Thursday, November 24, 2011

Hydrotherapeutic Spa, Part III: Ultrasonic Wave Energy / Cavitation

Credit: Carsten Clasohm, Kruger National Park, South Africa, 22 March 2006

The specific process that occurs with the air bubbles flowing through bath water out of the ceramic mat of the SG-2000, is called "cavitation." The Wikipedia article on this fascinating natural phenomenon explains:
Cavitation is a general term used to describe the behaviour of voids or bubbles in a liquid. Cavitation is usually divided into two classes of behaviour: inertial (or transient) cavitation and non-inertial cavitation. Inertial cavitation is the process where a void or bubble in a liquid rapidly collapses, producing a shock wave.

Inertial cavitation

Inertial cavitation was first studied by Lord Rayleigh in the late 19th century when he considered the collapse of a spherical void within a liquid. When a volume of liquid is subjected to a sufficiently low pressure it may rupture and form a cavity. This phenomenon is termed cavitation inception and may occur behind the blade of a rapidly rotating propeller or on any surface vibrating underwater with sufficient amplitude and acceleration. Other ways of generating cavitation voids involve the local deposition of energy such as an intense focussed laser pulse (optic cavitation) or with an electrical discharge through a spark. Vapour gasses evaporate into the cavity from the surrounding medium, thus the cavity is not a perfect vacuum but has a relatively low gas pressure. Such a low pressure cavitation bubble in a liquid will begin to collapse due to the higher pressure of the surrounding medium. As the bubble collapses, the pressure and temperature of the vapour within will increase. The bubble will eventually collapse to a minute fraction of its original size, at which point the gas within dissipates into the surrounding liquid via a rather violent mechanism, which releases a significant amount of energy in the form of an acoustic shock-wave and as visible light. At the point of total collapse, the temperature of the vapour within the bubble may be several thousand kelvins, and the pressure several hundred atmospheres.
Inertial cavitation can also occur in the presence of an acoustic field. Microscopic gas bubbles which are generally present in a liquid will be forced to oscillate due to an applied acoustic field. If the acoustic intensity is sufficiently high, the bubbles will first grow in size, and then rapidly collapse. Hence, inertial cavitation can occur even if the rarefraction in the liquid is insufficient for a Rayleigh-like void to occur. Ultrasonic cleaning baths usually utilise the inertial cavitation of microscopic gas bubbles for erosion of dirt from materials.

The physical process of cavitation inception is similar to boiling. The major difference between the two is the thermodynamic paths which precede the formation of the vapour. Boiling is when the local vapor pressure of the liquid rises above its local ambient pressure and sufficient energy is present to cause the phase change to a gas. Cavitation inception occurs when the local pressure falls sufficiently far below the saturated vapour pressure, a value given by the tensile strength of the liquid.

. . . Cavitation can also be a boon in ultrasonic cleaning devices. These devices effect cavitation using sound waves and use the collapse of the cavitation bubbles to clean surfaces.
A more concise definition is offered in the Wikipedia article "Cavitation Heaters":
Cavitation is the phenomenon where small and largely empty cavities are generated in a fluid, which expand to large size and then rapidly collapse. When the cavitation bubbles collapse, they focus liquid energy to very small volumes. Thereby, they create spots of high temperature and emit shock waves. The collapse of cavities involves very high energies.
A book that explains cavitation in extreme scientific detail, is Christopher Earls Brennen's Cavitation and Bubble Dynamics (Oxford University Press, 1995). Here is an example, from Chapter 3: "Cavitation Bubble Collapse":
However, as long as there is some gas present to decelerate the collapse, the primary importance of liquid compressibility is not the effect it has on the bubble dynamics (which is slight) but the role it plays in the formation of shock waves during the rebounding phase that follows collapse. Hickling and Plesset (1964) were the first to make use of numerical solutions of the compressible flow equations to explore the formation of pressure waves or shocks during the rebound phase. Figure 3.2 presents an example of their results for the pressure distributions in the liquid before (left) and after (right) the moment of minimum size. The graph on the right clearly shows the propagation of a pressure pulse or shock away from the bubble following the minimum size. As indicated in that figure, Hickling and Plesset concluded that the pressure pulse exhibits approximately geometric attentuation (like r-1) as it propagates away from the bubble.
For more of the same sort of ultra-technical scientific material from the same author, see: Fundamentals of Multiphase Flow (Cambridge University Press, 2005).

The ultrasonic (or ultrasound) waves created by the cavitation and collapse of the air bubbles are further explained in the article, "Ultrasonics":
In the realm of physics, ultrasonics falls under the category of studies in sound. Sound itself fits within the larger heading of wave motion, which is in turn closely related to vibration, or harmonic (back-and-forth) motion. Both wave motion and vibration involve the regular repetition of a certain form of movement; and in both, potential energy (think of the energy in a sled at the top of a hill) is continually converted to kinetic energy (like the energy of a sled as it is sliding down the hill) and back again.

Wave motion carries energy from one place to another without actually moving any matter. Waves themselves may consist of matter, as for instance in the case of a wave on a plucked string or the waves on the ocean. This type of wave is called a mechanical wave, but again, the matter itself does not undergo any net displacement over horizontal space: contrary to what our eyes tell us, molecules of water in an ocean wave move up and down, but they do not actually travel with the wave itself. Only the energy is moved.

. . . Frequency is measured in terms of cycles per second, or Hertz (Hz), named in honor of the nineteenth-century German physicist Heinrich Hertz. If a wave has a frequency of 100 Hz, this means that 100 waves are passing through a given point during the interval of one second. Higher frequencies are expressed in terms of kilohertz (kHz; 103 or 1,000 cycles per second) or megahertz (MHz; 106 or 1 million cycles per second.)

The article, "Principles of Ultrasound in Surgical Applications" explains - in layman's terms - the entire process in the SG-2000 spa: air bubbles collapse, forming ultrasonic waves (that in turn, produce more cavitation, in a violent mutual physical reaction) and the waves penetrate the body, causing internal warming:
Cavitation is the formation and collapse of microscopic vacuum bubbles in a liquid due to sudden pressure differentials. The bubble implodes on itself, instantaneously releasing tremendous amounts of temperature and pressure changes at the point of collapse, resulting in shock waves and strong shearing forces . . . As an ultrasonic wave propagates into tissue, it is absorbed and the energy is converted into heat.
Another article, in Science Daily (10 November 2006), describes something akin to the effects in bathwater of the SG-2000 spa:

Ultrasound in a liquid, just like any sound waves, causes oscillation of expansion and compression of the liquid. If the ultrasound is loud enough, the liquid can be pulled apart transiently forming millions of bubbles, each with a diameter smaller than a shaft of hair. These bubbles grow and contract with each sound wave and if conditions are just right, they can violently implode. These imploding bubbles form shock waves in the liquid, and Suslick previously has shown that these shock waves will drive suspended metal particles into one another at roughly half the speed of sound in the liquid . . . The ultrasonic waves occur 20,000 times a second, creating many high-speed collisions between solid particles . . .
Here is an example of an experimental medical application of ultrasonic shock waves, in technical scientific language:

Pulsed high-energy ultrasound shock waves (PHEUS), similar to those used for clinical lithotripsy, can deposit energy deep in tissue and thereby destroy the microvasculature of solid tumors. We investigated the potential of PHEUS, generated by an electromagnetic shockwave source (19 kV capacitor voltage, 1 Hz pulse frequency), as a local cancer-therapy modality alone and in combination with local tumor hyperthermia (43.5 C, 30 min). Copenhagen rats transplanted with the anaplastic Dunning-prostate-tumor sub-line R3327-AT1 received 1000 PHEUS pulses, which delayed tumor growth by one tumor-doubling time (5 days). Histopathology revealed hemorrhage, disruption of tumor vasculature, and necrosis in the focus of the sound field. Bromodeoxyuridine (BUdR) incorporation was significantly lower in PHEUS-treated tumors than in controls. Dynamic magnetic resonance imaging (MRI) studies using gadolinium-DTPA as contrast agent showed a strong reduction of tumor perfusion after PHEUS treatment, although this effect was partly reversible within 3 days after PHEUS. While hyperthermia alone produced no significant delay in tumor growth, the combination of PHEUS and hyperthermia produced tumor-growth delay by 2 tumor-volume-doubling times. The maximum growth delay was achieved when PHEUS and hyperthermia were separated by 24 hr at the time of maximum perfusion reduction indicated by MRI. Thus, the cytotoxic effect of PHEUS was enhanced by hyperthermia in the anaplastic prostate tumor R3327-AT1 grown on Copenhagen rats in a synergistic manner, due to blood-flow reduction. In conjunction with other agents, such as hyperthermia, PHEUS might become a local cancer-therapy modality in solid tumors accessible to ultrasound.

(Synergistic interaction of ultrasonic shock waves and hyperthermia in the dunning prostate tumor r3327-at1, Peter Huber et al, International Journal of Cancer, Vol. 82, Issue 1 [1999], 84-91)

Similarly, C.A. Speed, in his paper, "Therapeutic ultrasound in soft tissue lesions" (Rheumatology 2001; 40: 1331-1336), examines a host of beneficial effects of ultrasound:

Therapeutic ultrasound is one of the most common treatments used in the management of soft tissue lesions, which constitute the majority of rheumatic complaints.

. . . Ultrasound has since been used to treat a wide variety of disorders, from skin wounds to malignant tumours [2, 3]. It has become one of the most commonly used treatments in the management of soft tissue injuries, and it has been estimated that over a million NHS treatments annually involve its use . . .

. . .
Modified forms of ultrasound include phonophoresis and extracorporeal shock wave therapy (ESWT).

. . . Ultrasound may induce thermal and non-thermal physical effects in tissues (Table 3). Non-thermal effects can be achieved with or without thermal effects. Thermal effects of ultrasound upon tissue may include increased blood flow, reduction in muscle spasm, increased extensibility of collagen fibres and a pro-inflammatory response. It is estimated that thermal effects occur with elevation of tissue temperature to 40–45°C for at least 5 min . . .

. . .
ultrasound may be used for its thermal effects in order to relieve pain and muscle spasm to increase tissue extensibility, which may be of use in combination with stretching exercises to achieve optimal tissue length [39]. Lengthening with thermal doses of ultrasound has been demonstrated in the ligament of normal knees [40] and in scar tissue [41]. Once the tissue has been heated to an adequate level (considered to be 40–45°C [34]), the opportunity to stretch the tissues lasts for up to 10 min before the tissue cools . . .

Further Sources

3) Ultrasound and thrombolysis, Charles W Francis, Vascular Medicine, Vol. 6, No. 3, 181-187 (2001).

4) Therapeutic Ultrasound in Lower Extremity Wound Management, Christine Uhlemann, MD , The International Journal of Lower Extremity Wounds, Vol. 2, No. 3, 152-157 (2003).

5) The Effects of Low-Intensity Ultrasound on Medial Collateral Ligament Healing in the Rabbit Model, Karen J. Sparrow et al, The American Journal of Sports Medicine 33:1048-1056 (2005).

6) Ultrasound in Somochemistry.

7) Measurements of the High Pressure Ultrasonic Wave and the Cavitation Bubble by the Optodynamic Method, R. Petkovsek et al.

10) Twenty Years of Shock Wave Research at the Institute for Surgical Research,
Michael Delius, European Surgical Research 2002;34:30-36.

11) Shock Wave / Geophysical and Medical Applications, Kazuyoshi Takayama and Tsutomu Saito, Annual Review of Fluid Mechanics, Vol. 36: 347-379 (Volume publication date January 2004).

12) Acoustic Bubble Traps, Reinhard Geisler, Acoustical Society of America
ASA/EAA/DAGA '99 Meeting.

13) Study of low-frequency ultrasonic cavitation fields based on spectral analysis technique, Zhaofeng Liang et al, Ultrasonics, Volume 44, Issue 1 , January 2006, Pages 115-120.

14) Byl NN, McKenzie AL, West JM et al. Low dose ultrasound effect on wound healing: a controlled study with Yucatan pigs. Arch Phys Med Rehab 1992;73:656–64.

15) Shock-wave therapy is effective for chronic calcifying tendinitis of the shoulder, Loew M et al, J Bone Joint Surg Br. 1999 Sep;81(5):863-7.

16) The effects of therapeutic ultrasound on tendon healing. A biomechanical study. Enwemeka CS. Am J Phys Med Rehabil 1990 Oct;69(5):258.

Complete Series

I. Introduction

For further information on purchasing the SG-2000 home spa, and business opportunities as a distributor, contact

Matthew Tan Kim Huat:

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