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In a lecture by Purcell he mentions that he notices that there aren't any liquids with viscosities much less than that of water, even though they go up seemingly unbounded. In an endnote (endnote 1 in that copy), he mentioned that Weisskopf found a reason, but I haven't been able to find what that reason actually was.

Note that this is not about the AdS-CFT lower bound.

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Excellent question :-) – David Z Apr 18 '12 at 17:39
I think it is this paper in AJP. – Vijay Murthy Apr 18 '12 at 21:17
@VijayMurthy: that does look like the one. If you care about such things, I would be happy to accept the comment as an answer. An interesting answer may be to briefly summarise the arguments in that paper (which deals with a lot more than just the viscosity). – genneth Apr 19 '12 at 12:00
@genneth, I will try to summarize the paper when I have some time. You found it useful. That's more important...! – Vijay Murthy Apr 19 '12 at 12:12
Interesting - I would have assumed that liquids with non-polar molecules eg just diatomic N2 or O2 would be lower viscosity. – Martin Beckett Apr 19 '12 at 16:08

If "not much less than water" means "not an order of magnitude lower than water at room temperature" this is probably correct. However there are substances like with a viscosity 4 times less than that of water or with a viscosity 3 times less than water (at 20 degrees celcius). At lower temperatures (77K) you find liquid nitrogen with an viscosity less than 5 times that of water at room temperature. On the other side at 1K helium becomes a superfluid with effectively zero viscosity In that sense viscosity seems to behave similar to electric resistance, being lower with lower temperature. So without reading Weisskopf I guess it's simply room temperature which provides an lower limit to the viscosity of a fluid.

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