Brewing coffee and turbulence: The surprising link

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In 1883, Osborne Reynolds made a fascinating discovery while experimenting with water flow.

By injecting ink into water in a clear pipe, he observed that as the water’s speed increased, its flow changed from smooth and predictable (laminar) to chaotic and unpredictable (turbulent).

This transformation created localized turbulent patches, known today as “puffs.”

His work launched the field of fluid mechanics but also left many questions unanswered, such as why these transitions occur and how to measure them accurately.

Fast forward to today, an international research team led by Nigel Goldenfeld from the University of California San Diego and Björn Hof from the Institute of Science and Technology Austria has solved this long-standing mystery using statistical mechanics.

Their findings were published in Nature Physics.

One unique aspect of their research is the combination of fluid mechanics and statistical mechanics. Statistical mechanics typically deals with systems in equilibrium, but turbulence is different because energy continuously moves in and out of the fluid.

By examining the problem through this lens, the team discovered that fluid flow in a pipe undergoes a non-equilibrium phase transition, called directed percolation, at the point where it shifts from laminar to turbulent flow.

Imagine making coffee. When water flows through coffee grounds, it must move at a certain rate to make a good cup of coffee.

If it flows too fast, the coffee is weak; too slow, and the water spills. The ideal flow rate happens at what is known as the directed percolation transition. This concept, surprisingly, shares statistical properties with the transition from laminar to turbulent flow in fluids.

Goldenfeld and his team have been working on this problem for over a decade. In 2016, the Hof group demonstrated this transition in a circular setup. However, understanding it in a straight pipe posed challenges. Conducting experiments in a pipe would require an impractically long pipe and many years of data collection.

To overcome these challenges, the team used two approaches. First, they used pressure sensors to observe and measure the behavior of puffs in a pipe.

They inputted this data into a computer simulation, showing that puff behavior matched the directed percolation transition. Second, they used statistical mechanics to predict puff behavior mathematically, further confirming their hypothesis.

Their research revealed another unexpected discovery: like cars in a traffic jam, puffs can cause blockages in the pipe. These “puff jams” can form and dissipate randomly, similar to how traffic jams clear up without a clear reason.

At the critical transition point from laminar to turbulent flow, these puff jams tend to “melt,” exhibiting special statistical behavior.

Goldenfeld remarked, “This work not only solves the mystery of the laminar-turbulent transition in pipes but also shows how different scientific fields can illuminate difficult problems. Without statistical mechanics, understanding this fluid mechanics phenomenon would have been impossible.”

This breakthrough highlights the unexpected connections between everyday phenomena, like brewing coffee, and complex scientific problems, demonstrating the power of interdisciplinary research.