Compact Expansion of a Repulsive Suspension

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• Short-range repulsion is a fundamental force governing matter dynamics across scales.
• Understanding the collective behavior of repulsive particles is crucial for various scientific fields.

Purpose of the Study:

• To investigate the spreading dynamics of ensembles of repulsive particles.
• To contrast their behavior with diffusive spreading observed in Brownian particles.
• To elucidate the underlying mechanisms and scaling laws governing their expansion.

Main Methods:

• Theoretical analysis of particle interactions.
• Computational simulations of many-body dynamics.
• Experimental validation of theoretical predictions.

Main Results:

• Repulsive particle ensembles spread compactly with a sharp boundary.
• At high densities, dynamics follow nonlinear diffusion with t^{1/4} self-similar expansion.
• At longer times, thermal motion leads to classic t^{1/2} expansion.
• Logarithmic growth connects these regimes, influenced by nearest-neighbor interactions.

Conclusions:

• The spreading dynamics of repulsive particles are distinct from diffusive processes.
• Multiple scaling regimes govern the expansion, transitioning from nonlinear diffusion to thermal motion.
• Nearest-neighbor interactions play a key role in connecting these dynamic behaviors.