Scientists catch sperm ignoring a major law of physics

Swimmers and fish move through the water following much the same principle of "action-reaction" (for every action, an equal and opposite action applies). By the coordinated movement of their limbs, they displace the water and, in reaction, their bodies move forward despite the resistance of the water. But if they tried to swim in molasses, they'd never make it, as the resistance of the molasses would absorb all their energy and they'd never make it forward. The Scallop Theorem clearly demonstrates what happens in such fluids with high Reynolds coefficients. Newton's third law applies.

Yet, on another scale, single-celled algae and spermatozoa manage to advance rapidly and with ease in highly viscous fluids and over very large distances in proportion to their size. How do they get around Newton's implacable third law?

Symmetries and reciprocity

Mathematician Kenta Ishimoto's team set out to understand how these single-celled creatures snake their way through environments that, in principle, should paralyze their movement. When the third law applies, it does so symmetrically and reciprocally in environments in equilibrium; the solution to the problem posed lies in what are called "non-reciprocal and non-symmetrical interactions", which characterize chaotic systems and whose elements participate dynamically in the system, like birds in a murmuration or pedestrians on a sidewalk. By establishing relationships with their environment, they alter the conditions of equilibrium.

In the case of unicellular algae and spermatozoa, researchers have modeled the movement of cells and their flagella. In principle, a viscous fluid would dissipate the flagella's energy, preventing them from moving and exhausting them within minutes. And yet, somehow, the flagella manage to propel these cells without provoking any reaction from their environment.

The researchers discovered that flagella have developed an elasticity and flexibility on a microscopic scale that enables them to move without losing much energy in the surrounding colloid-like fluid, which are complex plasmas where interactions are non-reciprocal. As quantum physics researchers have named stealth particles with names like "charming" or "strange", the researchers called this property "strange elasticity".

"Using simple, solutionable models and biological flagellar waveforms for chlamydomonas algae and spermatozoa, we studied the strange flexural modulus to decipher non-local and non-reciprocal internal interactions within the material."

But this strange elasticity property does not fully explain the propulsion generated by the undulatory motion of the flagella. The researchers have therefore also derived a strange modulus of elasticity to describe the internal mechanics of flagella. Their investigations include "transverse responses", modified dislocation dynamics and topological waves. What is certain is that the greater the strange modulus of elasticity, the better the mobility in such fluids.

While these results may eventually help in the design of small micro-robots mimicking living materials, modeling methods can already be used to better understand the underlying principles of collective behavior.

To see the research - Odd Elastohydrodynamics: Non-Reciprocal Living Material in a Viscous Fluid - Kenta Ishimoto, Clément Moreau, Kento Yasuda - Physical Review Journal

Illustration - 610820594

References

Scallop Theorem - https://en.wikipedia.org/wiki/Scallop_theorem

Reynolds number - https://en.wikipedia.org/wiki/Reynolds_number

Murmuration - Dossier Thot Cursus - https://cursus.edu/en/files/13523/murmuration

Kenta Ishimoto - Professor of Applied Mathematics - Department of Mathematics, Kyoto University
https://www.math.kyoto-u.ac.jp/~kenta.ishimoto/

Odd Elastohydrodynamics: Non-Reciprocal Living Material in a Viscous Fluid - Physical Review Journal
https://journals.aps.org/prxlife/abstract/10.1103/PRXLife.1.023002

Odd Viscosity and Odd Elasticity
https://www.annualreviews.org/content/journals/10.1146/annurev-conmatphys-040821-125506

Experimental study of the nonreciprocal effective interactions between microparticles in anisotropic plasma
https://www.nature.com/articles/s41598-020-70441-z

A New Theory for Systems That Defy Newton's Third Law
https://www.quantamagazine.org/a-new-theory-for-systems-that-defy-newtons-third-law-20211111/