Casimir Effect within a Circular Topography

[chords]

Lately I've become rather obsessed with physics and in particular the casimir effect. I understand how it works, though I recently began wondering how this effect would act within a circular or a cylinder or something as such.

Would it make the circle cave in, thus the sides touching?
Would the circle remain round?

I cannot find many articles about this question, and although I do assume that the circle would simply cave in onto itself I still find this quite interesting and do seek other, more professional, eyes.

Thank you.

 

[mfb]

Can you explain the setup you have in mind? Which circle, where?
In a cylinder, there is a small force inwards. The force is the same everywhere, neglecting effects from the top and the bottom of the cylinder.