Is there a "default" MIME type?

The least specific official MIME type is application/octet-stream. Without any additional information, it says "here is a bunch of bytes, hopefully there is an application over on your end which knows what to do with them". Sometimes there is a file name which helps convey to the recipient what to do with the data.

"unknown" doesn't really add anything over this, except to confuse clients who don't support random unofficial MIME types. Ditto for application/binary; it's just a non-standard way of restating "octet-stream".

This is the answer to "What can I put in the Content-Type: header if I can't find an existing content type which adequately describes my data?" which is how I have interpreted this question. The proposed duplicate Unknown file type MIME? has a lengthy answer which discusses "How is my data interpreted if I don't put a valid Content-Type: header?" specifically in an HTTP context; the answer to that is protocol-specific (in email, for example, the default implied Content-Type: for MIME body parts which do not contain this header is text/plain; charset="us-ascii").