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The empirical observation of aggregation of dielectric particles under theinfluence of electrostatic forces lies at the origin of the theory ofelectricity. The growth of clusters formed of small grains underpins a range ofphenomena from the early stages of planetesimal formation to aerosols. However,the collective effects of Coulomb forces on the nonequilibrium dynamics andaggregation process in a granular gas -- a model representative of the abovephysical processes -- have so far evaded theoretical scrutiny. Here, weestablish a hydrodynamic description of aggregating granular gases thatexchange charges upon collisions and interact via the long-ranged Coulombforces. We analytically derive the governing equations for the evolution ofgranular temperature, charge variance, and number density for homogeneous andquasi-monodisperse aggregation. We find that, once the aggregates are formed,the system obeys a physical constraint of nearly constant dimensionless ratioof characteristic electrostatic to kinetic energy $\mathcal{B}(t)\le 1$. Thisconstraint on the collective evolution of charged clusters is confirmed both bythe theory and the detailed molecular dynamics simulations. The inhomogeneousaggregation of monomers and clusters in their mutual electrostatic fieldproceeds in a fractal manner. Our theoretical framework is extendable to moreprecise charge exchange mechanism, a current focus of extensiveexperimentation. Furthermore, it illustrates the collective role of long-rangedinteractions in dissipative gases and can lead to novel designing principles inparticulate systems.

Electrification in granular gases leads to constrained fractal growth