Cars rely on a variety of lubricants to keep their moving parts from becoming expensive glitter, and that’s all down to viscosity, the ability of a material to flow without deforming (known as shear). Lubricants need to be able to flow at different temperatures without becoming too thin to do their job of alleviating friction between surfaces. And as it turns out, there’s an upper limit to viscosity that’s well beyond the weights listed on each bottle of motor oil.
In practical terms, the upper limit of viscosity is unlimited. That’s because when you start to look at higher values for viscosity, the discussion moves away from recognizable fluids to the rock-forming minerals that flow beneath the planet’s surface under ridiculously high temperatures. Masaki Yoshida, a professor at Japan’s Ritsumeikan University, nonetheless decided to find the physical upper limit of viscosity, and published findings on this “absolute cosmic limit” in the Physics of Fluids journal last month.
Professor Yoshida came up with a number of 1030±2 pascal-seconds (Pa s), a measure of dynamic viscosity that expresses a material’s ability to flow a given amount per second under a given amount of pressure. To put that very large number in perspective, water has a viscosity of approximately 10-3 Pa s, while honey has a viscosity of about 101 Pa s. A material this viscous flows so slowly that the timeframe for any measurable movement exceeds the age of the Earth. In practical terms, such a material is rigid, which is why it’s generally not a subject of fluid-dynamics studies.
I’d be a bit frightened by the engine that could produce internal temperatures high enough to need a motor oil that viscous. Dynamic viscosity for motor oils is usually measure in millipascal-seconds (MPa s, or an equivalent), which is one-thousandth of a Pa s. For non-winter weights, that value is divided by the density of the oil (known as kinematic viscosity). And in both cases, the weight number you see on the bottle is determined by measuring viscosity at multiple temperatures and creating an index from those measurements.
To arrive at that “cosmic limit,” the study relied on decades of geodetic data (dealing with the shape of the Earth itself), laboratory rock-deformation experiments, and simulations based on knowledge of geological processes that unfold beneath the Earth’s surface over millions of years. Because the materials exhibiting the highest level of viscosities aren’t lubricants, they’re the building blocks of rocks, which flow when tectonic plates move.
What was the point of all this? For researchers, it eliminates the placeholder of “infinite viscosity” often used in fluid-dynamics studies, providing a concrete upper limit. Granted, it’s one so high as to not affect more conventional research, which is why scientists previously described viscosity as “infinite” in the first place. In a press release, Ritsumeikan University also claims the findings could be useful in studying geologic activity past and present, as well as high-viscosity non-Newtonian fluids, those with viscosity that changes when subjected to force (like ketchup, which gets thinner when you shake the bottle). It’s also a cool reminder that the same principles that keep your engine alive also keep the planet alive.