Researchers Develop Microswimmer That Defies Laws of Fluid Dynamics

Researchers at Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), the University of Liège and the Helmholtz Institute Erlangen-Nürnberg for Renewable Energy have developed a new microswimmer that defies the laws of fluid dynamics. The swimmer could have applications in areas like healthcare, where it could be used to transport drugs through the blood. 

The team’s model connsists of two beads connected by a linear spring, and it is propelled by completely symmetrical oscillations. According to the Scallop theorem, this should not be possible in fluid microsystems. 

The researchers’ findings were published in Physical Review Letters.

Scallops and the Swimmer

Scallops swim through water by clapping their shells together, and while the scallop is opening its shell for the next stroke, its large size propels it through the moment of inertia. The Scallop theorem, however, applies more or less depending on the fluid’s density and viscosity.

According to the theorem, a swimmer that makes symmetrical or reciprocal forward to backward motions, similar to the way a scallop opens and closes its shell, will likely result in very small movement. 

Dr. Maxime Hubert is a postdoctoral researcher in Prof. Dr. Ana-Suncana Smith’s group at the Institute of Theoretical Physics at FAU. 

“Swimming through water is as tough for microscopic organisms as swimming through tar would be for humans,” Dr. Hubert says. “This is why single-cell organisms have comparatively complex means of propulsion such as vibrating hairs or rotating flagella.”

The FAU team collaborated with researchers at the University of Liège and the Helmholtz Institute Erlangen-Nürnberg for Renewable Energy to develop a similar swimmer that appears to not be limited by the Scallop theorem. The fairly simple model operates with a linear spring that connects two different sized beads. The microswimmer is still capable of moving through the fluid when the spring expands and contracts symmetrically under time reversal. 

“We originally tested this principle using computer simulations,” says Maxime Hubert. ‘We then built a functioning model.”

The team tested the model by placing two steel beads, which were only a few hundred micrometres in diameter, on the surface of water inside a Petri dish. The contraction of the spring was represented by the surface tension of the water, and a magnetic field was used to achieve expansion in the opposite direction. This system caused the microbeads to periodically repel each other. 

Real-World Uses

The swimmer achieves self-propulsion due to the different sizes of the beads. 

According to Dr. Hubert, “The smaller bead reacts much faster to the spring force than the larger bead. This causes asymmetrical motion and the larger bead is pulled along with the smaller bead. We are therefore using the principle of inertia, with the difference that here we are concerned with the interaction between the bodies rather than the interaction between the bodies and water.”

While the system is not incredibly fast, it moves forward about a thousandth of its body length during each oscillation cycle. However, the most impressive and important factor of the new system is the simplicity of its construction and mechanism. 

The team says such a system could be used to develop tiny swimming robots, which could have many real-world uses in sectors like healthcare. For example, they could be used for drug transportation. 

“The principle that we have discovered could help us to construct tiny swimming robots,” says Dr. Hubert. “One day they might be used to transport drugs through the blood to a precise location.”