Freezing rate for water in supercooled ice

[Kyle Stevenso]

Bit of an odd one here, perhaps, but I'm hoping to get some back-of-the-envelope concept of how quickly a water channel that was melted into a block of -170 degree water ice would re-freeze. It's similar to trying to determine what would happen if I went ice-fishing on a comet in deep space -- would a 3' wide hole freeze back solid in just a few minutes, or would it take much longer? And if the hole / tunnel is increased to 6' wide, does it take four times as long? I realize much depends on the amount of water surface area in contact with the super-cooled ice -- which depends on the diameter of the tunnel -- but this is countered by the heat retention of the column of liquid ice, which is greater when the volume (and diameter) are greater. Trying to get even an order-of-magnitude estimate but my skills are failing me. Any help is immensely appreciated!

 

[LightHero]

Assuming the block of ice is at a constant temperature of -170°C, and that it is in a vacuum (no convective cooling from air), the hole/tunnel should re-freeze fairly quickly. The rate of freezing will depend on the surface area of the tunnel exposed to the cold ice and the heat retention of the liquid water inside. Generally speaking, the larger the surface area of the tunnel, the faster the water will freeze, and the larger the diameter of the tunnel, the slower the freezing process will be.To estimate the approximate time frame for re-freezing a 3' wide hole, one can assume that water has a specific heat capacity of 4.2 J/gK (at 0°C) and an ice density of 920 kg/m3. We can then calculate the amount of heat energy needed to freeze a certain mass of water – for example, a 3' wide tunnel would have a volume of approximately 1.2 m3 and thus a mass of 1.1 tonnes. This means that it would take approximately 4.7 MJ of energy to freeze this tunnel.Assuming the tunnel is initially filled with water at 0°C, and that the surrounding ice is at -170°C, then the rate of heat transfer from the water to the ice can be estimated using Newton's law of cooling. Assuming a constant heat transfer coefficient of 10 W/m2K, the rate of cooling would be approximately 3.3 kW. This means it would take approximately 1.4 hours to freeze the tunnel. If the tunnel was 6' wide, then this time would be doubled due to the increased volume of liquid water. Of course, these calculations are just back-of-the-envelope estimations and may not be accurate for all cases. The actual time frame for re-freezing will depend on a variety of factors such as the thermal properties of the ice, the temperature of the surroundings, the size and shape of the tunnel, the rate of heat transfer, etc.

 

[astrokreng]

The freezing rate of water in supercooled ice is a complex process and can vary depending on various factors such as temperature, pressure, and surface area. However, we can make some general estimations based on the information provided.

Firstly, it is important to note that the freezing rate of water in supercooled ice is much faster compared to regular ice. This is because the water molecules in supercooled ice are already in a highly organized state, making it easier for them to form into a solid structure.

In terms of the size of the water channel, a larger diameter would result in a longer freezing time due to the larger surface area in contact with the supercooled ice. However, as you mentioned, the heat retention of the column of liquid ice would also play a role. It is difficult to determine the exact relationship between the two without specific measurements, but it is safe to say that a larger diameter would result in a longer freezing time.

Another important factor to consider is the temperature of the supercooled ice. The lower the temperature, the faster the freezing rate. In your example, the temperature of -170 degrees would result in a relatively quick freezing time.

Overall, it is difficult to provide an accurate estimation without specific measurements and conditions. However, based on the information provided, it can be assumed that the freezing rate would be relatively fast, with a larger diameter resulting in a longer freezing time. Additional factors such as temperature and pressure would also play a role in the freezing rate.