at Urbana-Champaign...

 to measure effective emission temperatures in bubble clouds (multibubble sonoluminescence) of 5000 K, and more recently temperatures as high as 20,000 K in single bubble cavitation.

Bubble Shape Stability

The limit for the ambient size of the bubble is set by the appearance of instabilities in the shape of the oscillating bubble.
The shape stability thresholds depend on changes in the radial dynamics, caused by different liquid viscosities or driving frequencies. If the frequency is decreased, the parametric instability is suppressed as the stabilizing influence of viscosity can appear longer to suppress perturbations. However, the collapses of low-frequency-driven bubbles favor and earlier onset of the Rayleigh-Taylor instability. Larger bubbles can be stabilized to show sonoluminescence when not too high forcing pressures are applied. At low-frequency the water vapor becomes more important. The bubbles can be stabilizied by cooling the fluid, whereas more light is emitted.

Applications

Sonoluminescence might be a low energy source of neutrons for several applications, most notably in the development of a viable fusion reactor.

Bubble Fusion

It is speculated that the extremely high temperatures and pressures present on the interior of a collapsing bubble like those seen in SBSL may be sufficient to achieve thermonuclear fusion. This reaction is called acoustic inertial confinement fusion, or more commonly, bubble fusion
Bubble fusion
Bubble fusion, also known as sonofusion, is the non-technical name for a nuclear fusion reaction hypothesized to occur during a high-pressure version of sonoluminescence, an extreme form of acoustic cavitation...

.
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