Keeping in mind I have never done the "slow rust bluing" - it was my impression that various mixes were to create fumes - and the fumes created the red rust - which was converted to black rust. It is the "Express Rust Blue" that I have done that gets juice applied directly on to the metal. Is that mixed-up? I have a book with article by someone named John Bivins - he lists several bluing and browning recipes that he used along with his "damp box" - I do not think the solutions ever made direct contact with the metal - "Browning Solution - US Ordnance Manual 1841", "Fast Brown", "Niedner's Rust Blue", "Baker's Express Blue".
I have seen that John Bivins article, but don't recall which book it is in.
I an afraid you misunderstand the process. All of the browning/bluing solutions I am aware of are applied directly to the metal as explained by smokinbarrel. The same solution can be used for both browning and bluing. Only the process differs. After the solution is applied, the parts are hung in a warm and humid environment to rust. That is where the sweat box comes in and 90 degrees F and 90% RH are ideal.. They are periodically taken out, the loose rust is carded off, more solution is applied and they are put back in to repeat the process. It typically takes anywhere from about 5 to 8 cycles to develop good finish. To my astonishment, the bluing job I completed yesterday only took three 4-hour cycles. The red rust is ferric oxide. To get a black finish, you either boil or steam the rusted parts. The boiling water or steam converts the brown ferric oxide to black ferrous oxide. The parts can receive the conversion treatment either periodically during the rusting process or after it has been completed. I have not seen where it makes a difference.
That is an abbreviated explanation of the process.