Theory of Fluids Enters the 21st Century

In the second half of the 20th century, a conceptual tsunami swept through physics. The discovery that our world emerges from a microscopic world of molecules, which emerges from an even more microscopic world of subatomic particles (which in turn emerges from even stranger stuff) triggered the rewriting of our theories of matter. But the revolution didn’t reach fluids.

Their governing equations remained in their simple, vintage form: the Navier-Stokes equations, first developed in the 19th century. The Navier-Stokes equations are enormously successful at predicting how fluids flow and swirl. But they fail to account for the existence of swarms of microscopic bits that make up matter.

Now physicists have a theory that does. It is the fruit of a 20-year effort to rebuild the theory of fluids from the ground up. Along the way, physicists have come up with a whole new way of defining what it means to be a fluid, based on fundamental properties known as symmetries, and have shown that the Navier-Stokes equations are a consequence of symmetries, which explains why the equations take the forms that they do.

By understanding the origins of the Navier-Stokes equations, researchers have found a way to go beyond them, redefining what it means to be a fluid and predicting new behaviors that stem from the motions of microscopic particles. The trail to understanding fluids as the product of the microscopic world was blazed, ironically, by physicists thinking about some of reality’s biggest scales. It would take insights from researchers studying black holes and the universe at large to finally bring fluids into the modern era.

For centuries, scientists have understood the basics of fluids. In the 1750s, the mathematician Leonhard Euler adapted Newton’s second law of motion — the same one that gives us F = ma — to predict the motion of liquids. Euler’s equations work perfectly for “perfect” fluids, in which a current can flow forever because the fluid has no viscosity — a sort of intrinsic stickiness — to slow it down.

In the early 1800s, Claude-Louis Navier and George Gabriel Stokes gave Euler’s equations an upgrade. The new Navier-Stokes equations could handle any fluid, perfect or not. They could handle the way one fluid dissipates in another, like an ink drop spreading out to fill a glass of water, and the way fluids (including air, which is technically a fluid) experience friction.