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My reason for thinking that sand in a vacuum would be a good insulator is that heat cannot be conducted in a vacuum, and the area of contact between adjacent grains of sand is very small, which means heat would transfer between grains relatively slowly. Is this correct, or is there something I'm missing? Also, the sand is there instead of pure vacuum for structural support.

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    $\begingroup$ Good compared to what? Certainly it will be a worse insulator than just vacuum with no sand. $\endgroup$
    – The Photon
    Jun 5, 2022 at 15:45
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    $\begingroup$ You may be interested in this paper: dspace.mit.edu/bitstream/handle/1721.1/72769/29813396-MIT.pdf $\endgroup$ Jun 5, 2022 at 17:06
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    $\begingroup$ What would be the reason for filling the space with sand? You said, "...as the sand gets deeper." But, why would you want the space to be "deep?" A millimeter of empty space is as good as a meter of empty space for purpose of preventing heat transfer by convection and conduction. $\endgroup$ Jun 5, 2022 at 17:08
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    $\begingroup$ Is sand in coffee a good drink? I think so because coffee is a good drink, and if the sand grains are too far and few between, there is hardly any contact between them and your tongue. $\endgroup$
    – Kaz
    Jun 6, 2022 at 8:19
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    $\begingroup$ Sand is used to fill hot plates to get even thermal contact with uneven specimens so I would say no. $\endgroup$
    – DKNguyen
    Jun 7, 2022 at 0:13

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Simply put: If sand in vacuum had a heat conductivity close to that of vacuum, i.e., at least much closer to zero than the heat conductivity of the silicon dioxide (aka glass) it consists of, something similar would have to be true for sand in air.

But: the heat conductivity (all numbers from the German Wikipedia) of dry sand (in air, I suppose) is 0.58 W/(m·K), while that of glass is 0.76 W/(m·K) and that of air is 0.026 W/(m·K). So, if (air-filled) sand is that far (i.e., 20 times!) away from pure non-convective air (even though the total contact area between grains is supposedly minute), replacing air with vacuum will most likely change nothing significant.

Don't ask me why this is so. Nevertheless it is an interesting question, especially because you probably thought of the sand providing the mechanical support for the vacuum against the outside pressure.

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Powder filled vacuum (I don't know if sand per se is used for this purpose) is in fact used in cryogenic insulation, and can be better than vacuum alone, because vacuum alone is susceptible to radiant heat transfer and also a type of heat conduction that happens because the mean free path of the remaining molecules (in the less than perfect vacuum) is large, so the individual molecules can bounce between the inner and outer walls like ping pong balls, transferring heat. The powder interrupts these transfer modes, while having a very low conductivity itself.

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    $\begingroup$ What kind of powder? $\endgroup$ Jun 7, 2022 at 2:09
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    $\begingroup$ I have heard of silica being used. You can look up Vacuum Insulated Panels, or powder filled vacuum insulation for more information $\endgroup$
    – RC_23
    Jun 7, 2022 at 2:13
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Comparing sand in air to sand in vacuum:

The sand in vacuum is less conductive than sand in air in all reasonable conditions.

The reason is, the air conducts some heat and vacuum doesn't, air can even facilitate convection, on the other hand, air does not interfere much with radiative heat exchange between the sand grains.

Comparing sand in vacuum to vacuum:

Here, things get more complex.

At high enough temperatures, the radiative heat exchange will dominate (it increases as T^4). Sand will absorb part of the radiation and will radiate some of it back to the source, e.g. the exchange will be slowed down.

On the other hands, at low enough temperatures, the radiative heat exchange will be of much less importance and the heat conduction of the grains will dominate. I.e. at low temperatures, the sand will improve the heat exchange in vacuum.

Comparing sand to a single, continuous blob (stone) of the same material

Again, we depend on temperature. Sand will exchange heat better if the radiative exchange dominates, else it is the stone.

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    $\begingroup$ I think considering radiative heat exchange is very relevant: The answer will depend on the temperature. You could improve this answer by providing an estimate for the temperature above which sand is better than pure vacuum. $\endgroup$ Jun 6, 2022 at 14:52
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It sounds reasonable. But there are a few more things to consider.

How good a vacuum are you talking about? If you mean just good enough to make a better insulator, likely yes. But if you are pulling a vacuum just to get an insulator, there are likely better ways. A vacuum thermos bottle does this. It does not use sand, just vacuum. To make this work, it supports the inner bottle only at the neck.

If you need a vacuum for other reasons, you likely need a good vacuum with a very low residual pressure. Possibly you want it clean, with very little contamination. Putting sand in it may spoil it.

Sand has a lot of surface area. All that surface can contain contaminants. Sand is like dirt. You don't really know what is in it. Some grains may be contaminants. Typically you heat up a vacuum chamber like an oven to evaporate contaminants. If some grains are made of or contain something that evaporates at high temperature, heating will bring it out.

There are a lot of crevices. Air molecules deep in the sand have a long twisted path to get out, where they can be pumped away. It will take a long time to pump down.

If you really need a bed on which you lay something and want that bed to be insulating, perhaps larger ceramic beads would be better. They can be clean, round, and insulating at high temperature.

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"the area of contact between adjacent grains of sand is very small, which means heat would transfer between grains relatively slowly"

But there are many small grains so there are many contact points. You're focusing on one factor and neglecting counterbalancing factors so you cannot say from just one statement or even both statements on their own.

As grain size decreases, would you say it approaches empty space? Or a solid? The answer is solid so it's certainly going to be better conductor than a coarser medium like gravel since it is a better approximation of a solid block of silica.

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Assume the sand can be approximated as tiny incompressible spheres. A homogeneous sand mixture (vacuum or air) will have a packing efficiency of between 60% and 70% (approximately). So the overall thermal resistance of the sand will be 65% sand and 35% either vacuum (best thermal resistor) or some other material (thermal resistance worse than a vacuum). So sand mixed and held in a vacuum will have better insulating properties than sand mixed with air and held at a constant pressure.

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    $\begingroup$ How does the overall thermal resistance follow? Doesn't it depend on the mechanism of conduction? $\endgroup$ Jun 7, 2022 at 1:52
  • $\begingroup$ If the 35% void were filled with silver particles instead of air wouldn't the overall resistance drop due to conduction? How is it different with a vacuum which offers no conductive path? $\endgroup$ Jun 7, 2022 at 15:45

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