EPJ E Highlight - Modelling reversibility transitions in soft athermal materials

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Published on 21 October 2025

By accounting for long-range interactions between suspended particles, a new model provides a more accurate description of how soft athermal materials transition between reversible and irreversible states.

When soft athermal materials like foams, emulsions, or particle suspensions are gently shaken or sheared back and forth, they can learn to move in perfect rhythm: after each cycle, every particle returns to its original place. But if the driving becomes too strong, that tidy choreography breaks down, and particles wander irreversibly. This reversible–irreversible transition marks the boundary between an ordered and a chaotic state in driven soft matter. So far, however, researchers have struggled to recreate these properties through theoretical models – making it more difficult for them to understand how soft athermal materials behave in real-world applications.

Through new research published in EPJ E, a team led by CNRS researchers Romain Mari and Eric Bertin at Grenoble-Alpes University introduces a new and improved model, which reproduces the reversible–irreversible transition far more accurately. Their approach offers fresh insights into the deeply complex behaviours of soft athermal materials, and could help researchers to develop their application across a diverse range of real-world scenarios.

In previous studies, theorists have modelled this phenomenon with the Random Organisation Model (ROM). It predicts a sharp reversible-irreversible transition, beyond which chaos grows rapidly as the driving increases. However, many experiments on real suspensions show smoother, ‘convex’ transitions, suggesting that something important is missing from the idealised model.

In their study, Mari and Bertin’s team introduce a more generalised form of the ROM, which accounts for how particles influence each other via the forces they exert on the surrounding fluid. With their improved model, the researchers showed that the transition becomes convex when the interaction forces decay slowly with distance. These long-range interactions generate collective diffusive motion with reduced temporal fluctuations but enhanced spatial fluctuations, leading to a loss of ‘hyperuniformity’, a subtle form of large-scale structural order previously linked to the reversible-irreversible transition.