From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: can sound waves boil water?
Organization: University of Virginia
Date: Thu, 24 Dec 1992 17:34:18 GMT

In article <1992Dec22.173302.7146@murdoch.acc.Virginia.EDU> crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>In article <1992Dec22.151439.29874@nuscc.nus.sg> eng10370@nusunix1.nus.sg (CHEW JOO SIANG) writes:
>>I was thinking of this the other day - we all know that a microwave oven
>>works by resonating the water molecules at its natural frequency - this
>>causes a rise in its temperature. The question is, can we do the same
>>with sound waves - using it to resonate the water molecules. I know that
>>you need incredibly high frequecies to achieve it but is the concept
>>sound theoretically?
>
>    a)  That is not the way microwaves work.  Try "Dielectrics and Waves"
>        by Von Hipple, available at research libraries everywhere.
>    b)  Yes, one can induce boiling and cavitation by sound. Try 
>        "Cavitation" by Young, available at research libraries everywhere,
>        and any treatise on ultrasonics.
>    c)  Depending on what you mean by 'incredibly high' frequencies
>        and 'resonate', your statements above may not be an accurate
>        portrayal of the physical circumstances under which this happens.

     I didn't have time the other day, but here goes.  Yes, there are several
     phenomena that could reasonably be construed as 'boiling' in liquid
     (specifically water for the purposes of this discussion) under the
     influence of sound.  Two that come to mind are a) cavitation
     and b) heating.  Cavitation involves the extremely localized creation
     of the necessary thermal conditions for vapor-phase creation, while 
     heating comes simply from the fluid's absorption of sound energy averaged
     over time and space.  
  
     Focusing solely on heating, a fluid is characterized by a certain
     attenuation of the incident sound wave.  A part of this attenuation
     (usually a large part) is due to heat generation in the medium
     and is described by an absorption or attenuation coefficient.  For
     a homogeneous medium like water, the two coefficients are the same.
     In general, the absorption is less than the attenuation. For 
     water, typical coefficients are:

           Freq (MHz)          \alpha (dB/cm)

           0.2                 0.000088
           1.0                 0.0022
           10.0                0.22
           100.0               22.0

     In monged units, the heating rate due to the sound waves can easily be 
     given by 

            Heating rate = 0.055 * \alpha * I

     where \alpha is given in dB/cm, I is the intensity of the incident 
     radiation given in W/cm^2 and heating rate is given in cal/cm^3-s.
     So if we have a 10 Mhz plane wave of field average intensity 10 W/cm^2
     incident on a very thin flat water plate, we will see a roughly
     0.121 cal/cm^3-s heating rate.  For other shapes we could easily
     determine the local time-averaged intensity and integrate the 
     above expression over space to determine the global heating rate.

     Now comes the reason for the monged units.  In water, of course, 
     if you put 1 cal into 1 cm^3 you get a 1 C increase in temperature
     (subject to various conditional caveats).  So, in the above situation,
     you'll get about 0.121 C a second temperature rise, or a roughly
     7 C a minute.
	
     So, how 'realistic' is this in the context of the usual ultrasound
     device that the ob-gyn slaps on your wife's burgeoning belly?  Not very,
     for the simple reason that they don't want to boil the fetus.
     Typical spatial-peak temporal average (SPTA) limits on such 
     equipment (pulsed doppler devices) run about about 120-155 mW/cm^2 
     intensity.  Spatial-peak pulse averages are much lower, about 
     18-22 mW/cm^2.

     This is not to say that you couldn't boil your coffee with a properly
     constructed device.

     Further reading on sonic heating of bone, tissues and fetuses
     can be had by visiting your local medical library or local 
     radiologist.  Most of the information in the above was gleaned from 
     "Biological Effects of Ultrasound" edited by Nyborg and Ziskin.

     Now if only someone could give me a good experimental attenuation
     coefficient in 24 K deuterium.

                                 dale bass
-- 
C. R. Bass                                          crb7q@virginia.edu        
Department of Mechanical, 
     Aerospace and Nuclear Engineering
University of Virginia                              (804) 924-7926