Let's do some sums:
Consider a Faraday Law calculation:
Suppose a car is traveling at 60 mph and using fuel at the rate of 30 mpg. If we assume that to have any influence at all on fuel consumption, it must be producing enough H2 to constitute 1% of the fuel that is being burned, the calculation becomes:
At 60mph, in 1 second it travels 60/3600 miles = 1.66 E-2 miles.
At 30mpg, this is equal to 1.66E-2/30 = 5.6E-4 gal
5.6E-4 gal = 2.1 mL gas
Assuming density of 0.8, 2.1 mL = 1.68 g gas
For 1% = .0168 g H2
Now, what current is required to produce .0168 g H2 in 1 second?
Equation is 2H+ + 2e- = H2
Now, .0168 g H2 = .0084 mol H2 = .0168 mol e-
.0168 x 96,500 = 1621 coulombs
Now, 1621 C/s = 1621 amps (a ridiculous figure for any automotive system to generate).
If we work on a 1% molar ratio (rather than mass), the number is somewhat smaller (assuming octane as the fuel) at about 14 amps.
Now, in real terms, taking into account the sort of inefficiencies one encounters when trying to make gases electrolytically, I'd imagine that equates to at least 40-50 amps. At 12V, that requires about 600W power, which is a fair drain on an electrical system.
As well as that, before the H2 can increase your fuel efficiency, it must first make up the 600W that is required to make it in the first place. And all this from a mixture in which the H2 molecules number one in every 100.
In terms of the various positive testimonies regarding why this works, I'd say they fall into three categories:
1. Outright lies by people who want you to buy something they are selling.
2. The placebo effect. Those who have put time and money into installing a device like this WANT it to work. Thus, when doing their "test" they inadvertently drive a little lighter on the pedal with their device installed, or use noncomparitive data and so on.
3. People install a device onto an engine that is running too rich. In plumbing the device into their system, they don't seal the joints properly, and air enters the system, thus leaning the mixture and improving the economy.
And you know that something like this is happening when people make these claims for a diesel. At least for petrol, there is a theoretical case for improving efficiency with H2 if you can get enough of it in there. But for a diesel - the autoignition temp for H2 is 571 deg, way above any form of diesel fuel. It thus won't ignite by compression, and will only start to burn after the diesel has ignited - it will therefore actually retard the process.
But finally, there is one overwhelming reason why we know this cannot work - with car companies spending millions - possibly billions - trying to outdo each other for fuel efficiency, no one (that I've heard of) has either installed a device like this or even mentioned it.
It seems to me like the height of naivety to believe that you can just bolt a device onto an engine - any device - and instantly achieve the type of fuel savings that the combined efforts of the world's automotive brains cannot. Even the fabled Toyota Prius, which went to the lengths of using dynamos as brakes in attempt to harness leftover energy, was a failure, with a recent survey by the RACV finding that a small Hyundai Getz was more fuel efficient.