Aerosol Deposition in the Vicinity of a Stagnation Point

A method is presented to compute the trajectories of aerosol particles in the vicinity of a stagnation point and thus to obtain their rates of deposition. According to this method a particle starts its motion on the initial streamline, moves from one streamline to another under the influence of inertia, and touches the collector surface while on the interceptional streamline. The method takes advantage of the fact that in stagnation flow close to the splitting streamline most of the changes take place in a small region of high streamline curvature. The method of singular perturbation analysis is applied to calculate the particle trajectory in this region. This paper considers small Stokes numbers for which the particles are shown to have a stopping distance equal to their Stokes number. The computation of the particle trajectories depends on the ratio of these stopping distances s to the radii of curvature of the fluid streamline r. For large and medium s/r ratios the trajectories exhibit boundary layer type behavior, while for small ratios no such behavior is seen. Two examples demonstrate the use of the present theory. The first is that of particle sedimentation in a fibrous filler. The second is the sedimentation of small particles in potential plane-stagnation flow. The results compare very favorably with available numerical or exact solutions.