Predicted Deposition of Submicrometer Particles Due to Diffusion and Electrostatics in Viscous Axisymmetric Stagnation-Point Flow

Abstract

Various mathematical solutions to the convective-diffusion equation for noninteracting Brownian particles were carried out to predict deposition of submicrometer particles onto a flat surface in viscous, three-dimensional (axisymmetric) stagnation-point flow at clean-room velocities (∼ 100 cm/s). The particle deposition aspects modeled included electrostatics, inasmuch as both diffusion and electrostatics are the dominant mechanisms expected. The results were obtained in terms of dimensionless groups for deposition, convective-diffusion, and electrostatic attraction. It was found that the deposition velocity can be well approximated by a simple combination of the convective-diffusion velocity and the eletro-static velocity. These results are translated into practical terms, examples are given, and the predictions are compared with predictions made by other methods. A disk 20 cm in diameter charged to 2000-V potential is shown to attract a particle 0.1 μm in diameter so as to produce an electrostatic deposition velocity 180 times larger than the diffusion deposition velocity, giving it a deposition velocity nearly equal to that of a particle 10 μm in diameter settling under gravity.