Just for curiousity is there a way to send a private message through any SF facility to another SF user?
As Michael said, no such thing.
If you really need to contact someone directly and the exchange cannot be in the public, the best thing to do is post some contact information in your profile and nudge the other person in that direction with a comment ping.
If you don't want to put contact details/hints in your profile, another possibility is setting up a Stackchat and exchanging details with burn on click links once you're reasonably certain you're chatting in realtime.
So far this is the only thing that has saved @HåkanLindqvist from me attempting to become bestest internet DNS buddies with him. Or at least until I get around to stalking him on social media.
Stack Exchange has no private message facilities for general use.
There is, however, a private message facility for moderators to contact users in regard to serious moderation issues. Messages sent via this interface are copied to all moderators and all Stack Exchange community team members. For the most part you should hope you never see this interface. :)