FUTO EVT 513
Contaminants Kinetics and Equilibrium
From Daniel Vallero, in Fundamentals of Air Pollution (Fifth Edition), 2014
Air pollutant transport and fate focus on the kinetics and equilibria of the processes leading to the
release, behavior in environmental compartments, and movement among compartments. These
same physical and chemical processes take place within an organism after uptake. The
importance of the factors can be very different within the organism. For example, the
degradation or activation of a pollutant may be much faster in the presence of organic catalysts,
i.e. enzymes.
The reaction rates and equilibria differ, as do residence times and half-lives of chemical
processes. However, the laws of thermodynamics and motion apply at every level of interest to
air pollution, from cells to the planet.
Advection
The most straightforward physical pollutant transport process arguably is advection (JAdvection).
Advection is the transport of matter within the streamlines of a fluid, that is, with the water or
airflow. Most of the total volume and mass of pollutants moved in the environment occur by
advection. As evidence, another name for advection is bulk transport. During advection, a
contaminant is moved along with the fluid or, in the language of environmental science, the
environmental medium. It is a passive form of transport because the contaminant moves along
with the transporting fluid. That is, the contaminant would not move if it was not in the medium.
The contaminant is merely “hitching a ride” on the fluid as it moves through the environment
Environmental fluids move within all the media and matrices discussed in previous chapters,
such as the flow of air and water, between soil particles, within sediment, in unconsolidated
materials underground, and in the open surface waters and atmosphere.
Advection occurs within a single medium and among media. The rate and direction of transport
are completely determined by the rate and direction of the flow of the media. The simplest bulk
transport within one environmental medium or compartment is known as homogeneous
advection, where only one fluid is carrying the contaminant. The three-dimensional rate of
homogeneous, advective transport is simply the product of the fluid medium's flow rate and the
concentration of the contaminant in the medium:
(8.1)N=QC
where Q is the flow rate of the fluid medium (e.g., m3 s−1) and C is the concentration of the
chemical contaminant being transported in the medium (e.g., μg m−3). Therefore, the units for
three-dimensional advection are mass per time (e.g., μg s−1). For example, the homogeneous
advection of air containing 100 μg m−3 vinyl chloride (gas phase) flowing at 10 m3 s−1
is 1000 μg s−1 or 1 mg s−1. Thus, this plume of vinyl chloride can be characterized as a 1-mg m−3
plume until it is further diluted in the atmosphere. Heterogeneous advection refers to those cases
where there is a secondary phase present inside the main advective medium, for example, the
presence of particulate matter (i.e., suspended solids) carried by wind. Heterogeneous advection
involves more than one transport system within the compartment. In the vinyl chloride case
above, if particle matter (PM) is also flowing in the plume and the PM has a concentration of
100 μg m−3 and vinyl chloride makes up 0.05 of this PM concentration, then the aerosol phase of
vinyl chloride in the plume is 5 μg m−3 and the homogeneous particle-phase advection is
5 μg m−3 × 10 m3 s−1 = 50 μg s−1. This value must be added to the gas-phase homogeneous
calculation, so that the heterogeneous (gas and particle phases) vinyl chloride advection would
be 1000 s−1 (gas) + 50 μg s−1 (PM) = 1050 μg s−1. Thus, not only the concentration of the
dissolved fraction of the contaminant must be known but the concentration of chemical in and on
the solid particles must also be known.
Heterogeneous advection is a common transport mechanism for highly lipophilic compounds or
otherwise insoluble matter that is often sorbed to particles as compared with dissolved in water.
This may be similar to chemical transport, such as when metals form both lipophilic and
hydrophilic species (e.g., ligands), depending upon their speciation. Many biomolecules and
other complex organic compounds, such as the polycyclic aromatic hydrocarbons and
polychlorinated biphenyls, are relatively insoluble in water. Therefore, most of their advective
transport is by attaching to particles. In fact, lipophilic organics are likely to have orders of
magnitude greater concentrations in suspended matter than is dissolved in the water. Another
example of advective transport is atmospheric deposition of contaminants. The sorption of
contaminants to the surface of atmospheric water droplets is known as wet deposition and
sorption to solid particles is known as dry deposition. The process where these contaminants are
delivered by precipitation to the earth is advection.
Rather than three-dimensional transport, many advective models are represented by the onedimensional mass flux equation for advection, which can be stated as:
(8.2)JAdvection=v¯ηe[c]
where v¯ = average linear velocity (m s−1), ηe = effective porosity (percent, unitless), and
c = chemical concentration of the solute (kg m−3)
The equation for flux in two dimensions is
(8.3)JAdvection=v¯[c]
Two-dimensional fluxes are an expression of the transport of a contaminant across a unit area.
This rate of this transport is the flux density (see Fig. 8.5), which is the contaminant mass
moving across a unit area per time. In most environmental applications, fluid velocities vary
considerably in time and space (e.g., think about calm vs. gusty wind conditions). Thus,
estimating flux density for advection in a turbulent fluid usually requires a time integration to
determine average concentrations of the contaminant. For example, a piece of air monitoring
equipment may collect samples every minute, but the model or calculation calls for an hourly
value, so the 60 values are averaged to give one integrated concentration of the air pollutant. For
example, if the atmospheric concentration of pollutant A is 15 ng m−3 and it is moving a velocity
of 0.1 m s−1, the average flux density of the pollutant A as it moves downwind can be calculated
as:
Flux density of an imaginary cross-sectional area across which contaminant flux is calculated in
the atmosphere.
[A]=15ngm−3
JAdvection=v¯[c]=(0.1ms−1)(15ngm−3)=1.5ngm−2
Human Effects of Particulate Exposure
Another important consideration related to atmospheric loadings and particulate size
distributions concerns the potential for human effects on inhalation. The body’s defenses in the
upper respiratory tract are adequate to trap more than 50% of particles larger than about 2 μm in
diameter when present in the air breathed. However, particles smaller than this are not efficiently
captured by the upper respiratory tract. These “respirable particulates” penetrate the lungs to the
alveolar level. Here, the more vigorous Brownian motion of the small aerosols increases their
collision frequency with the moist walls of the alveoli, thus trapping a large proportion of them
at these sites. This occurs in an un-ciliated region of the respiratory system which is unable to
degrade or flush out accumulated material, particularly if the inhaled aerosol is inert or insoluble.
Hence, any physiological effect of the presence of these foreign substances is aggravated, which
tends to increase the incidence of respiratory illness experienced in areas that have high
concentrations of polluting aerosols in this size range. The efficiencies of many types of air
pollution control equipment for the lower aerosol size range is poor, an important consideration
when selecting from process emission control options.
Advection
Advection is usually the dominant process for contaminant transport in the subsurface. It refers
to the transport of the contaminant caused by the bulk movement of flowing groundwater. The
advective flow velocity or the average linear groundwater velocity included in the advection
term of Eq. 1 depends on the average (bulk) properties, essentially the average permeability, of
the aquifer material and the average hydraulic gradient between two points, and can be
quantified using Darcy's law (Eq. 2):
(2)v=k×i
where v is the groundwater velocity (m s− 1), k is the hydraulic conductivity of the aquifer
(m s− 1), and i is the hydraulic gradient. However, this approach is too simple to evaluate
contaminant transport, as it does not take into account other processes happening in the
subsurface, such as dispersion, diffusion, or sorption that also affect the groundwater flow rate
within the aquifer.
The one-dimensional advective flux of a contaminant carried out by groundwater through the
aquifer porous medium can be expressed by Eq. 3:
(3)J=vx×Cne
where J is the mass flux per unit area per unit time (mg m− 2 s− 1), vx is the average linear
groundwater velocity in the direction of the groundwater flow (m s− 1), C is the concentration of
the contaminant (mg L− 1), and ne is the effective porosity of the geological medium.