Well, the part has been sitting in alum in a jam jar ,in an old baby bottle warmer for hours,lots of bubbling but not much has dissolved yet .
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Don’t expect a quick result. The bubbles suggest the right Alum is being used – the wrong one will either not work or be very slow. The reaction will also be slowed down by any oil on the tap.
Another possibility is that the remedy dates to back to well before HSS was invented, and you have an HSS tap. Carbon tool steel taps are probably more reactive than HSS, which contains corrosion resistant elements like Tungsten and Chromium. Should still work, but even slower than usual.
As far as I know, no-one has tested Alum performance on different steels, or what happens when the wrong Alum is used.
There was a device that put 3 steel prongs into the grooves so broken taps could be unscrewed. My homemade version wasnt strong enough, and I suspect the commercial version was too weak also. Anyone know?
For fast removal, all that’s needed is a spark eroder.
Dave