# What would be the optimal diameter of gold grains if you want to fill a pool with them and swim in it?

I was wondering, if I were to fill a pool with gold/gold dust, what would be the optimal diameter of the grains to minimalize the friction to a point at which you would be able to swim in it ((and if swimming is not possible, what size would pose the least resistance))?

This is assuming the grains are spherical and the normal gold-on-gold friction coefficient applies.

Thanks!

• What a bizarre question...I mean, it's interesting, but also bizarre (+1) – Zach466920 Jul 12 '16 at 20:30
• It wouldn't matter how small you made them, they would always clump together to form an almost solid material, as gold does not have any oxide layers, so the interatomic forces at the surface are almost the same as in the bulk of the material. You could probably make a colloidal gold suspension that one can swim trough, though. – CuriousOne Jul 12 '16 at 20:39
• I would make shallow balls like those found in kids playgrounds, my guess is that it could work better than any solid size – Wolphram jonny Jul 12 '16 at 20:41
• Just a side note: the human body is about 10x less dense than randomly packed gold spheres, so we shouldn't sink no matter how small the particles. – lemon Jul 12 '16 at 20:48
• Also, I don't mind running some hard sphere simulations if anyone has a good idea of what to measure. – lemon Jul 12 '16 at 20:49

It's not so much about a grainsize. As long as the grains are big enough to aloud air(gas) flow through them, you can make them liquid by"Fluidization";

"Fluidization (or fluidisation) is a process similar to liquefaction whereby a granular material is converted from a static solid-like state to a dynamic fluid-like state. This process occurs when a fluid (liquid or gas) is passed up through the granular material."

Basically You can easily swim in Gold, sand or any solid granular material if you fill a whirlpool with it, and blow air through it like shown in this video.

Edit: The given comment forces me to expand the answer. This is about Buoyanycy. It has nothing to do with density. (Explained in video at 6 min->) Another aspect is terminal velocity. If the gas speed is higher than the terminal velocity of the object floating in fluidized granulars, then the object will raise to the surface.

The terminal velocity of Human is 53 m/s, which means that it can be written;

$$\frac{v^2}{2}=\frac{p}{\rho}$$

Where we know the $$\rho=19.32$$ (Gold, $$kg/m^3$$) and $$v=53 m/s$$, so we can solve;

$$\frac{v^2\rho}{2}=p=27134 Pa$$

Which alouds us to solve the maximum granulat size. The area of the granulat is;

$$A=\pi r^2$$ And the weight of the granulat is;

$$m= \rho \frac{4}{3} \pi r^3$$

Which produces a simplifed model to calculate the maximum $$r$$, as $$p=\frac{F}{A}$$ and $$F=ma$$ and $$a=g$$, so

$$p=\frac{\rho \frac{4}{3} \pi r^3 g}{\pi r^2}=\rho \frac{4}{3} \pi r g$$

So the r can be solved to be;

$$\frac{3p}{4 \pi g}=r$$

Which with $$p=27134 Pa$$ gives r= 660 m.

(Somehow I don't believe this answer's magnitude, but I leave it here, and get back to it later. Good night)

• Not really : gold is so dense the gas velocity necessary to fluidize it would be so high that a human would be blown away. – blacksmith37 Jun 20 '19 at 18:27
• @blacksmith37 Not really. Basically Pressure=velocity. The big object like human will sink in the granulars (gold), because the smaller (gold) particles are blown around it. Denser material only needs higher starting pressure. At the surface of the granulars the pressure is atmospheric. And the gas has a maximum velocity causing the granulars to produce gaps where the flow can go through. – Jokela Jun 20 '19 at 18:46
• There would be personnel hazards involved in trying to swim in a fluidized bed. If a person doesn't wear a sealed helmet with its own air supply, you would expect the fluidized particles to get in his/her nose, mouth, lungs, eyes, and ears. THAT would be one terrible way to die! – David White Jun 20 '19 at 19:20