The rate of coagulation of a dilute polydisperse system of sedimenting spheres

Abstract

We consider a dilute dispersion containing small rigid particles in a Newtonian fluid. These spherical particles are of different size and density, and they settle relative to one another under the action of gravity. When the particles become close, they exert an attractive van der Waals force on each other, and doublets are formed when two particles come into contact as a result of this force. The rate at which doublets are formed is calculated using a trajectory analysis to follow the relative motion of pairs of particles.We restrict our attention to dispersions where the Péclet number is large (negligible Brownian motion) and where the Reynolds number is small (negligible fluid inertia). However, the effects of the inertia of the particles on their trajectories are included, and these are measured by the Stokes number. A key dimensionless parameter is identified, denoted by Qij which provides a measure of the relative importance of gravity and the van der Waals force. An asymptotic solution to the trajectory equations is presented for large values of this parameter in the case of zero Stokes number. This asymptotic solution is then complemented by numerical computations of the particle trajectories. Application to typical hydrosol and aerosol dispersions is presented, and, in particular, a comparison is made between the effects of van der Waals forces and Maxwell slip in promoting collisions between aerosol particles.