Chirality inversion and odd transport in a suspension of living rotors

Isabelle Eisenmann; Pedro Cosme; Hannah van Sterkenburg; Hugo Franca; Titouan Seguy; Maria Tatulea-Codrean; Maziyar Jalaal

AI summary · arXiv: 2610.41016v1 · cond-mat.soft

Chirality inversion and odd transport in a suspension of living rotors

Isabelle Eisenmann, Pedro Cosme, Hannah van Sterkenburg, Hugo Franca, Titouan Seguy, Maria Tatulea-Codrean, Maziyar Jalaal

Original paper Submitted to arXiv on 29 Oct. 2026 License: CC BY-NC-ND 4.0 Also in: fr

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The essentials

Living microalgal rotors form a percolating chiral fluid whose collective rotation reverses cellular chirality, while even and odd diffusion respond differently to network connectivity.

Question

How does the internally driven rotation of living cells shape collective organization and transport as cell density increases? In particular, can it produce chirality inversion and alter odd transport near percolation?

Method

The authors studied uniflagellar Chlamydomonas reinhardtii cells, measuring individual and collective motion, tracer flow fields, cluster structure, and transport across packing fractions. They combined these experiments with a hydrodynamic model and numerical simulations; the percolation threshold was approximately φc ≃ 0.08, and odd and even diffusivities were estimated from position-velocity correlations.

Findings

Result Individual cells spin clockwise, while hydrodynamic pairs orbit counterclockwise.
See the passage in the paper
Strikingly, although individual cells spin CW, pairs orbit CCW (Fig. 3a).
Result The measured cluster statistics and scaling are consistent with two-dimensional percolation, with a critical packing fraction near 0.08.
See the passage in the paper
Several signatures of this geometrical transition - the cluster size distribution, its fractal dimension, the divergence of the mean finite-cluster size, and the scaling of cluster perimeter with size (SI) - are compatible with the two-dimensional percolation universality class, with a critical density $\phi_{c}\simeq 0.08$ [58].
Result The mean-squared displacement crosses from short-time superdiffusion to long-time diffusion across all studied packing fractions.
See the passage in the paper
The mean-squared displacement (MSD) shows a crossover from superdiffusive motion at short times, with $\langle\Delta r^{2}\rangle\sim t^{1.5}$, to diffusive motion at long times at all packing fractions (Fig. 4f).
Result Even diffusion increases with packing fraction, whereas odd diffusion is non-monotonic and peaks near the percolation threshold.
See the passage in the paper
While collisions generally hinder diffusion in passive systems, here $D_{\parallel}$ increases linearly with $\phi$.
Authors’ interpretation The authors interpret the opposite trends of even and odd diffusion as evidence that the two transport components respond differently to network connectivity.
See the passage in the paper
Overall, these results show that percolation strongly reshapes both even and odd transport: while even diffusion increases monotonically with connectivity, odd diffusion decreases above the critical percolation threshold, highlighting its distinct sensitivity to network topology.

Limitations

The proposed mechanism by which transverse forces frustrate phase separation is a hypothesis, and the authors state that it lacks a theoretical description in this regime.
See the passage in the paper
We hypothesize that transverse forces continuously break clusters apart, a mechanism that appears generic to chiral active systems [45, 34, 31], but lacks a theoretical description in this regime.
The numerical model is intended to identify important interaction ingredients rather than quantitatively reproduce the experimental dynamics.
See the passage in the paper
Rather than attempting a quantitative reproduction of the experimental dynamics, we use this model to identify which ingredients of the particle interactions are most important for destabilising persistent, locked configurations and promoting different collective behaviours.

Why it matters

The authors argue that internally driven living rotors can produce collective behaviors unlike externally driven rotors, including chirality inversion and percolation. Their results connect odd transport to suspension connectivity and motivate further study of transport across geometrical transitions in chiral active matter.

Written by AI from the paper. Passages are checked word for word against the text we analysed; the rest may contain errors.

AI-generated keywords: microscopic chirality active rotors hydrodynamic interactions percolation odd diffusion

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Comprehensive Summary
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Original abstract

The paper examines how microscopic chirality in living particles shapes collective motion and transport. Specifically, the authors ask whether suspensions of self-actuated rotors behave like systems of externally driven spinning particles, and how collective organization affects ordinary and chirality-dependent diffusion. The experiments use uniflagellar mutants of the microalga *Chlamydomonas reinhardtii*. Unable to swim, individual cells spin in place at approximately 4 Hz. The researchers tracked cells and passive tracer beads in microfluidic chambers, measured the flow around isolated cells, and imaged suspensions across a range of cell densities. They combined these measurements with a low-Reynolds-number hydrodynamic model and simulations of small groups of interacting particles. The model represents each cell’s flagellum and body using force and torque singularities, accounts for the nearby wall, and enforces zero net force and torque on the fluid. The measured flow around an isolated cell forms a spiral rather than the simple vortex expected from an externally torqued rotor. Fluid moves counterclockwise toward the cell out to roughly three cell radii, then reverses direction. Beyond about seven radii, the signal becomes indistinguishable from noise. The model attributes this pattern to the balance between the rotating body and the flagellum’s internally generated beat. The rotation-averaged flow decays steeply with distance: in the far field, the radial component scales approximately as the inverse fourth power of distance, while the azimuthal component scales as the inverse sixth power. Hydrodynamic attraction draws neighboring cells together. Pairs orbit counterclockwise despite the clockwise spin of individual cells, typically maintaining a separation of about 20 micrometers, or four to six cell radii. Their orbital frequencies agree with the predicted flow across the measured range. Small clusters of up to four cells tend to rotate as persistent structures, while larger groups rearrange and behave like fluids. Simulations suggest that noise or variation in cell size can disrupt otherwise stable, locked configurations. At higher densities, clusters merge into a dynamic, system-spanning network. Several cluster statistics are consistent with two-dimensional percolation, with a critical area fraction near 0.08. Cells remain fluid-like rather than forming a positionally ordered lattice, and their neighborhoods continue to change. Mean bond-survival times decrease from more than 100 seconds in dilute suspensions to about 10 seconds at higher densities. Transport measurements reveal short-time superdiffusion, with mean-squared displacement scaling approximately as time to the power of 1.5, followed by ordinary diffusion at long times. The authors also calculate an even diffusion coefficient, which describes transport along a density gradient, and an odd diffusion coefficient, which describes transport perpendicular to it. Even diffusion increases approximately linearly with packing fraction. By contrast, odd diffusion peaks near the percolation threshold and declines at higher densities. The authors tentatively attribute this pattern to changes in the available cluster-boundary perimeter. These results suggest that percolation affects the two forms of transport differently. The study concludes that internal actuation and torque balance can reverse chirality between individual cells and collective motion, while network connectivity reshapes odd transport. Its main limitations are the use of a single mutant alga in confined, wall-bounded, effectively two-dimensional observations; a deliberately minimal hydrodynamic model with manually fitted parameters; and a still-hypothetical explanation for the maximum in odd diffusion. The work establishes an experimental platform and identifies associations between percolation and transport, but it does not show that the observed trends are universal across living rotors or other systems.

When Living Rotors Move Together, Their Spin Can Change Direction

Microscopic organisms can do more than swim: some spin in place, stirring the fluid around them. What happens when many such living rotors gather? In “Chirality inversion and odd transport in a suspension of living rotors,” Isabelle Eisenmann, Pedro Cosme, Hannah van Sterkenburg, Hugo Franca, Titouan Seguy, Maria Tatulea-Codrean et al. investigate how individual rotation shapes collective motion and particle transport.

The study finds a striking contrast: individual cells spin clockwise, yet neighboring cells orbit one another counterclockwise. As cell density rises, those interactions build a shifting network, and transport changes in ways that depend on direction. The results connect the organization of a living suspension to both ordinary diffusion and a less familiar, sideways form of diffusion.

A living rotor that cannot swim

The researchers studied uniflagellar mutants of the microalga Chlamydomonas reinhardtii. Because these cells cannot swim normally, they spin in place at about four rotations per second. This made them useful for examining how a self-actuated spinner affects nearby fluid and other particles.

In microfluidic chambers, the team tracked cells and passive tracer beads, measured fluid flow around isolated cells, and imaged suspensions at different cell densities. They paired these experiments with a low-Reynolds-number hydrodynamic model and simulations of small groups. The model represented the cell body and flagellum as sources of force and torque, included the influence of a nearby wall, and required the cell’s net force and torque on the fluid to balance.

A spiral flow, not a simple whirlpool

An externally driven spinning object might be expected to create a straightforward vortex. The living cell’s flow was more complicated: it formed a spiral. Fluid moved counterclockwise toward the cell to a distance of roughly three cell radii, then reversed direction. Beyond about seven radii, the measured signal faded into the noise.

The model suggests that this pattern arises from a balance between the rotating cell body and the flagellum’s internally generated beat. In other words, a living rotor is not simply equivalent to a particle turned by an external motor. Its internal actuation changes the surrounding flow.

The flow also weakened rapidly with distance. In the far field, the radial component fell approximately with the fourth power of distance, while the azimuthal component fell with the sixth power. These steep declines help explain why the interactions are strongest among nearby cells.

Clockwise spinners, counterclockwise pairs

Hydrodynamic attraction draws neighboring cells together. Once paired, the cells orbit counterclockwise—even though each one spins clockwise. They typically stay about 20 micrometers apart, equivalent to roughly four to six cell radii. Across the distances measured, their orbital frequencies matched the model’s predictions.

Small groups of up to four cells often formed persistent, rotating structures. Larger groups were less locked together: they rearranged and behaved more like a fluid. Simulations suggest that noise or variation in cell size can disrupt stable configurations that might otherwise persist.

From clusters to a changing network

At higher densities, clusters merged into a dynamic network that spanned the system. Several measures of cluster organization were consistent with two-dimensional percolation, with a critical area fraction near 0.08. This is the approximate density at which separate clusters connect into a system-wide structure.

Despite that connectivity, the cells did not settle into a positionally ordered lattice. Their local neighborhoods kept changing. The average time that a pair of cells remained connected fell from more than 100 seconds in dilute suspensions to around 10 seconds at higher densities. The network was therefore connected, but not static.

Two forms of diffusion respond differently

Tracking the cells revealed two stages of motion. At short times, their mean-squared displacement grew approximately as time to the power of 1.5, a sign of superdiffusion. At longer times, the motion crossed over to ordinary diffusion.

The researchers also distinguished between two components of diffusion:

Even diffusion describes transport along a density gradient.
Odd diffusion describes transport perpendicular to a density gradient.

Even diffusion increased approximately linearly with cell packing fraction. Odd diffusion behaved differently: it reached a maximum near the percolation threshold, then decreased as density rose further. The authors tentatively suggest that this peak may reflect changes in the available perimeter along cluster boundaries. That explanation remains a hypothesis, rather than a demonstrated mechanism.

What the findings do—and do not—show

The study shows that internal actuation and torque balance can make collective motion turn in the opposite direction from individual spinning. It also identifies an association between network connectivity and odd transport: the two forms of diffusion do not respond to increasing density in the same way.

There are important limits. The work examines one mutant alga in confined, wall-bounded chambers, where motion is effectively two-dimensional. Its hydrodynamic model is deliberately minimal, and some parameters were fitted manually. Most notably, the proposed reason for the odd-diffusion maximum has not yet been confirmed.

These results do not establish that the same patterns will appear in all living rotors or other active systems. Instead, they provide an experimental platform and a clear set of questions for future work: how widespread is chirality inversion, and how does changing network structure produce sideways transport?

Created on 02 Nov. 2026

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Weekly letter Presented in "Physics of matter and light this week" of 2 November 2026. Physics of matter and light this week: Hidden order, from atomic bonds to distant clocks

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Chirality inversion and odd transport in a suspension of living rotors

The essentials

Question

Method

Findings

Limitations

Why it matters

Read further

Definitions

When Living Rotors Move Together, Their Spin Can Change Direction

A living rotor that cannot swim

A spiral flow, not a simple whirlpool

Clockwise spinners, counterclockwise pairs

From clusters to a changing network

Two forms of diffusion respond differently

What the findings do—and do not—show

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