Once you are sure the only steel part is the one you want to remove, mix as much alum as will dissolve in a small container (I use a tiny glass jar). I try to keep mine warm in a double boiler on very low (you want the solution warm, not hot), it allows more alum to dissolve in the water. After a couple of days, the broken screw will be gone. I usually only do this on weekends so I can keep an eye on it, and add water if necessary. Starting on Friday evening, the screw is usually gone by Sunday.
If you don't heat it up, you may have to wait a bit longer as mentioned above. You will see the steel part turn black in a few hours, that's a sign that it's working. Be patient, an it will work.