Slow and long-ranged dynamical heterogeneities in dissipative fluids

Area of Science:

• Physics
• Soft Matter Physics
• Granular Materials

Background:

• Granular fluids exhibit complex dynamics, including dynamical heterogeneities and arrest.
• Understanding the approach to jamming is crucial for predicting material behavior.

Purpose of the Study:

• To investigate the nature of dynamical heterogeneities in a 2D bidisperse granular fluid near the jamming transition.
• To characterize the spatial organization of slow-moving particles and their relationship to the glass transition.

Main Methods:

• Identification and analysis of slow particle clusters, determining their size (Nc) and radius of gyration (RG).
• Calculation of fractal dimension (df) for these clusters.
• Analysis of the four-point structure factor (S4(q,t)) and dynamical susceptibility (χ4(t)).
• Finite size scaling analysis of dynamical quantities.

Main Results:

• Slow particles form fractal clusters with a dimension increasing with packing fraction (ϕ).
• Cluster size distribution exhibits scaling, approaching an algebraic decay at the jamming point (ϕc).
• The four-point structure factor shows scaling and increasing range as jamming is approached.
• Dynamical susceptibility and correlation length diverge as predicted for a non-equilibrium glass transition.

Conclusions:

• Direct evidence is provided for fractal structures formed by immobile particles near jamming.
• The observed scaling and divergences strongly suggest a non-equilibrium glass transition.
• The transition appears largely independent of the coefficient of restitution.