A TURBULENT-BROWNIAN MODEL FOR AEROSOL COAGULATION

Aerosol coagulation is a process by which small particles of the aerosol join together to form larger particles, still within aerosol size. This process takes place continuously, and causes the aerosol to change in time. The process may be useful or harmful, according to the use made of the aerosol. There are several mechanisms that influence the coagulation process, but two are the most important. One is Brownian diffusion, which causes particles to come into contact and stick together. The other is due to relative motion induced by spatial turbulent fluctuations in a turbulent flow field. Each of these mechanisms has been investigated rather widely, but always alone, i.e., Brownian motion only or turbulent flow only. Still, in many important cases coagulation is affected by both mechanisms operating simultaneously. The present investigation considers a model in which coagulation takes place between two spherical particles of different sizes, placed in a turbulent flow field. The motion of the larger particle is dominated by the mean flow and by the turbulent fluctuations. The smaller particle is also affected by the turbulent fluctuations, but its motion is modified by the Brownian motion. Both particles are assumed to be smaller than the smallest scale of the turbulence. A coordinate system is connected to the larger particle and the flow field around this particle is obtained by the solution of the Stokes equations in this local coordinate system. The motion of the smaller particle to the larger one is dominated by the turbulent convection in the flow, and modified by the local Brownian motion. The coagulation problem is solved also without the Brownian motion, thus providing both rates of coagulation for larger particles, and isolating the effect of the Brownian motion for smaller particles.