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I have a bottle of vodka that has a load of gold flakes suspended in it. It has been sat still for over 24 hours and the flakes are all still suspended within the liquid: they have not risen to the surface or sunk to the bottom. Any ideas as to the physics behind this?

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It is important when thinking about this to recall that gold leaf can be easily (i.e. with low tech tool and no measuring equipment to speak of) prepared only a few molecules thick, so that the surface area to volume ratio of this stuff is very high indeed. –  dmckee Dec 24 '13 at 18:13
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3 Answers

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The viscosity of water ethanol mixtures isn't especially high, though the wetting properties of vodka may make it seem oily. Actually water ethanol mixtures are highly non-ideal: both water and ethanol have a viscosity of about 1 mPa.s at room temperature, but a mixture can achieve a viscosity of over 3 mPa.s. See this paper or Google for many such tables.

The real reason gold leaf will stay suspended for so long is that it is extraordinarily light. The thickness of gold leaf is around 100nm, and since the density of gold is 19300 kg/m$^3$ a flake of gold leaf 1mm by 1mm weighs just 2 $\mu g$ so the downward force due to gravity is 20 nano-Newtons. At such low forces water is viscous enough to keep the gold suspended for long periods.

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Could you estimate "long periods"? Is it hours, days, months? –  Bernhard Dec 25 '13 at 9:04
@Bernhard: I must admit that I shied away from estimating a time because I'd have to go away and Google the various numerical factors for viscous drag on a flat plate. In any case the day/night temperature cycle will probably generate enough convection currents to keep the flakes suspended. Once Christmas is over I'll get Googling and see if I can estimate a timescale. –  John Rennie Dec 25 '13 at 12:29
Probably an first estimation based on a rigid sphere would give a good first idea, so $v=F/20\mu R$, which, when plugging in numbers would be around $1mm/s$. Probably plugged in some wrong numbers, because this seems a bit large (or Stokes drag is to rough of an estimate) –  Bernhard Dec 25 '13 at 12:49
My thinking is that thermal motion/entropy/convection would probably overwhelm gravitational settling. –  lionelbrits Dec 25 '13 at 15:28
Until I see micrographs to prove otherwise I will continue to suspect gold leaf has a pretty smooth surface. The roughness is obviously well below the micron scale or it wouldn't be shiny. –  John Rennie Dec 25 '13 at 18:58
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My theory. The gold weighs the same as the vodka it displaces. Therefore it suspends rather than sinks or floats.

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Theory? Density can be quickly compared. Right? –  Bernhard Dec 27 '13 at 14:40
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I'd imagine the viscosity of the vodka is pretty high, and this is why the gold flakes are not rising or sinking within the bottle. Moreover, the viscosity of Vodka has no absolute numerical value as brands vary, but it's pretty high.

Here's an useful link on the viscosity of alcohols.

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The viscosity of vodka is high? I don't know much about alcoholic drinks, but as far as I understand vodka is practically nothing but a ~40% solution of ethanol in water, neither of which has a high viscosity. I suspect the true answer has to do with convection currents sustained by the evaporation/condensation of the volatile alcohol, but I can't be sure. –  Nicolau Saker Neto Dec 24 '13 at 16:56
Better link on the viscosity of water/(ethyl)alcohol mixtures. Also, you can see a difference in the behavior of high proof vodka and that of water in a glass, though at least some of that must be surface tension related rather than viscosity related. Around 80-100 proof this stuff is (only) 2 to 3 times as viscous as pure water (temperature dependent). –  dmckee Dec 24 '13 at 18:16
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