Titanium isn't even tarnished by aquea regia. (acid solution that dissolves gold)
I occasionally have to dissolve titanium where I work, and the only thing that will
put a dent in it is hydrofluoric acid.
DO NOT, use anything containing hydrofluoric acid.
The only common household cleaner that contains hydrofluoric acid is Whink Rust Remover.
WhinkFurther, avoid any situation where titanium can come into contact with phosphoric acid
and an electrical current. The latest Popular Science had an interesting article on how
you can apply a relatively permanent blue/purple/red/yellow rainbow color to titanium by simply
applying an electrical current to titanium in phosphoric acid.
Other than that, you can immerse it in the strongest acids without harm.
It will laugh at detergents, or any gun cleaner you can throw at it.
Edit: The same can't be said of the aluminum frame. Keep it away from all acids and caustics,
and chlorinated solvents. This includes many gun cleaners.