Thermal equilibration of soot charge distributions by coagulation

Flame generated soot particles acquire a symmetric electrical charge distribution shortly after inception. Coagulation between soot particles causes the electrical charge to evolve to a Boltzmann distribution characterized by the flame temperature. When the soot is removed from the flame and allowed to coagulate further, the charge temperature (as defined via the Boltzmann distribution) is observed to fall to room temperature over a period of a few seconds. The resulting charge distribution is independent of the initial condition, e.g., the height in the flame at which the soot is sampled. In effect, coagulation acts to equilibrate the electrical charge distribution with the surrounding gas temperature even though the process is itself irreversible. The experimental observations are reproduced by a kinetic coagulation model that includes Coulomb forces between the colliding particles. In the case of diesel soot, a charge temperature of ∼1100K is found at the vehicle tailpipe, presumably because cooling by coagulation remains incomplete over the transit time from engine to tailpipe.