How Tiny Swimmers Put the “Super” in Superfluid

For Superman and Supergirl, it’s alien DNA. For Spiderman, it’s the bite. For Iron Man, it’s the suit. But for some “superfluids,” it’s the tiny, self-propelled swimmers that are the source of their power.

Self-propelled bodies can decrease the viscosity of a fluid to zero through their
random diffusion and spreading process.
Image Credit: Sho Takatori and John Brady / APS.

Consider two cups, one filled with water and one filled with honey. Turn them upside down at the same time and it’s no surprise that the water flows out much faster. This is because the honey is thicker, more resistant to changing its shape. This is the property known as viscosity. Superfluids, being “super” in their ability to flow, have a viscosity of zero.

The viscosity of a fluid depends on its ingredients. If you’ve made gravy or sauces from scratch before, you probably know that you can thicken a liquid by adding cornstarch. The cornstarch particles spread out through the liquid and reduce how easily it can flow, increasing its viscosity.

At really low temperatures, helium-3 and helium-4 naturally demonstrate superfluidity, and it may occur in neutron stars and other strange states of matter as well. In recent years, research has shown that adding self-propelled bacteria (like E. coli) can reduce a fluid’s viscosity to zero, resulting in a superfluid-like material. New work by Sho Takatori and John Brady at the California Institute of Technology that will soon be published in Physical Review Letters adds another dimension to our understanding of why.

“Usually, to make fluids (like water) flow through a pipe, we need to impose a pressure difference between the ends of the pipe. When we turn on the sink faucet at home, water flows out because there is a pressure difference between the ends of the pipe. Alternatively, when we tilt a pipe towards the ground, hydrostatic pressure difference causes the fluid to travel downhill with gravity,” says Takatori.

However, fluids filled with swimming bacteria or microscopic self-propelled bodies can make a fluid flow even where there is no imposed pressure difference. “If this effect is strong enough, the fluid can (in theory) flow uphill against the force of gravity,” Takatori continues.

Since this discovery, researchers have been intensely studying why adding microswimmers to a fluid has this effect. We may be able to harness energy from bacteria by exploiting this interaction, perhaps even powering microelectronics or improving medical devices as a result. However, doing so requires a detailed understanding of the physics involved.

Conventional theories go something like this. Self-propelled bacteria spread out within a fluid. As each individual swims, it disturbs the fluid in its local area. The collective result of all of this motion adds together and changes how easily the fluid flows. For example, if the swimmers collectively push in the same direction that the fluid is already flowing, it flows more easily (the viscosity decreases). If they push in the opposite direction, the fluid flows more slowly (the viscosity increases). If the fluid isn’t moving but the collective push of the swimmers is strong enough, the fluid can begin flowing. If the collective push is strong enough to overcome the pull of gravity, the fluid can flow uphill.

In this new work, Takatori and Brady developed a simple mechanical model of a microscopic, self-propelled body swimming in a fluid. They mathematically studied how such a particle moves and diffuses through a fluid. Based on the result, they expanded the model to study how lots of these particles spread out through a fluid and generate a stress in the fluid. It turns out that this new source of stress impacts the viscosity of the fluid. This is something conventional theories have not considered: the random diffusion of self-propelled bodies can cause the fluid suspension to “stretch” and reduce the overall viscosity.

Next, the researchers tested their model by comparing it to experiments. They input data on the bacteria, fluids, and conditions of previous experiments into a simulation based on their model. Running the simulation gave viscosity predictions that were a good match to the actual results of the experiments.

Future experiments can test the model even more extensively. Under some conditions, the impact of random diffusion on viscosity is larger than in others. In addition, there are circumstances where this new model predicts different behavior than conventional models. New experiments could measure what actually happens under such conditions and whether reality matches these new predictions.

At this point, superfluids aren’t protecting citizens and saving lives, but that could change. As we learn more about what makes these fluids “super”, it should become clear whether and how we can use them to our advantage. Some comic book superheroes may rely on supernatural powers, but in the real world, harnessing physics may be just as powerful.

Kendra Redmond

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