Advanced #67

Viscosity and Prandtl number increase strongly with decreasing temperature

Upon cooling, the viscosity and Prandtl number of water increase unusually strongly.

Scientific Explanation

All liquids become more viscous when cooled, but water’s viscosity increase is unusually steep. Viscosity nearly doubles between 25 and 0 degrees Celsius, rising from 0.89 to 1.79 millipascal-seconds. In the supercooled regime, the increase accelerates dramatically.

Alongside viscosity, the Prandtl number also rises steeply. The Prandtl number is the ratio of momentum transport (viscosity) to heat transport (thermal conductivity) and indicates whether momentum or heat is transported faster in a flow. For water, the Prandtl number climbs from about 1.7 at 100 degrees Celsius to over 13 at 0 degrees Celsius — an increase by nearly a factor of eight.

The steep rise in both quantities is caused by the progressive strengthening of the hydrogen bond network at low temperatures. The colder water gets, the more ordered ice-like structures form. These impede momentum exchange (flow) more strongly than heat transport, driving up the Prandtl number.

Viscosity and Prandtl Number vs Temperature Dual-axis chart showing water viscosity and Prandtl number both increasing steeply at low temperatures. Viscosity rises from about 0.3 mPa s at 100 degrees C to about 1.8 mPa s at 0 degrees C. The Prandtl number rises from about 1.7 at 100 degrees C to about 13 at 0 degrees C. Viscosity (mPa·s) Prandtl Number Temperature (°C) 0 25 50 75 100 0 1.0 1.8 0 7 13 Viscosity Prandtl Number Viscosity & Prandtl Number vs. Temperature
Viscosity and Prandtl number of water rise steeply upon cooling — a sign of increasing structural order.

Everyday Relevance

The steep viscosity increase upon cooling explains why cold water flows noticeably slower through narrow pipes than warm water. In thermal engineering, the high Prandtl number of cold water has practical consequences: in heat exchangers, the boundary layer at low temperatures is thinner, affecting heat transfer rates. Engineers must account for this when designing heating systems, cooling circuits, and industrial processes.

In nature, this effect is also significant: water in cold polar seas is considerably more viscous, influencing ocean current patterns and nutrient transport.