Collective motion of macroscopic spheres floating on capillary ripples: Dynamic heterogeneity and dynamic criticality

Abstract: When a dense monolayer of macroscopic slightly polydisperse spheres floats on chaotic capillary Faraday waves, a coexistence of large scale convective motion and caging dynamics typical for jammed systems is observed. We subtract the convective mean flow using a coarse graining and reveal subdiffusion for the caging time scales followed by a diffusive regime at later times. To test the system in the light of dynamic criticality, we apply the methods of dynamic heterogeneity to obtain the power-law divergent time and length scales as the floater concentration approaches the jamming point. We find that these are independent of the application of the coarse graining procedure. The critical exponents are consistent with those found in dense suspensions of colloids indicating universal stochastic dynamics.

• The paper demonstrates that subtracting convective flows via coarse graining reveals distinct subdiffusive and diffusive regimes.
• It shows that dynamic heterogeneity intensifies near jamming transitions, quantified through four-point correlation functions and dynamic susceptibility.
• Critical scaling laws with exponents near -1.4 and -3.9 underscore universal dynamic criticality in dense particulate systems.

Collective Motion of Macroscopic Spheres on Capillary Ripples

The paper presents a detailed investigation into the dynamic behaviors of a dense monolayer of macroscopic spheres floating on capillary Faraday waves, with particular attention paid to dynamic heterogeneity (DH) and dynamic criticality (DC). The study examines the interplay between large-scale convective motions and localized caging dynamics akin to those found in jammed systems.

Significantly, the authors apply a coarse graining (CG) method to subtract the convective mean flow from the observed dynamics, enabling a focus on the subtle, yet crucial, subdiffusive and diffusive regimes which are pivotal at various time scales. The experimental setup allows for a unique examination of systems perturbed by chaotic capillary interactions and the erratic dynamics that they engender. The spheres, subjected to attractive capillary forces, display complex motion when in dense configurations, thereby serving as a promising model for studying dynamic phenomena near jamming transitions.

Central to the paper is the exploration of how dynamic heterogeneity in collective events evolves as the system approaches its densest configuration. The paper identifies clear signatures of DH through the application of dynamic susceptibility and the four-point correlation function—tools commonly utilized in glass and jamming studies. The authors successfully demonstrate an increase in fluctuation scales, both temporally and spatially, when nearing critical packing fractions.

From a broader perspective, the study engages with dynamic criticality literature, fitting power-law exponents to several indicators of dynamic behavior. The observed critical exponents align with those detected in dense colloidal suspensions, thus insinuating comparable stochastic dynamics across similar systems. This underscores the potential universality of dynamics near jamming transitions across diverse particulate systems.

On the numerical front, the authors report a dynamic correlation length scaling consistent with expected power-law relationships, such as $\xi^\ast \sim (\phi_J - \phi)^{\lambda}$, yielding $\lambda \approx -1.4$. Additionally, the dynamic time scales, represented as $\tau^\ast$, were found to scale as $(\phi_J - \phi)^{\eta}$ with $\eta \approx -3.9$. These findings not only resonate well with previous experimental observations in sheared microgel systems but also reinforce the theoretical framework underpinning dynamic criticality.

In terms of practical implications, the study adds to the understanding of dynamic heterogeneity and criticality, providing insights that could be critical for both fundamental research and applications requiring precise control of particle dynamics, such as in material science and engineering. The observed universality in exponents provides a predictive basis for analogous systems that may exhibit dynamic phase transitions.

Moving forward, future developments might seek to reconcile the differences between theoretically predicted jamming points and experimentally observed maxima in sphere concentration. Such efforts could further illuminate the mechanics underpinning the transition from fluid-like to solid-like behavior in particulate systems.

This paper makes a significant contribution towards understanding the collective behavior of particulate systems in dynamic settings, situating capillary-driven spheres as an effective platform for probing critical dynamics underexperimental conditions.