Abstract
This paper presents a simple, unified theory of deposition that is applicable for particles of any size, and reproduces very closely experimentally measured variation in deposition velocity with particle relaxation time. Apart from providing physical insight, the theory offers a simple, fast and reliable computational tool of practical use to aerosol engineers. The predictions are at least as accurate as the state-of-the-art particle-tracking calculations but require much less computational time. The theory includes the effects of thermophoresis, turbophoresis, electrostatic forces, gravity, lift force and surface roughness. The theory consists of writing the particle continuity and momentum conservation equations in their proper form and then performing Reynolds averaging. This procedure results in an expression for the particle flux which consists of three distinct terms for each of which a clear physical interpretation is available. The first term is a diffusive flux due to Brownian motion and turbulent fluctuation, the second is a diffusive flux due to temperature gradient (thermophoresis), and the third is a convective flux that arises primarily as an interaction between particle inertia and the inhomogeneity of the fluid turbulence field (turbophoresis). The lift force and electrostatic forces also contribute to this convective flux. It is shown that it is crucial to include the particle momentum equation in the analysis as this gives an estimate of the mentioned convective slip velocity of the particles. Absence of this equation in many previous studies which included only the particle continuity equation necessitated postulations such as stopping distance models. Only the dominant terms in the continuity and momentum equations are retained in the present analysis which give almost the same answer as with a calculation retaining all terms, but the former is more amenable to direct physical interpretation. The method of Reynolds averaging is general, and other effects not included in this study, e.g. pressure diffusion can easily be incorporated by including the appropriate forces in the particle momentum equation. The present study includes the effects of surface roughness, and the calculations show that the presence of small surface roughness even in the hydraulically smooth regime significantly enhances deposition especially of small particles. Thermophoresis can have equally strong effects, even with a modest temperature difference between the wall and the bulk fluid. For particles of the intermediate size range, turbophoresis, thermophoresis and roughness are all important contributors to the overall deposition rate.
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