From `bash` documentation, [Brace Expansion][2] section:

> **Brace expansion is performed before any other expansions, and any
> characters special to other expansions are preserved in the result**. It
> is strictly textual. Bash does not apply any syntactic interpretation
> to the context of the expansion or the text between the braces. To
> avoid conflicts with parameter expansion, the string ‘${’ is not
> considered eligible for brace expansion.

In your case, `bash` will do brace expansion first, produce result `{Alpha,Bravo,Charlie}`.

If you can control `$find_dir` variable content, you can use `eval`:

    eval "find Directory/{$find_dir} arg1 arg2"