# ISCST3 Tech Guide

## 6.3.2 Deposition Velocities

A resistance method is
used to calculate the deposition velocity , v_{d}. The
general approach used in the resistance methods for estimating v_{d}
is to include explicit parameterizations of the effects of Brownian
motion, inertial impaction, and gravitational settling. The
deposition velocity is written as the inverse of a sum of resistances
to pollutant transfer through various layers, plus gravitational
settling terms (Slinn and Slinn, 1980; Pleim et al., 1984):

where,

v_{d} = the deposition velocity (cm/s),

v_{g} = the gravitational settling velocity (cm/s),

r_{a} = the aerodynamic resistance (s/cm), and,

r_{d} = the deposition layer resistance (s/cm).

Note that for large
settling velocities, the deposition velocity approaches the settling
velocity (v_{d} 6 v_{g}), whereas, for small settling
velocities, v_{d} tends to be dominated by the r_{a}
and r_{d} resistance terms.

In addition to the
mass mean diameters (microns), particle densities (gm/cm^{3}),
and the mass fractions for each particle size category being modeled,
the dry deposition model also requires surface roughness length (cm),
friction velocity (m/s), and Monin-Obukhov length (m). The surface
roughness length is specified by the user, and the meteorological
preprocessor (PCRAMMET or MPRM) calculates the friction velocity and
Monin-Obukhov length for input to the model.

The lowest few meters of the atmosphere can be divided into two layers: a fully turbulent region where vertical fluxes are nearly constant, and the thin quasi-laminar sublayer. The resistance to transport through the turbulent, constant flux layer is the aerodynamic resistance. It is usually assumed that the eddy diffusivity for mass transfer within this layer is similar to that for heat. The atmospheric resistance formulation is based on Byun and Dennis (1995):

stable(L > 0):

unstable (L < 0):

where,

u_{*} = the surface friction velocity (cm/s),

k = the von Karman constant (0.4),

z = the height above ground (m),

L = the Monin-Obukhov length (m),

z_{d} = deposition reference height (m), and

z_{o} = the surface roughness length (m).

The coefficients used in the atmospheric resistance formulation are those suggested by Dyer (1974). A minimum value for L of 1.0m is used for rural locations. Recommended minimum values for urban areas are provided in the user's guides for the meteorological preprocessor programs PCRAMMET and MPRM.

The approach used by Pleim et al. (1984) to parameterize the deposition layer resistance terms is modified to include Slinn's (1982) estimate for the inertial impaction term. The resulting deposition layer resistance is:

Where:

The gravitational settling velocity, v_{g} (cm/s), is calculated as:

Where:

and, x_{2}, a_{1},
a_{2}, a_{3} are constants with values of 6.5 x 10^{-6},
1.257, 0.4, and 0.55 x 10^{-4}, respectively.

The Brownian diffusivity of the pollutant (in cm/s) is computed from the following relationship:

where T_{a} is
the air temperature (EK).

The first term of Eqn. (1-83), involving the Schmidt number, parameterizes the effects of Brownian motion. This term controls the deposition rate for small particles. The second term, involving the Stokes number, is a measure of the importance of inertial impaction, which tends to dominate for intermediate-sized particles in the 2-20 µm diameter size range.

The deposition algorithm also allows a small adjustment to the deposition rates to account for possible phoretic effects. Some examples of phoretic effects (Hicks, 1982) are:

THERMOPHORESIS: Particles close to a hot surface experience a force directed away from the surface because, on the average, the air molecules impacting on the side of the particle facing the surface are hotter and more energetic.

DIFFUSIOPHORESIS:
Close to an evaporating surface, a particle is more likely to be
impacted by water molecules on the side of the particle facing the
surface. Since the water molecules have a lower molecular weight than
the average air molecule, there is a net force toward the surface,
which results in a small enhancement of the deposition velocity of
the particle.

A second effect is that the impaction of new water vapor molecules at
an evaporating surface displaces a certain volume of air. For
example, 18 g of water vapor evaporating from 1 m^{2} will
displace 22.4 liters of air at standard temperature and pressure (STP)
conditions (Hicks, 1982). This effect is called Stefan flow. The
Stefan flow effect tends to reduce deposition fluxes from an
evaporating surface. Conversely, deposition fluxes to a surface
experiencing condensation will be enhanced.

ELECTROPHORESIS: Attractive electrical forces have the potential to assist the transport of small particles through the quasi-laminar deposition layer, and thus could increase the deposition velocity in situations with high local field strengths. However, Hicks (1982) suggests this effect is likely to be small in most natural circumstances.

Phoretic and Stefan
flow effects are generally small. However, for particles in the range
of 0.1 - 1.0 µm diameter, which have low deposition velocities,
these effects may not always be negligible. Therefore, the ability to
specify a phoretic term to the deposition velocity is added (i.e., v_{d}N
= v_{d} + v_{d(phor)}, where v_{d}N is the
modified deposition velocity and v_{d(phor)} is the phoretic
term).

Although the magnitude
and sign of v_{d(phor)} will vary, a small, constant value of
+ 0.01 cm/s is used in the present implementation of the model to
represent combined phoretic effects.