Coagulation of like-charged Brownian Particles*

We study the coagulation rate of Brownian particles dispersed in a gaseous medium. Particles are small enough so that their inertia is negligible. Most previous calculations of the Brownian-induced coagulation rate have considered that the particle pairs interact through continuum hydrodynamics and van der Waals attraction forces at close separations allow the collision and subsequent coagulation. However, the continuum approximation of the hydrodynamic interactions is no longer valid when the gap thickness between the surface is less than the mean-free path of the surrounding fluid medium and the non-continuum lubrication interactions lead to surface-to-surface contact in finite time. The Knudsen number, defined as the ratio of the mean-free path to the medium to the average radius of the interacting particles, measures the effects of non-continuum interactions. We calculate the Brownian-coagulation rate in the presence of non-continuum lubrication resistances. We also report the effect of van der Waals and electrostatic forces on the coagulation rate while particles interact with each other through non-continuum hydrodynamics.