# Does water expand uniformly in a rigid container that is open on one end?

Lets say there is a semi-rigid container (made of plastic, say). It is filled 90% full of water and put in a freezer standing upright. The top of the container is open. When the water freezes, my understanding is that it expands roughly uniformly in all directions: https://www.reddit.com/r/askscience/comments/278z5x/when_water_freezes_does_it_expand_uniformly_in/ So my question is: will the ice stop expanding uniformly once it reaches the walls of the container? Will it only expand along one axis once it reaches these walls?

I also know that water freezes from top to bottom due to density changes upon freezing: Why does water freeze from top to bottom So, I imagine the water will freeze at the top of the water line, and then the block of ice will be pushed upwards in the container as it continues to freeze. Is this true? Will the side walls experience no pressure unless the container is closed? Or will the container still bulge at the sides? If it does bulge, then what causes the ice to continue to expand towards the side walls?

• youtu.be/sIt4RXSzYOo – physicopath Dec 21 '16 at 20:09
• I do not think that "water freezes top to bottom" is a correct statement. It freezes where it is cold. And also the speed of cooling is important. – physicopath Dec 21 '16 at 20:13
• Sorry, I do get that. I think the "top to bottom" saying comes from observing lakes freeze. The ground acts as an insulator, so the top of the water freezes first. This can be observed in thick-walled containers as well. – jasonbcox Dec 21 '16 at 21:34
• From the video, it looks like the water in contact with any wall of the container freezes first and pushes the water out of the top. Very interesting. The bottle doesn't appear to bulge at all through this process. – jasonbcox Dec 21 '16 at 21:35

Here is my understanding - it will depend on the exact shape of the container and the conductive properties of the walls.

As you say, the surface of the liquid will freeze first. There are two reasons for this. First, water at 0 °C has lower density than water at 4 °C, so "cold water rises to the top". And since the coldest water will freeze first (barring effects of nucleation), freezing will start with a film on the surface.

However, once all the liquid reaches a temperature of 0 °C, any location where water can lose the heat of fusion can in principle become ice. If the walls are sufficiently conductive, eventually the water adjacent to the walls will freeze more rapidly than the water below the ice at the surface (as the layer of ice gets thicker it starts to act as an insulator). And once you have a region of ice "on all sides of the container", the increase of volume that accompanies further freezing will result in isostatic increase in pressure inside the "ice pressure vessel". In principle this will result in pressure in all directions - and since the ice at the top will typically be thicker (and therefore stiffer) you can imagine more pressure will be applied laterally.

If the container is quite shallow, and / or the walls quite insulating, freezing may continue in the top-down way. It depends...

• I see. So in a more extreme case where you have a thin-walled steel container (ie. the container is very thermally conductive), then there would definitely be pressure issues on the container walls. Also, the container I'm imagining is just a simple smooth-walled tube that is closed on the bottom so that it can hold water. – jasonbcox Dec 21 '16 at 18:36
• Yes that's my understanding. – Floris Dec 21 '16 at 18:53
• Under certain conditions you get ice spikes. – Keith McClary Dec 22 '16 at 3:58
• I thought about the container shape some more. If I had a cone-shaped container with the point facing downwards, the freezing should occur bottom-up due to increased surface-to-volume ratio near the bottom, and as a result it should significantly reduce pressure on the side walls. Does this sound correct? – jasonbcox Dec 22 '16 at 20:10
• @jasonbcox if you have sufficient conductivity through the walls, then yes that would encourage growth from the bottom up. But only in small vessels, and if the water is already uniformly at 0°C. Remember that in a larger vessel (lakes etc) 4 °C water will drop to the bottom (highest density). If you start with "warm" water, the cone shape may not be sufficient to ensure bottom-up freezing. – Floris Dec 22 '16 at 20:15