The scientific magazine Physical Review E in March 2004 had announced the publication of an article on the contraversial subject which raised resistance and discussions two years ago - Taleyarkhan et al. (2002).
Covered in the Science a Gogo -
The subject is on the production of Nuclear Fusion reactions with ultrasound impact. Researchers from Rensselaer Polytechnic Institute (RPI), Purdue University, Oak Ridge National Laboratory (ORNL) and the Russian Academy of Science (RAS) publishing the second time publications restating that they have replicated and extended previous experimental and simulation results that indicated the occurrence of nuclear fusion using an acoustical implosion of gas bubbles in a small reservoir.
The small size gas bubbles in the liquid compressed so quickly and abruptly that temperature in the bubbles can reach millions of degrees and some of the hydrogen atoms in the solvent molecules explained as being fused, producing a flash of light, energy and neutrons.
In their 2002 paper authors did the modeling and numerical simulation actually for the ONE bubble - Taleyarkhan et al. (2002), Nigmatulin et al. (2002).
For the modeling and simulation were used.
Gas Mass Conservation Equation:
Gas Momentum Conservation Equation:
Gas Energy Conservation Equation:
Liquid Mass Conservation Equation:
Liquid Momentum Conservation Equation:
Liquid Energy Conservation Equation:
plus the equations of state for the gas and the liquid.
We will omit the part related to the D-D neutron fusion production rate process and its model. Not because I don't believe in the event of neutrons production, but because it is not relevant right now to the point. I am more concerned with the lower scale assumption of "effective temperature to approximate the behavior of the electrons and ions in the plasma".
As long as the problem exists for not a single bubble, but for the millions and millions of bubbles, generating the rise in sizes and implosions, interacting one with another, this is the problem which has at first and at least the three scale phenomena (accounting for the atomic and nuclear (while probably the fourth scale to consider) features, those need to be described by taking into the model) those would be nice to model; and the weight of the Interscale and other VAT equations scaled (the second and the third) phenomena through the additional terms should be substantial.
As we have seen in the other so far solved (even exactly) the two-scale VAT problems -
the additional interscale induced phenomena are not just presented and not seen in the one scale models. That does not mean they do not exist.
We have shown in this website (and in my publications) for few cases the strong interconnection between the interface tied phenomena - not diagnosed via the one scale physical and mathematical models, and the Lower and Upper scale balances. The one case is so pure affirmative while concerning the energy balance - I mean the superlattice conductive heat transfer and electrostatics displacement fields-
Using exact calculations (everyone can repeat those) it is shown that in the one scale (lower) solutions the energy or displacement are not balanced for the very known traditionally solved problems!
And this issue might be the major one, when critics start to calculate the energy balances for the phase and different scale phenomena in these "sonofusion" processes in a tedious way.
My reservation is that this outstanding problem, which had the publications including that one in March 2004, as to extend the advances obtained prior to the year (2004) as in the one published in 2002, this problem needs to be considered and stated as the three scale problem. And simulated at least using the two neighboring scales, because the three scale models so far have been only stated with great assumptions.
My major kind of reservations is that in this process - in some part of it (final) at least, evidences of high temperature in the two-phase mixture speak in a favor of plasma presence in the bubble! That drags a consideration into the territory where also the plasma physics model(s) of the two scale should be induced and be part of the whole model and simulation. Well, with the one more scale in the phenomena - the plasma Upper scale, the scale of the very process that was claimed - the hot fusion by sonoluminescense - of which presence in these experiments (there were other later experiments - with 2004, 2006 publications) is so far disagreed by many.
Taleyarkhan, R.P., West, C.D., Cho, J.S., Lahey, R.T.Jr., Nigmatulin, R.I., Block, R.C., "Evidence for Nuclear Emissions During Acoustic Cavitation," Science, 295, March 8, pp. 1868-1873, 2002.
Nigmatulin, R.I., Lahey, R.T.Jr., Taleyarkhan, R.P., "The Analysis of Bubble Implosion Dynamics. Supplement #2," Science on Line, pp. 1-15, 2002.
Nigmatulin, R.I., Dynamics of Multiphase Media, Hemisphere, New York, 1991.
We will continue checking the moves there from time to time and publish in this sub-section some interesting data regarding this claim for hot fusion by sonoluminescense.