| 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. |
