Water, Water Everywhere, but Not Hot Enough to Sink

Water has lots of odd properties. Normally, we think of fluids as being less dense when they get warmer. Hot air balloon rides, for example, would be much less exciting if warmer things tended to sink. However, one of the weirder properties of water is that unlike most liquids, its density doesn’t always decrease with temperature.

Water has lots of odd properties. Normally, we think of fluids as being less dense when they get warmer. Hot air balloon rides, for example, would be much less exciting if warmer things tended to sink. However, one of the weirder properties of water is that unlike most liquids, its density doesn’t always decrease with temperature. Up until about 4 degrees C, the density of water actually increases as a function of temperature. There are some fascinating physical chemistry reasons behind this involving the various supramolecular structures of water.

However, let’s take a look as it relates to engineering…

We are working on insulative technology for temperature sensitive vaccine storage, which requires very low thermal transfer to keep vaccines cold for long periods of time. Our current protocol to measure the thermal transfer in a device involves a technique we affectionately refer to as CoW (cold water warm-up). In CoW, the device is first filled with a large volume of near freezing water. Then, we place the device inside a warm environmental chamber and measure the temperature of the water inside the device as it warms up.  We can then fit the temperature response to a model that predicts how long the system will last when it’s loaded up with vaccines and ice instead of just cold water.

Interestingly, over the several days that it takes for our device to warm up by a few degrees, we can actually observe the density inversion of water inside our own system! Plotted above is the temperature trace from two thermocouples that were inserted into the device at the beginning of an experiment. You can see that, right at the temperature where fresh water has its density maximum (3.9 degrees), very interesting fluid dynamics show up. Before the inversion point, the bottom (green) thermocouple is in contact with water that is slightly warmer, and thus denser than the top (blue) thermocouple. Once the inversion hits, and density laws as we commonly think of them take over, the denser water at the bottom thermocouple is colder than the water at the top thermocouple. Looking at the graphs in reverse, the bottom graph shows that the denser liquid is always on the bottom, as we’d expect. But, when we cross-reference this with the top graph, we can see that the hotter fluid is on the bottom before the inversion, and on top after!

Also note that before the inversion, the two traces are fairly close together, but after the inversion, they are much further apart. This is because heat leak in the device is highest in the “neck,” which is at the top of the device. So, below the inversion point, water is warmed most rapidly at the neck, which then increases in density, rapidly sinking to the bottom of the device. And, voilà, we have an efficient convective cell (at least, efficient on the time scale of our multiple day experiment). However, after the inversion, the warm fluid tends to stay at the top, the cold fluid stays at the bottom, and heat transfer is dominated by slower conduction, instead of “efficient” convection.