# Electrification in granular gases leads to constrained fractal growth

## TL;DR

This paper develops a hydrodynamic model for charged granular gases, revealing how electrostatic forces constrain cluster growth and lead to fractal aggregation, supported by theory and molecular dynamics simulations.

## Contribution

It introduces a novel theoretical framework for analyzing charge-driven aggregation in granular gases, highlighting a universal energy ratio constraint and fractal growth behavior.

## Key findings

- Electrostatic forces constrain cluster energy ratios to be less than or equal to one.
- Aggregation proceeds in a fractal manner influenced by Coulomb interactions.
- The model is validated by molecular dynamics simulations.

## Abstract

The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from the early stages of planetesimal formation to aerosols. However, the collective effects of Coulomb forces on the nonequilibrium dynamics and aggregation process in a granular gas -- a model representative of the above physical processes -- have so far evaded theoretical scrutiny. Here, we establish a hydrodynamic description of aggregating granular gases that exchange charges upon collisions and interact via the long-ranged Coulomb forces. We analytically derive the governing equations for the evolution of granular temperature, charge variance, and number density for homogeneous and quasi-monodisperse aggregation. We find that, once the aggregates are formed, the system obeys a physical constraint of nearly constant dimensionless ratio of characteristic electrostatic to kinetic energy $\mathcal{B}(t)\le 1$. This constraint on the collective evolution of charged clusters is confirmed both by the theory and the detailed molecular dynamics simulations. The inhomogeneous aggregation of monomers and clusters in their mutual electrostatic field proceeds in a fractal manner. Our theoretical framework is extendable to more precise charge exchange mechanism, a current focus of extensive experimentation. Furthermore, it illustrates the collective role of long-ranged interactions in dissipative gases and can lead to novel designing principles in particulate systems.