Just another note on Petkovs' experiment:
the generators output is 0-5v, this is very small voltage. On the oscilliscope you can see a few different voltages shown: left bottom of oscilliscope screen: ch1: 1.00v ( yellow)
middle bottom of osc. screen: 270mV Ch2? ( blue)
right top of oscilliscope screen: varies from 1 to 2v ( I think this is range setting?)
Anyhow if Ch1 ( yellow) is 1 volt, that a very tiny voltage, and ch.2 ( blue) I assume is voltage across resistor which gives indication of the current?
I've spent quite alot of time trying to find any information of low voltage pulses creating sound waves in water, I've not been able to find anything on it, so if sound is involved it would seem to be a new phenomenon not reported ( or not found by me). There are plenty of references to high voltage sound waves created in water, but are related to explosive gas release.
I'm just trying to make some sense out of Petkovs' results, and at the moment I cant find a relationship between the resonance points he found and sound waves in water.
It certainly doesn't help that i dont understand the oscilliscope results he shows, I'm hoping some others out there might be able to give some detailed synopsis of his experiment.

how about the frequencies he found for minimum current draw ( indicated by change in phase relationship of ch1 and ch2).
Is there any pattern: between 7.3mhz, 27mhz and 45mhz
7.3/27=0.2703030303repeater ( aprox 1/3)
27/45=0.6 ( a nice round number)( approx 2/3 but is actually 3/5)
7.3/45=0.162 ( a nice round number)

45/27=1.66666repeat ( 1 and 2/3 exact)
27/7.3=3.6986301repeat ( aprox 3 and 2/3)
45/7.3=6.16438356repeat (another repeater)

Ok just tried a pattern finder program it gave these three options:
e squared, 27,45
7pi/3,27,45
73/10,27,45
doesn't help me much!

I cant really make any pattern out of it.Just messing with the numbers to see if I can see a pattern there. Is it possible to predict the next resonant frequency from these numbers?
I think Petkov has found something but I've no idea what he has found!

ok something different;
lets use Petkovs' data in a different way:
lets say 2.5mm  gap is first harmonic ( which means wavelength is 5mm) gives 7.3mhz
then using v=f*lambda gives
vel=7300000*0.005=36,500m/s or 36.5km/s ( way faster than speed of sound in water)
Using the other frequencies ( 27mhz ( 135km/s) and 45mhz( 225km/s)) as first harmonic gives even higher speeds.
Unless  Petkov has missed a lower frequency resonance it seems speed of sound not related to the resonances? For a 2.5mm gap ( first harmonic use 5mm wavelength) and using the formula above with speed of sound in water of 1.484km/s gives resonance at 297khz, using speed of sound in water of 1.6km/s gives first harmonic resonance of  320khz.
To get a first harmonic resonance of 7.3mhz would require a speed of sound in water of 36.5km/s which would appear way to high.

Just a thought:
would it be the velocity of the water molecules being vibrated back and forth which is related to these frequencies? I quick search shows the particle velocity is lower than the wave propogation speed
from
https://en.wikipedia.org/wiki/Particle_velocity
says:
Particle velocity should not be confused with the speed of the wave as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity.

could it be an 'electrical' wave that is propogating across the water gap?
Could it be the electrical wave has resonance and travels at the speeds indicated by Petkovs' data?

Petkov mentions the dc bias turns to an ac bias at higher frequencies, as mentioned earlier i dont understand dc/ac bias, but I am wondering is it possible the water molecules vibrate back and forth in response to the polarity at the plate surfaces. The back and forth vibration could be looked at as analagous to ac current, in that an electrical wave travels along a copper wire in both directions, but the electrons only vibrate a small amount back and forth? Could it be the back/forth vibration of the water molecules that are giving an ac bias?
Is it possible there is a vibrational wave induced in the water by the molecular motion of the water molecules at the water/metal interface, that then propogates across the water, but it doesn't travel at the speed of sound, is this possible?

Since the frequencies are ultrasound range ( mhz), I looked up the speed of ultrasound waves in distilled water and its only slightly higher than khz frequency sound waves.

one more thought:
in air shock waves travel faster than sound waves, I wonder if a type of shock wave could be occuring in the water, which travels faster than a normal sound wave, that might be a possible explanation for Petkovs' data.

just one more note: last night whilst researching I came across an article that mentioned there is water reorientation next to electrically polarised metal plates, they used x-ray diffraction to confirm water re-orientation occurs on both pos and neg plates ( sorry I didn't bookmark the article address).( from memory oxygen goes towards pos plate and away from neg plate, but it only happens very close to the plates.....I think)
It would suggest that if there is a wave propogation initiated by re-orientation of water molecules next to the plates when the plates are polarised ( dc field set up), that the re-orientation of the water molecules would create a wave on both the negative and positive plates. That might have some influence, rather it should influence the resonant frequency if wave propogation through water is at play in stans systems i.e. rather than a wave emminating from pos plate only ( as per stans diagram in spherical electrolyser), it would emminate from both plates. That will influence the standing wave pattern dramatically. So there is some possibility that 1st harmonic resonant frequency will not be accurate way to determine resonant frequency.

heres an interesting research paper on ion flow in pure water near charged positive electrode,
pure water contains ions of h+ and oh- which are spontaneously produced.
http://rspa.royalsocietypublishing.org/content/468/2137/18
( definitely worth reading this paper)
Since these ions are charged and can move freely given a voltage gradient it might be of interest to understand current flow through stans cells. The paper is only for voltages below 1 volt, but there are some good references and interesting information.
for example the paper states:
The H+ ion is hydrated and becomes the hydronium ion, H3O+; the H3O+ ion may exist as a complex such as Embedded Image or Embedded Image (Brüesch & Christen 2004). The H3O+ and OH− ion number densities are small (6×1019 m−3) compared with the number density of H2O molecules (3.32×1028 m−3); however, the H3O+ ions have an important function in defining the pH of water.

So going back to valyonpz quoting stan in his last video, stan mentions water molecules travelling from one plate to another ( which I took as meaning a wave passing through the water). Is it possible these ions are travelling from one plate to the other, I doubt as they travel quite slowly?
In this paper at low voltages the distance from the plate that is influenced by the electric field is tiny ( in the order of microns) eg at low voltage ( 0.4v) at a distance of 5micron from the metal charged plate the hydroniums ions are basically at normal concentration.
The Morrow–Sato equation is also of interest ( current flow induced between two charged plates with water inbetween them, using voltage/area of plates etc).
Its quite an interesting paper as double layer formation on the plate surfaces takes some time, in the order of seconds to fully form, so for a fast pulsed voltage such as in stans system, the current flow will always be at maximum ( it doesn't give time for complete double layer formation which slows down current flow across the water).

It also gives some nice data on pure water eg conductivity of pure water of 5.68 μS m−1

this is an interesting result;
The maximum electric field at each electrode at equilibrium is very high; it is of the order of 1.5 MV m−1 for an applied potential of 0.4 V
So for a very small applied voltage, the potential at the surface of the plate ( i.e. the double layer, or nanometre scale of aligned atoms right next to the plate) gives a huge voltage potential

another interesting paper, relating to extreme high voltages and double layer phenomenon
 but is quite theoretical is:

http://www.tuks.nl/pdf/Reference_Material/Dielectric_breakdown_Avalanche_Multipactor/Joshi%20-%20Microscopic%20analysis%20for%20water%20stressed%20by%20high%20electric%20fields%20in%20the%20prebreakdown%20regime%20-%20JAP_96.pdf

It does state that :
Dynamic motion of ions could result in potential instabilities
and shock waves as have been observed

But that relates only to quite high voltage that I believe were way way above what stan was using.

this paper is probably not directly relevant, but its interesting design for generating electricity using double layer capacitance ( with salt solution and mechanical movement of plates)
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4891717/

paper i need to read over
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4170795/

suggests above 1volt or so, double layer conditions dont follow standard equations

I was just looking up self-resonant frequency measurement of capacitors.
Seems a capacitor within itself displays self-resonance, heres a video on it:

https://www.youtube.com/watch?v=C3wYMZ_cjdQ

I wonder if Petkovs' experiment was measuring the self resonant frequency of a water capacitor?
Though he got more than one frequency.

just a bit more searching on resonant frequencies of capacitors, this short article gives some good info on series/parallel resonant frequencies of capacitors, it also shows the multiple frequencies can be measured.
http://www.johansontechnology.com/srf-prf-for-rf-capacitors

is it possible following the scenario given in the article above, that 7.3mhz is the serial resonance, 27mhz is the first parallel resonance and 45mhz the second parallel resistance?
It also mentions that up to the serial resonant frequency the capacitor acts as a dc blocking inductor ( maybe this relates to Petkovs comments about dc/ac bias).
Also of interest is the 'trick' used in making capacitors to widen the useable frequency range by using horizontal interlocked plates , connect to vertical electrodes, perhaps a similar trick can be used with electrolysers to widen the useable frequency range i.e. matching the vic with the water capacitor might be easier to achieve with horizontal or similar setup of the electrodes, assuming that the bubbles can still escape somehow.

an article linked that looks into capacitance between electrodes ( carbon ) and the surface double layer that produces the capacitance.
http://pubs.acs.org/doi/abs/10.1021/acs.jpcc.5b08409?journalCode=jpccck
Its not specifically for water, but various ionic liquids dissolved in water, important part is that the surface area of the electrode is directly linked to the capacitance i.e. capacitance is created at the electrode surface by only a nanometre scale layer of water molecules, the bulk of the water molecules inbetween the electrodes is not creating capacitance, just a tiny tiny tiny thin layer right next to the electrodes. In theory a huge surface area could be created in a tiny space, the limiting factor to surface area will be bubble removal from the voltage zone.
Lets say theoretically the bubbles were not a limiting factor in hho production, it would be possible to have a huge surface area even in say a 1mm  cube, since capacitance determined on the nanometre scale, its just an interesting thought, that if bubbles could be instantaneously removed somehow from the voltage zone, you could have an electrolyser even on a microscopic scale producing huge amounts of hho.......though in reality.......probably not possible to remove the hho gas in a  microscopic scale electrolyser.

another paper on capacitance of water/electrode interface, its theoretical based on formulas,
probably not particularly useful, unless your interested in what factors effect capacitance at the water/electrode interface.
http://www.electrochemsci.org/papers/vol9/91105885.pdf
It is of interest though as its calculations are based on pure water without ions present, which might explain why stans system can use pure water ( capacitance is still produced by alignment of water molecules at the electrode surface), as far as I can tell it doesn't take into account oh and h ions which are spontaneously produced in water.
It has some information on how the voltage bias of electrode drops with distance from electrode ( it appears to be me it drops very rapidly) but since the units used are complex I cant be sure of that, unfortunately I cant relate the voltage units used in the paper, to the voltages used in stans systems.

another paper, this one is worth a look at, its not about hho generation, but its a device that produces electrical potential by varying the capacitance of pure water drop between two conducting plates.
http://www.nature.com/articles/ncomms2485

Its relevant for a couple of reasons:
1. its shows how to manipulate the nanometer scale stern layer ( capacitance) in pure de-ionised water.
2. Perhaps more importantly: it shows that water bewteen two electrodes should be represented as   
 ELECTRODE: CAPACITOR: RESISTOR( water ): CAPACITOR: ELECTRODE

As far as I'm aware in trying to match the Vic to the water cell, the water cell has been treated as a capacitor. But it is really two capacitors ( stern layers ) with water inbetween them !!( the resistive part )
So one electrode ( say positive) attracts negative ions  and negative side of water molecule towards it........the electrode ( pos ) and polarised water molecule next to it and any negative ions ( neg ) .......form one capacitor.........same on the other electrode but polarity reversed.
Any calculations wont be exactly correct, since the water is being treated as one capacitor, whereas in reality its really two capacitors with water inbetween.
Also this might explain why stans vic coils are slightly different number of windings!
I have never been able to understand why it was required, but now I think there is a possible way to understand it as follows:
the positive electrode will have a different thickness stern layer ( due to attracting negative ions/oxygen side of water molecules and any other negative ions in the water)
the negative electrode attracts different ions and the other side of the water molecule, its capacitance will be different to the stern layer near the positive electrode ( i.e. different thickness).............
So basically you have two slightly different capacitances at the positive and negative electrode......hence the need for slightly different number of windings on the vic coils.
I think this might be rather useful information for doing simulations are calculations for vic coils. I shall draw a diagram later and post it here to make clear what I mean.

this diagram should make it clear, its not a water capacitor.......
its a water DOUBLE capacitor

I'm still lacking information on how the electric field varies across the water capacitor, there is a process called 'screening' where the movement of the ions towards electrodes, or change in angle of the water molecules acts to cancel out the electric field.
The electric field diminshes rapidly across the stern layer, one calculation gives a debye length of one micron for pure water, that means the field diminishes to near zero across one micron width of water molecules, just due to oh and h ion movement.
see
http://www.owlnet.rice.edu/~phys534/notes/week10_lectures.pdf

Though it takes time for the ions to move, its not instantaneous process. It does though suggest that the bulk of the water might not be aligned since the electric field is screened out by the ion movement to the electrodes and water realignment next to the electrodes. Its complex stuff.

why I think the water capacitor should be modelled as a double capacitor:
One of the Vic coils has to be tuned, but if you look at the water capacitor as just one capacitance both vic coils should have the same number of turns. If it was just one capacitance there would be no need for tuning one of the vic coils.
If you look at the water capacitor as two capacitors ( which is what I think it is and as it matches all the theories on metal/electrolyte interfaces ) then it is easy to see why one vic needs to be tuned. One electrode has a different capacitance to the other electrode ( i.e. one electrode has a different water orientation and collected ions). Looking at the water capactior as just one capacitor its not possible to explain why one vic coil has a different number of turns to the other vic coil.
Is it possible to measure the capacitance across each electrode? I dont think it would be possible as the layer in the water next to the metal is so thin it wouldn't be possible. What would a capacitance meter be measuring between the electrodes, I'm guessing it would be the sum of both capacitances. It might also explain why the predicted frequencies for the vic coil resonances are not possible to determine accurately.
The more I look into metal/electrolyte interactions the more complex it becomes, it seems the capacitance across just one metal/electrode interface can be further broken down into smaller components that produce the capacitance but shouldn't be needed in stans system to go that far.
Also each capacitance across each electrode/water interface ( i.e. the pos and neg electrodes) will have its own internal resistance and inductance. It seems the idea of bilayer capacitance of metal/water interfaces ( and other interfaces) goes way back to helmholtz era, so Stan would have most certainly been  aware of this.
Because its not possible to measure the capacitance on each electrode its probably simpler to just view the water capacitor as a single capacitor, but it does leave some things unexplained ( such as the variable vic coil on one side of the water capacitor).
It might be possible to work out the capacitance on each electrode by working backwards from inductance/resonant frequencies of the two vic coils after tuning, but I haven't tried to do it.
So its really only academic that there are two capacitances at play, since there values are not directly measurable with a meter. But it is of value in trying to understand how stans systems works.
The other issue to tackle is how far the electric field reaches into the water, the electric field in the bulk of the water will rapidly diminish as the capacitance on each electrode builds up
as it acts to screen ( blocks ) the electric field. It will depend on the pulse time on how much capacitance builds up, and therefore how much of the bulk water is screened from the electric field. On the other hand the electric field strength across the bilayer increases over time due to build up of ions and water reorientation, the field strength across the bilayer is higher voltage than the voltage delivered to the electrodes, probably significantly higher.
It may even be that high voltage across the bilayer in combination with the discharge of the capacitance give rise to the breaking of the water molecule bond ( rather than a physical shaking of the water molecule to break the bond).
In most of stans drawings it appears that all the water molecules inbetween the electrodes are aligned by the field, that might be true for a very short time period, at the beginning of the first pulse. Whether or not the pulse time is short enough in stans system to allow significant field right across the water capacitor I have no idea, but i suspect most of the action is occuring very close to the electrodes.

a bit more research extending from alexander petkovs last video, seems there is quite alot of information available on fequency scans of pure water between electrodes. Searching for the term " impedance spectroscopy pure water " leads to many results. It also leads to a whole new area for me, including impedance measurements that have imaginary and real terms.......what the?
Heres an example of one very detailed paper, it has results for pure water ( though the paper is looking at a transitor/mosfet using pure water ( results compared to non-pure water with ions added)
http://www.nature.com/articles/srep13088?WT.ec_id=SREP-639-20150818&spMailingID=49344620&spUserID=MzcwNDE0MDA3NzMS1&spJobID=742811467&spReportId=NzQyODExNDY3S0
So I'm coming to conclusion the more I search the more I find there are huge amounts of information pertaining to studies that offer some insight into stans research, but finding that information is time consuming and not always straight forward. But there is no end to the discoveries that can be made.
Attached pictures; first  from a paper that used a particular circuit to model water between electrodes, seems there are different ways to model it, some use the bulk water as another capacitor, so that you have three capacitors in series, if the bulk water is reorientated due to the electric field it can also act as capacitor.
Second picture shows alternate more complicated model, which takes into account movement of ions towards charged electrodes.

research paper on impedance spectroscopy of pure water ( and other types) with stainless steel 316 ( and 304 ). Only goes up to 1mhz on frequency scans.
http://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=2663&context=etd_theses

Main aim of the theses is to predict corrosion rates in 316 stainless steel electrodes in pure water and other environments.

just a short note on using glass as insulator between electrodes and water, this study:

https://books.google.com.au/books?id=S1sFCAAAQBAJ&pg=PA368&lpg=PA368&dq=pure+di+water+frequency+scan&source=bl&ots=0ruhbwoWIx&sig=l4dls18id_gBpb63j5SfrF0OCqo&hl=en&sa=X&ved=0ahUKEwih37G4lbnQAhWlF8AKHfYMAgEQ6AEIJTAC#v=onepage&q=pure%20di%20water%20frequency%20scan&f=false

shows that glass that is placed in pure water, influences the impedance frequency by the transfer of sodium or calcium ions into the water ( h ions are absorbed apparently), this is interesting and the glass is not even in contact with the electrodes. They also mention the bilayer effect at the electrode surfaces influences the impediance.
Of interest it shows that the pure water between electrodes ( platinum) is purely resistive ( no capacitance component) between 100hz and 1khz, outside of that range bilayer capacitance plays a role ( observed by shift in phase angle ).

it seems that in order to understand impedance spectroscopy of water, its necessary to undersund two different types of graphs;
1. nyquist plots
1. bode plots
The nyquist plots show phase angle/real impedance , the bode plots show impedance/frequency.
The nyquist plots I do not as yet understand, I believe the y-axis relates to phase angle and the x-axis shows the actual impedance. The Bode plots are straight forward showing freq/impedance.
The graphs are done with ac voltage as far as I can tell, but should give some insight into capacitance/resistance of water with induce voltage across electrodes. I shall find some of these graphs and post results.

just going back to possibility of acoustic waves being involved in stans system, it appears there is a mechanism to form acoustic waves electrically.
This paper mentioned another form of producing acoustic waves in water, which is purely electrically driven through a conductor, but the conductor requires to have a weak static magnetic field present. I dont think stan used magnets to produce static magetic field though, so its probably not relevant but certainly very interesting.
https://www.ncbi.nlm.nih.gov/pubmed/12051429
but I believe this only applies to highly conductive electrolytes so probably not of interest.