The Effect of Weak Shear-induced Motion on Brownian Coagulation of Aerosol Particles

The coagulation rate of a dilute polydisperse aerosol dispersion of particles is considered for small Peclet number, which provides a measure of the ratio of the relative shear-induced motion to Brownian motion between two rigid spherical aerosol particles. The asymptotic form of the relative velocity of two unequal particles immersed in a simple shear flow when they are far apart is obtained. Using a singular perturbation method, a two term expansion for the dimensionless coagulation rate (Nusselt number) as function of the Peclet number is developed. In the limit of the radius of one of the two spheres becoming small, the result agrees with the dimensionless mass transfer rate to an aerosol particle at small Peclet number.