Unless someone wants to take 3-4 photos of cotton for you... don't hold your breath.
(Of course, minutes after I post this, someone
will post 27 different views of... a piece of cotton

)
I don't have a camera, so... I'm going to describe this as if you have no method of measuring anything (because who knows what you do or don't have)... but I am assuming that you have some Q-tips. Everyone has Q-tips, right? So, everything in "increments of Q-tip".
For a 3/32" ID coil... starting with a relatively flat piece removed from an "unrolled" (yes, they unroll ;-)) cotton ball, with a
starting width roughly that of two Q-tip heads and a thickness of a Q-tip shaft... with lightly dampened fingers, rolled down to, about the diameter of a Q-tip shaft.
Now... that may not sound like much to start with and maybe even a bit thin... but that's relatively dry, and compressed. Once it's in the coil and wet - well, you know.
(Forgot to mention... a Q-tip shaft, is about .003" less than 3/32")