  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.
