|frozen ice in cup|
We expected a flat surface as one would see on the surface of a frozen lake. The questions we had were 1) Why did this happen? 2) How can we make a flat surface from the process?
The difference from the freezing of water in a ceramic mug in a freezer and that in a lake is that the mug was exposed to -20F environment from all directions, while the lake water got cold only from top surface. So the freezing process should be different.
In a lake the freezing process is best illustrated by the following figures:
Since cold water at 4C has smallest volume and highest density, it will sink to the bottom, so the body of lake water can not freeze until the whole body of water reached 4C - not more natural convection from freezing water. At this time as surface water continue to cool to 0C, the freezing water density will decrease, and the surface will continue to cool down without sinking. So in a lake the ice forms at the surface and moving downward. The reason we typically not seeing bulging ice could be a) the lake bed will deform due to the increase of the volume of the freezing process; 2) formed ice can tolerate small volume increase from water right beneath it turning to ice.
Freezing in the mug in a freezer is quite different. It is expected that the water would start to freeze from the water in contact with the mug as well as the top of the water surface. So one would expect that the water would freeze from its outer surface inward. During the freezing process, there should be a stage when there is a layer of ice on the outer surface of the water in the mug and its inner body is still liquid. At this stage the ice surface should be flat - despite the fact that when water becomes ice it increases its volume because ice can tolerate small volume change. As more and more ice formed in the center, the volume change will be larger, as mug is much stiffer than ice, the only direction the increased volume can move is toward the top surface of the ice - which would crack to release the confinement to the center and allow the volume increase to occur.
We conducted a series tests to verify the reasoning, and we found that the frozen surface was flat at ~ 1 hour time, and there is a liquid center in the frozen water. When we left the mug in the freezer for 2 hours or longer, the water in the mug was fully frozen and a bulge formed with evidence of cracking at the top surface - exactly as what was observed in the first test. As we figured out the reason we found the answer to our second question as well.
We also observed that the flat surface in a partially frozen mug was not exactly flat. There was a very shallow wave shape to the surface. Upon observation, it is believed to be caused by the steady humming (vibration) of the refrigerator.
This process enabled us one more time to remind Nicholas that science fair project is for learning how to conduct scientific research, and is to explore and find reasons for unexpected observations. Figuring out unexpected observations led to the solution of this small problem and many great scientific discoveries.
Note: If you are observant, curious and tend to connect dots. You might ask why ice cube made in the freezer has flat surface. This becomes an interesting brain exercise in light of our observation.