Aerosol Chemistry and Physics - Aerosols: Measurement, Dosimetry, and Health Effects - page 163

the third term accounts for iltration removal due to air recirculation in a heating/cooling system
with a ilter. Only the irst of these terms is independent of particle size. The second term—
particle deposition to various indoor surfaces—is dependent upon both particle size and surface
orientation while the third term incorporates iltration eficiency, which is inherently particle size
dependent.
Other terms, represented here by T, can be added to the equation to account for particle
transformation processes (Nazaroff and Cass, 1989) that can either add or remove particles or shift
the particle size spectrum. Coagulation, for example, removes small particles and creates (fewer)
larger ones, although for this process to be signiicant, the number concentrations of small particles
need to be elevated. Coagulation has been observed in studies of environmental tobacco smoke
where small particle concentrations exceed ∼10 5 cm −3 (Klepeis et al., 2003). Studies of hygroscopic
growth of various indoor aerosols have shown mixed effects—in some cases very little change in
particle size was observed, while in other situations, for example, wood smoke, the mass median
diameter increased (Dua et al., 1995; Dua and Hopke, 1996).
As a inal example of transformation processes, phase change has been observed to alter par-
ticle concentrations indoors. In particular, ammonium nitrate aerosol, a major component of
ambient aerosols in the western United States, is volatile and exists in equilibrium with its gas-
phase constituents, ammonia and nitric acid. When these aerosols enter buildings via iniltra-
tion or ventilation, the temperature and relative humidity conditions may change, driving the
equilibrium toward dissociation into the gas-phase species. These species in turn interact with
indoor surfaces—especially nitric acid—leading to additional equilibrium dissociation. Under
these conditions, indoor concentrations of ammonium nitrate particles are signiicantly reduced
(Lunden et al., 2003a,b).
In order to illustrate the main features of the mass balance equation and to keep the number of
variables tractable, we drop the iltration and transformation terms from Equation 6.8 and simplify
some of the variables to yield

dC (d )
dt

λ P(d )C (d ) R(d ) S (d )] + [ +

i p in p o p p i p

(6.9)

=

∑

V − λ C (d ) C (d ) − k (d )

in i p i p j p

j

If we assume that the indoor space is well mixed and that the various terms vary slowly with time,
the average indoor concentration can be approximated by the steady-state solution

λ P(d )C (d ) R(d ) S (d )]/V

k (d )
j

+ [ +

in p o p p i p

(6.10)

C (d ) =

+ ∑

i p

λ

in p

j

Equation 6.10 is useful in “well-controlled” situations, such as laboratory-based experiments or
where indoor sources, for example, are operated to produce high concentrations of aerosols so that
variable contributions from outdoors, etc. can be neglected. This equation does help illustrate the
balance between typical indoor aerosol sinks and sources.
However, in “real-world” situations, as would be the case in examining or estimating the
transport and fate of aerosols in actual buildings, two important parameters in Equation 6.9 are
often time-varying, outdoor aerosol concentrations and iniltration rates—especially in houses
where mechanical systems are not used to supply ventilation air. If there is suficient time-series
information on the variability of these two parameters, then a “forward-marching” approach with
a small time step, Δt, can be used, as has been recently demonstrated in the analysis of particle
penetration data (Thatcher et al., 2003). The form of this equation is