I was looking closely at this picture:

Then I bounced over to this testing:
http://jnaudin.free.fr/html/bifvsbuk.htm
Then it hit me. The water is acting as a capacitor but only to cause the delay in a typical LC circuit. It's this delay that allows you to create a magnetic flux in the core of the VIC, otherwise with the windings the way they are, it would buck. Think about it, you lay one winding right next to the other. Notice the two windings have exactly opposite electron flow even though they have nearly identical physical placement. What is it going to do...? Zippo without that special little water capacitor in between. Now if you can hang with me so far, the really cool part is what happens during the pulse rest when the magnetic flux should drop?
My theory is this: It can't dump back out the input side because of the diode and behind the diode there probably isn't much of current path even if it swings negative and dumps in the opposite direction it was charged in. So it has to go out the water side. But here is the way cool part... There are a whole mess of windings on the core, but they are tightly wound together and since there is no path back out the input side, it is my theory the tightly wound bifilar wires act as a shunt against the flux field dissipating. Again, the flux can't be dumped out the input side so it doesn't even try. As a wild guess four fifths of the input coil side are seen to the dropping flux as only a shunt and the last one fifth of the windings towards the output side does all the dissipating of the magnet flux.
Right or wrong, hang with me just a bit longer. So what I'm thinking is you charge up the coil through a long pair of wires, establish the flux, then pause, dump the flux through a small number of turns on the output side. High voltage, low current pulses in; low voltage, high current pulses out into the water. And SMASH! You have electrolysis with high voltage pulses instead of the typical high current DC way.
So if you think I'm on to something, let me add just a hair more to the pie. I think the output windings of this bifilar coil are extremely critical and must be tuned within 95% to get the VIC to function. First thing, they current must be high on the output, but the voltage still needs to be just high enough to initiate the electrolysis. Second thing, you tune this by the number of "unshunted" turns of wire on the output side to get the correct voltage ratio. What do I mean by "unshunted"? I mean the two wires are no longer piggy-backed right next to each other. Lots of various configurations here, but I think the easiest to understand is simply separating them physically from each other. On the input side they are side by side and on the output side they have 3mm between them. Or... Maybe we have say eight more turns on one wire than the other. You get what I mean right. The trick is to partly turn a bifilar coil into a conventional transformer but kill any (as much as you can) back EMF in the process.
Stan mentioned the timing is critical and has to be tuned to the water, the cell and probably the particular VIC being used. I do think using a little Arduino would make this fairly easy and... The WFC itself is part of the LC circuit, so it may actually help tune itself to some degree.
Anyway, it just made sense to me that the electrolysis is still happening with current, it's just by using the VIC we still only have to pay for it with voltage giving us a total wattage on the input much less than the output.

Then I bounced over to this testing:
http://jnaudin.free.fr/html/bifvsbuk.htm
Then it hit me. The water is acting as a capacitor but only to cause the delay in a typical LC circuit. It's this delay that allows you to create a magnetic flux in the core of the VIC, otherwise with the windings the way they are, it would buck. Think about it, you lay one winding right next to the other. Notice the two windings have exactly opposite electron flow even though they have nearly identical physical placement. What is it going to do...? Zippo without that special little water capacitor in between. Now if you can hang with me so far, the really cool part is what happens during the pulse rest when the magnetic flux should drop?
My theory is this: It can't dump back out the input side because of the diode and behind the diode there probably isn't much of current path even if it swings negative and dumps in the opposite direction it was charged in. So it has to go out the water side. But here is the way cool part... There are a whole mess of windings on the core, but they are tightly wound together and since there is no path back out the input side, it is my theory the tightly wound bifilar wires act as a shunt against the flux field dissipating. Again, the flux can't be dumped out the input side so it doesn't even try. As a wild guess four fifths of the input coil side are seen to the dropping flux as only a shunt and the last one fifth of the windings towards the output side does all the dissipating of the magnet flux.
Right or wrong, hang with me just a bit longer. So what I'm thinking is you charge up the coil through a long pair of wires, establish the flux, then pause, dump the flux through a small number of turns on the output side. High voltage, low current pulses in; low voltage, high current pulses out into the water. And SMASH! You have electrolysis with high voltage pulses instead of the typical high current DC way.
So if you think I'm on to something, let me add just a hair more to the pie. I think the output windings of this bifilar coil are extremely critical and must be tuned within 95% to get the VIC to function. First thing, they current must be high on the output, but the voltage still needs to be just high enough to initiate the electrolysis. Second thing, you tune this by the number of "unshunted" turns of wire on the output side to get the correct voltage ratio. What do I mean by "unshunted"? I mean the two wires are no longer piggy-backed right next to each other. Lots of various configurations here, but I think the easiest to understand is simply separating them physically from each other. On the input side they are side by side and on the output side they have 3mm between them. Or... Maybe we have say eight more turns on one wire than the other. You get what I mean right. The trick is to partly turn a bifilar coil into a conventional transformer but kill any (as much as you can) back EMF in the process.
Stan mentioned the timing is critical and has to be tuned to the water, the cell and probably the particular VIC being used. I do think using a little Arduino would make this fairly easy and... The WFC itself is part of the LC circuit, so it may actually help tune itself to some degree.
Anyway, it just made sense to me that the electrolysis is still happening with current, it's just by using the VIC we still only have to pay for it with voltage giving us a total wattage on the input much less than the output.