How to send a direct private message to a Twitter user who does not follow me.
In most cases, it’s not possible. Some accounts have the ability to declare they’ll accept direct messages from all followers, but that’s a very rare account state. In the majority of cases, the recipient of a direct message must be following the sender.
You can send direct message to all your followers by using one the two ways. First method is, use application to do this and second method is use wesbites for this…if you want you can read this article to get a complete idead about this http://stopusifyoucan.com/direct-message-to-all-followers/
Have a nice day