I would like to know, what are the characteristics of "Wildfire" (as opposed to normal fire) in the Game of Thrones TV Series?
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According to the TV Series, burning wilfire is capable of melting the following substances;
"The Substance burns so hot it melts wood, stone... even steel... and, of course, flesh!. The Substance burns so hot it melts flesh... like tallow."
Assuming the maester is correct, it will burn hot enough to melt steel (at approx 1500°C) and stone (at approx 1200°C). Although they explicitly mention melting wood, the reality is that the temperature required to achieve such a feat (approx 3500°C) strongly suggests that this is mere hyperbole.
From the same canon source, we also know that it combusts readily in the presence of urine and burns with a green flame.
While there are a variety of elements that burn with a green flame (including copper, antimony, selenium, tellurium, thallium and barium) the only one of these elements that would readily react with the water in urine is Barium which would cause steam, heat and highly combustible hydrogen gas, potentially leading to an explosion.
Wildfire is stored as a greenish transparent liquid. According to Bronn it's highly combustible and can explode from merely being handled ungently.
The wildfire that was used to coat Baris' 'Flaming sword' is composed of "Isopropyl Alcohol" and kept alight with "a small pilot light". The flame was artificially coloured using CGI effects by Pixomondo, who won an Effects Emmy for the series.
According to various fan sites, the liquid version is allegedly distilled water mixed with glycol and green food colouring although I've been unable to locate a canon confirmation.
If you're after more of an historical perspective, there is an extensive reference on the subject of wildfire on the GoT Wikia
Since it's apparent that you're talking about the substance known as wildfire in the English originals, it's almost certainly based on Greek fire, a Byzantine naval weapon whose formula has been lost, and so we can only speculate on what exactly it was.