# The effects of electrostatic and inertial forces on the diffusive deposition of small particles onto large disks: Viscous axisymmetric stagnation point flow approximations

## Abstract

Fine particles can deposit on microelectronic parts during their manufacture and cause damage. Prediction of the rates of deposition is important in planning to reduce such losses. Analytic expressions were developed and Monte Carlo simulations (Brownian dynamics) were carried out to predict deposition rates of sub-micron particles in viscous axisymmetric stagnation point flow. Diffusive, inertial and electrostatic deposition mechanisms were incorporated in the analysis. The electrostatic forces considered included the Coulombic force on a charged particle in an electric field and the image force on a charged particle near a conducting plane. Analytical solutions to the convective-diffusion equation, in the absence of inertial effects, showed that for a Boltzmann charge equilibrium, the electrostatic image force did not appreciably enhance deposition for a free-stream velocity of 50 cm s-1. However, the Coulomb electrostatic attraction of a charged particle towards a charged surface greatly enhanced deposition, assuming a field from the disk approximately equivalent to having a disk 20 cm in diameter (80 pF capacitance) at 2000 V. Some areas for future study are suggested by these results. Brownian dynamics simulations carried out for particles of the order of 1 μm in diameter at a much higher velocity (30 m s-1) demonstrated an interaction between inertial and diffusive deposition that produced inertially enhanced deposition at Stokes values below the critical value, St < 0.15. Where inertia and electrostatic effects were negligible, the simulations matched the known solution for stagnation flow deposition due to diffusion. In the Appendix is presented a derivation of the Langevin equation governing single-particle motion in a fluid that is not uniform in temperature as well as in velocity. © 1989.