Aerosol

(Redirected from Aerosols)
Mist and clouds are aerosols.

An aerosol is a colloid of fine solid particles or liquid droplets, in air or another gas.[1] Aerosols can be natural or artificial. Examples of natural aerosols are fog, forest exudates and geyser steam. Examples of artificial aerosols are haze, dust, particulate air pollutants and smoke.[1] The liquid or solid particles have diameter mostly smaller than 1 μm or so; larger particles with a significant settling speed make the mixture a suspension, but the distinction is not clear-cut. In general conversation, aerosol usually refers to an aerosol spray that delivers a consumer product from a can or similar container. Other technological applications of aerosols include dispersal of pesticides, medical treatment of respiratory illnesses, and combustion technology.[2] Diseases can also spread by means of small droplets in the breath, also called aerosols.

Aerosol science covers generation and removal of aerosols, technological application of aerosols, effects of aerosols on the environment and people, and a wide variety of other topics.[1]

Definitions

Photomicrograph made with a Scanning Electron Microscope (SEM): Fly ash particles at 2,000× magnification. Most of the particles in this aerosol are nearly spherical.

An aerosol is defined as a colloidal system of solid or liquid particles in a gas. An aerosol includes both the particles and the suspending gas, which is usually air.[1] Frederick G. Donnan presumably first used the term aerosol during World War I to describe an aero-solution, clouds of microscopic particles in air. This term developed analogously to the term hydrosol, a colloid system with water as the dispersing medium.[3] Primary aerosols contain particles introduced directly into the gas; secondary aerosols form through gas-to-particle conversion.[4]

Various types of aerosol, classified according to physical form and how they were generated, include dust, fume, mist, smoke and fog.[5]

There are several measures of aerosol concentration. Environmental science and health often uses the mass concentration (M), defined as the mass of particulate matter per unit volume with units such as μg/m3. Also commonly used is the number concentration (N), the number of particles per unit volume with units such as number/m3 or number/cm3.[6]

The size of particles has a major influence on their properties, and the aerosol particle radius or diameter (dp) is a key property used to characterise aerosols.

Aerosols vary in their dispersity. A monodisperse aerosol, producible in the laboratory, contains particles of uniform size. Most aerosols, however, as polydisperse colloidal systems, exhibit a range of particle sizes.[7] Liquid droplets are almost always nearly spherical, but scientists use an equivalent diameter to characterize the properities of various shapes of solid particles, some very irregular. The equivalent diameter is the diameter of a spherical particle with the same value of some physical property as the irregular particle.[8] The equivalent volume diameter (de) is defined as the diameter of a sphere of the same volume as that of the irregular particle.[9] Also commonly used is the aerodynamic diameter.

Size distribution

The same hypothetical log-normal aerosol distribution plotted, from top to bottom, as a number vs. diameter distribution, a surface area vs. diameter distribution, and a volume vs. diameter distribution. Typical mode names are shows at the top. Each distribution is normalized so that the total area is 1000.

For a monodisperse aerosol, a single number—the particle diameter—suffices to describe the size of the particles. However, more complicated particle-size distributions describe the sizes of the particles in a polydisperse aerosol. This distribution defines the relative amounts of particles, sorted according to size.[10] One approach to defining the particle size distribution uses a list of the sizes of every particle in a sample. However, this approach proves tedious to ascertain in aerosols with millions of particles and awkward to use. Another approach splits the complete size range into intervals and finds the number (or proportion) of particles in each interval. One then can visualize these data in a histogram with the area of each bar representing the proportion of particles in that size bin, usually normalised by dividing the number of particles in a bin by the width of the interval so that the area of each bar is proportionate to the number of particles in the size range that it represents.[11] If the width of the bins tends to zero, one gets the frequency function:[12]

${\displaystyle \mathrm {d} f=f(d_{p})\,\mathrm {d} d_{p}}$

where

${\displaystyle d_{p}}$is the diameter of the particles
${\displaystyle \,\mathrm {d} f}$ is the fraction of particles having diameters between ${\displaystyle d_{p}}$ and ${\displaystyle d_{p}}$ + ${\displaystyle \mathrm {d} d_{p}}$
${\displaystyle f(d_{p})}$ is the frequency function

Therefore, the area under the frequency curve between two sizes a and b represents the total fraction of the particles in that size range:[13]

${\displaystyle f_{ab}=\int _{a}^{b}f(d_{p})\,\mathrm {d} d_{p}}$

It can also be formulated in terms of the total number density N:[14]

${\displaystyle dN=N(d_{p})\,\mathrm {d} d_{p}}$

Assuming spherical aerosol particles, the aerosol surface area per unit volume (S) is given by the second moment:[14]

${\displaystyle S=\pi /2\int _{0}^{\infty }N(d_{p})d_{p}^{2}\,\mathrm {d} d_{p}}$

And the third moment gives the total volume concentration (V) of the particles:[14]

${\displaystyle V=\pi /6\int _{0}^{\infty }N(d_{p})d_{p}^{3}\,\mathrm {d} d_{p}}$

One also usefully can approximate the particle size distribution using a mathematical function. The normal distribution usually does not suitably describe particle size distributions in aerosols because of the skewness associated a long tail of larger particles. Also for a quantity that varies over a large range, as many aerosol sizes do, the width of the distribution implies negative particles sizes, clearly not physically realistic. However, the normal distribution can be suitable for some aerosols, such as test aerosols, certain pollen grains and spores.[15]

A more widely chosen log-normal distribution gives the number frequency as:[15]

${\displaystyle \mathrm {d} f={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {(d_{p}-{\bar {d_{p}}})^{2}}{2\sigma ^{2}}}}\mathrm {d} d_{p}}$

where:

${\displaystyle \sigma }$ is the standard deviation of the size distribution and
${\displaystyle {\bar {d_{p}}}}$ is the arithmetic mean diameter.

The log-normal distribution has no negative values, can cover a wide range of values, and fits many observed size distributions reasonably well.[16]

Other distributions sometimes used to characterise particle size include: the Rosin-Rammler distribution, applied to coarsely dispersed dusts and sprays; the Nukiyama-Tanasawa distribution, for sprays of extremely broad size ranges; the power function distribution, occasionally applied to atmospheric aerosols; the exponential distribution, applied to powdered materials; and for cloud droplets, the Khrgian-Mazin distribution.[17]

Physics

Terminal velocity of a particle in a fluid

For low values of the Reynolds number (<1), true for most aerosol motion, Stokes' law describes the force of resistance on a solid spherical particle in a fluid. However, Stokes' law is only valid when the velocity of the gas at the surface of the particle is zero. For small particles (< 1 μm) that characterize aerosols, however, this assumption fails. To account for this failure, one can introduce the Cunningham correction factor, always greater than 1. Including this factor, one finds the relation between the resisting force on a particle and its velocity:[18]

${\displaystyle F_{D}={\frac {3\pi \eta Vd}{C_{c}}}}$

where

${\displaystyle F_{D}}$ is the resisting force on a spherical particle
${\displaystyle \eta }$ is the viscosity of the gas
${\displaystyle V}$ is the particle velocity
${\displaystyle C_{c}}$ is the Cunningham correction factor.

This allows us to calculate the terminal velocity of a particle undergoing gravitational settling in still air. Neglecting buoyancy effects, we find:[19]

${\displaystyle V_{TS}={\frac {\rho _{p}d^{2}gC_{c}}{18\eta }}}$

where

${\displaystyle V_{TS}}$ is the terminal settling velocity of the particle.

The terminal velocity can also be derived for other kinds of forces. If Stokes' law holds, then the resistance to motion is directly proportional to speed. The constant of proportionality is the mechanical mobility (B) of a particle:[20]

${\displaystyle B={\frac {V}{F_{D}}}={\frac {C_{c}}{3\pi \eta d}}}$

A particle traveling at any reasonable initial velocity approaches its terminal velocity exponentially with an e-folding time equal to the relaxation time:[21]

${\displaystyle V(t)=V_{f}-(V_{f}-V_{0})e^{-{\frac {t}{\tau }}}}$

where:

${\displaystyle V(t)}$ is the particle speed at time t
${\displaystyle V_{f}}$ is the final particle speed
${\displaystyle V_{0}}$ is the initial particle speed

To account for the effect of the shape of non-spherical particles, a correction factor known as the dynamic shape factor is applied to Stokes' law. It is defined as the ratio of the resistive force of the irregular particle to that of a spherical particle with the same volume and velocity:[22]

${\displaystyle \chi ={\frac {F_{D}}{3\pi \eta Vd_{e}}}}$

where:

${\displaystyle \chi }$ is the dynamic shape factor

Aerodynamic diameter

The aerodynamic diameter of an irregular particle is defined as the diameter of the spherical particle with a density of 1000 kg/m3 and the same settling velocity as the irregular particle.[23]

Neglecting the slip correction, the particle settles at the terminal velocity proportional to the square of the aerodynamic diameter, da:[23]

${\displaystyle V_{TS}={\frac {\rho _{0}d_{a}^{2}g}{18\eta }}}$

where

${\displaystyle \ \rho _{0}}$ = standard particle density (1000 kg/m3).

This equation gives the aerodynamic diameter:[24]

${\displaystyle d_{a}=d_{e}\left({\frac {\rho _{p}}{\rho _{0}\chi }}\right)^{\frac {1}{2}}}$

One can apply the aerodynamic diameter to particulate pollutants or to inhaled drugs to predict where in the respiratory tract such particles deposit. Pharmaceutical companies typically use aerodynamic diameter, not geometric diameter, to characterize particles in inhalable drugs.[citation needed]

Dynamics

The previous discussion focussed on single aerosol particles. In contrast, aerosol dynamics explains the evolution of complete aerosol populations. The concentrations of particles will change over time as a result of many processes. External processes that move particles outside a volume of gas under study include diffusion, gravitational settling, and electric charges and other external forces that cause particle migration. A second set of processes internal to a given volume of gas include particle formation (nucleation), evaporation, chemical reaction, and coagulation.[25]

A differential equation called the Aerosol General Dynamic Equation (GDE) characterizes the evolution of the number density of particles in an aerosol due to these processes.[25]

${\displaystyle {\frac {\partial {n_{i}}}{\partial {t}}}=-\nabla \cdot n_{i}\mathbf {q} +\nabla \cdot D_{p}\nabla _{i}+\left({\frac {\partial {n_{i}}}{\partial {t}}}\right)_{growth}+\left({\frac {\partial {n_{i}}}{\partial {t}}}\right)_{coag}-\nabla \cdot \mathbf {q} _{F}n_{i}}$

Change in time = Convective transport + brownian diffusion + gas-particle interactions + coagulation + migration by external forces

Where:

${\displaystyle n_{i}}$ is number density of particles of size category ${\displaystyle i}$
${\displaystyle \mathbf {q} }$ is the particle velocity
${\displaystyle D_{p}}$ is the particle Stokes-Einstein diffusivity
${\displaystyle \mathbf {q} _{F}}$ is the particle velocity associated with an external force

Coagulation

As particles and droplets in an aerosol collide with one another, they may undergo coalescence or aggregation. This process leads to a change in the aerosol particle-size distribution, with the mode increasing in diameter as total number of particles decreases.[26] On occasion, particles may shatter apart into numerous smaller particles; however, this process usually occurs primarily in particles too large for consideration as aerosols.

Dynamics regimes

The Knudsen number of the particle define three different dynamical regimes that govern the behaviour of an aerosol:

${\displaystyle K_{n}={\frac {2\lambda }{d}}}$

where ${\displaystyle \lambda }$ is the mean free path of the suspending gas and ${\displaystyle d}$ is the diameter of the particle.[27] For particles in the free molecular regime, Kn >> 1; particles small compared to the mean free path of the suspending gas.[28] In this regime, particles interact with the suspending gas through a series of "ballistic" collisions with gas molecules. As such, they behave similarly to gas molecules, tending to follow streamlines and diffusing rapidly through Brownian motion. The mass flux equation in the free molecular regime is:

${\displaystyle I={\frac {\pi a^{2}}{k_{b}}}\left({\frac {P_{\infty }}{T_{\infty }}}-{\frac {P_{A}}{T_{A}}}\right)\cdot C_{A}\alpha }$

where a is the particle radius, P and PA are the pressures far from the droplet and at the surface of the droplet respectively, kb is the Boltzmann constant, T is the temperature, CA is mean thermal velocity and α is mass accommodation coefficient.[citation needed] The derivation of this equation assumes constant pressure and constant diffusion coefficient.

Particles are in the continuum regime when Kn << 1.[28] In this regime, the particles are big compared to the mean free path of the suspending gas, meaning that the suspending gas acts as a continuous fluid flowing round the particle.[28] The molecular flux in this regime is:

${\displaystyle I_{cont}\sim {\frac {4\pi aM_{A}D_{AB}}{RT}}\left(P_{A\infty }-P_{AS}\right)}$

where a is the radius of the particle A, MA is the molecular mass of the particle A, DAB is the diffusion coefficient between particles A and B, R is the ideal gas constant, T is the temperature (in absolute units like kelvin), and PA∞ and PAS are the pressures at infinite and at the surface respectively.[citation needed]

The transition regime contains all the particles in between the free molecular and continuum regimes or Kn ≈ 1. The forces experienced by a particle are a complex combination of interactions with individual gas molecules and macroscopic interactions. The semi-empirical equation describing mass flux is:

${\displaystyle I=I_{cont}\cdot {\frac {1+K_{n}}{1+1.71K_{n}+1.33{K_{n}}^{2}}}}$

where Icont is the mass flux in the continuum regime.[citation needed] This formula is called the Fuchs-Sutugin interpolation formula. These equations do not take into account the heat release effect.

Partitioning

Condensation and evaporation

Aerosol partitioning theory governs condensation on and evaporation from an aerosol surface, respectively. Condensation of mass causes the mode of the particle-size distributions of the aerosol to increase; conversely, evaporation causes the mode to decrease. Nucleation is the process of forming aerosol mass from the condensation of a gaseous precursor, specifically a vapour. Net condensation of the vapour requires supersaturation, a partial pressure greater than its vapour pressure. This can happen for three reasons:[citation needed]

1. Lowering the temperature of the system lowers the vapour pressure.
2. Chemical reactions may increase the partial pressure of a gas or lower its vapour pressure.
3. The addition of additional vapour to the system may lower the equilibrium vapour pressure according to Raoult's law.

There are two types of nucleation processes. Gases preferentially condense onto surfaces of pre-existing aerosol particles, known as heterogeneous nucleation. This process causes the diameter at the mode of particle-size distribution to increase with constant number concentration.[29] With sufficiently high supersaturation and no suitable surfaces, particles may condense in the absence of a pre-existing surface, known as homogeneous nucleation. This results in the addition of very small, rapidly growing particles to the particle-size distribution.[29]

Activation

Water coats particles in an aerosols, making them activated, usually in the context of forming a cloud droplet.[citation needed] Following the Kelvin equation (based on the curvature of liquid droplets), smaller particles need a higher ambient relative humidity to maintain equilibrium than larger particles do. The following formula gives relative humidity at equilibrium:

${\displaystyle RH={\frac {p_{s}}{p_{0}}}\times 100\%=S\times 100\%}$

where ${\displaystyle p_{s}}$ is the saturation vapor pressure above a particle at equilibrium (around a curved liquid droplet), p0 is the saturation vapor pressure (flat surface of the same liquid) and S is the saturation ratio.

Kelvin equation for saturation vapor pressure above a curved surface is:

${\displaystyle \ln {p_{s} \over p_{0}}={\frac {2\sigma M}{RT\rho \cdot r_{p}}}}$

where rp droplet radius, σ surface tension of droplet, ρ density of liquid, M molar mass, T temperature, and R molar gas constant.

Solution to the General Dynamic Equation

There are no general solutions to the general dynamic equation (GDE);[30] common methods used to solve the general dynamic equation include:[31]

• Moment method[32]
• Modal/sectional method,[33] and
• Quadrature method of moments[34][35]/Taylor-series expansion method of moments,[36][37] and
• Monte Carlo method.[38]

Generation and Applications

People generate aerosols for various purposes, including:

Some devices for generating aerosols are:[2]

Stability of generated aerosol particles

Stability of nanoparticle agglomerates is critical for estimating size distribution of aerosolized particles from nano-powders or other sources. At nanotechnology workplaces, workers can be exposed via inhalation to potentially toxic substances during handling and processing of nanomaterials. Nanoparticles in the air often form agglomerates due to attractive inter-particle forces, such as van der Waals force or electrostatic force if the particles are charged. As a result, aerosol particles are usually observed as agglomerates rather than individual particles. For exposure and risk assessments of airborne nanoparticles, it is important to know about the size distribution of aerosols. When inhaled by humans, particles with different diameters are deposited in varied locations of the central and periphery respiratory system. Particles in nanoscale have been shown to penetrate the air-blood barrier in lungs and be translocated into secondary organs in the human body, such as the brain, heart and liver. Therefore, the knowledge on stability of nanoparticle agglomerates is important for predicting the size of aerosol particles, which helps assess the potential risk of them to human bodies.

Different experimental systems have been established to test the stability of airborne particles and their potentials to deagglomerate under various conditions. A comprehensive system recently reported by Ding & Riediker (2015)[44] is able to maintain robust aerosolization process and generate aerosols with stable number concentration and mean size from nano-powders. The deagglomeration potential of various airborne nanomaterials can be also studied using critical orifices. This process was also investigated by Stahlmecke et al. (2009).[45] In addition, an impact fragmentation device was developed to investigate bonding energies between particles.[46]

A standard deagglomeration testing procedure could be foreseen with the developments of the different types of existing systems. The likeliness of deagglomeration of aerosol particles in occupational settings can be possibly ranked for different nanomaterials if a reference method is available. For this purpose, inter-laboratory comparison of testing results from different setups could be launched in order to explore the influences of system characteristics on properties of generated nanomaterials aerosols.

Detection

Aerosol can either be measured in-situ or with remote sensing techniques.

In situ observations

Some available in situ measurement techniques include:

Remote sensing approach

Remote sensing approaches include:

Size selective sampling

Particles can deposit in the nose, mouth, pharynx and larynx (the head airways region), deeper within the respiratory tract (from the trachea to the terminal bronchioles), or in the alveolar region.[47] The location of deposition of aerosol particles within the respiratory system strongly determines the health effects of exposure to such aerosols.[48] This phenomenon led people to invent aerosol samplers that select a subset of the aerosol particles that reach certain parts of the respiratory system.[49] Examples of these subsets of the particle-size distribution of an aerosol, important in occupational health, include the inhalable, thoracic, and respirable fractions. The fraction that can enter each part of the respiratory system depends on the deposition of particles in the upper parts of the airway.[50] The inhalable fraction of particles, defined as the proportion of particles originally in the air that can enter the nose or mouth, depends on external wind speed and direction and on the particle-size distribution by aerodynamic diameter.[51] The thoracic fraction is the proportion of the particles in ambient aerosol that can reach the thorax or chest region.[52] The respirable fraction is the proportion of particles in the air that can reach the alveolar region.[53] To measure the respirable fraction of particles in air, a pre-collector is used with a sampling filter. The pre-collector excludes particles as the airways remove particles from inhaled air. The sampling filter collects the particles for measurement. It is common to use cyclonic separation for the pre-collector, but other techniques include impactors, horizontal elutriators, and large pore membrane filters.[54]

Two alternative size-selective criteria, often used in atmospheric monitoring, are PM10 and PM2.5. PM10 is defined by ISO as particles which pass through a size-selective inlet with a 50% efficiency cut-off at 10 μm aerodynamic diameter and PM2.5 as particles which pass through a size-selective inlet with a 50% efficiency cut-off at 2.5 μm aerodynamic diameter. PM10 corresponds to the “thoracic convention” as defined in ISO 7708:1995, Clause 6; PM2.5 corresponds to the “high-risk respirable convention” as defined in ISO 7708:1995, 7.1.[55] The United States Environmental Protection Agency replaced the older standards for particulate matter based on Total Suspended Particulate with another standard based on PM10 in 1987[56] and then introduced standards for PM2.5 (also known as fine particulate matter) in 1997.[57]

Atmospheric

Aerosol pollution over Northern India and Bangladesh

Three types of atmospheric aerosol have a significant effect on Earth's climate: volcanic; desert dust; and human-made. Volcanic aerosol forms in the stratosphere after an eruption as droplets of sulfuric acid that can last up to two years, and reflect sunlight, lowering temperature. Desert dust, mineral particles blown to high altitudes, absorb heat and may be responsible for inhibiting storm cloud formation. Human-made sulfate aerosols, primarily from burning oil and coal, affect the behavior of clouds.[58]

Although all hydrometeors, solid and liquid, can be described as aerosols, a distinction is commonly made between such dispersions (i.e. clouds) containing activated drops and crystals, and aerosol particles. Atmosphere of Earth contains aerosols of various types and concentrations, including quantities of:

Aerosols can be found in urban Ecosystems in various forms, for example:

The presence of aerosols in the earth's atmosphere can influence its climate, as well as human health.

Effects of Aerosols

• Aerosols interact with the Earth's energy budget in two ways, directly and indirectly.
E.g., a direct effect is that aerosols scatter sunlight directly back into space. This can lead to a significant decrease in the temperature, being an additional element to the greenhouse effect and therefore contributing to the global climate change.[60]
The indirect effects refer to the aerosols interfering with formations that interact directly with radiation. For example, they are able to modify the size of the cloud particles in the lower atmosphere, thereby changing the way clouds reflect and absorb light and therefore modifying the Earth's energy budget.[59]
• When aerosols absorb pollutants, it facilitates the deposition of pollutants to the surface of the earth as well as to bodies of water.[60] This has the potential to be damaging to both the environment and human health.
• Aerosol particles with an effective diameter smaller than 10 μm can enter the bronchi, while the ones with an effective diameter smaller than 2.5 μm can enter as far as the gas exchange region in the lungs,[61] which can be hazardous to human health.

References

1. ^ a b c d Hinds, 1999, p. 3
2. ^ a b Hidy, 1984, p. 254.
3. ^ Hidy, 1984, p. 5
4. ^ Hinds, 1999, p. 8
5. ^ Colbeck, 2014, Ch. 1.1
6. ^ Hinds, 1999, pp. 10-11.
7. ^ Hinds, 1999, p. 8.
8. ^ Hinds, 1999, p. 10.
9. ^ Hinds, 1999, p. 51.
10. ^ Jillavenkatesa, A; Dapkunas, SJ; Lin-Sien, Lum (2001). "Particle Size Characterization". NIST Special Publication. 960-1.
11. ^ Hinds, 1999, pp. 75-77.
12. ^ Hinds, 1999, p. 79
13. ^ Hinds, 1999, p. 79.
14. ^ a b c Hidy, 1984, p. 58
15. ^ a b Hinds, 1999, p 90.
16. ^ Hinds, 1999, p 91.
17. ^ Hinds, 1999, p 104-5
18. ^ Hinds, 1999, p. 44-49
19. ^ Hinds, 1999, p. 49
20. ^ Hinds, 1999, p. 47
21. ^ Hinds, 1991, p 115.
22. ^ Hinds, 1991, p. 51
23. ^ a b Hinds, 1999, p. 53.
24. ^ Hinds, 1999, p. 54.
25. ^ a b Hidy, 1984, p. 60
26. ^ Hinds, 1999, p. 260
27. ^ Baron, P. A. & Willeke, K. (2001). "Gas and Particle Motion". Aerosol Measurement: Principles, Techniques, and Applications.
28. ^ a b c DeCarlo, P.F. (2004). "Particle Morphology and Density Characterization by Combined Mobility and Aerodynamic Diameter Measurements. Part 1: Theory". Aerosol Science & Technology. 38 (12). doi:10.1080/027868290903907.
29. ^ a b Hinds, 1999, p.288
30. ^ Hidy, 1984, p62
31. ^ Friedlander, S. K. (2000). Smoke, Dust and Haze: Fundamentals of Aerosol Behavior (2nd ed.). Oxford University Press, New York.
32. ^ Hulburt, H. M., and Katz, S. (1964). Some Problems in Particle Technology: A Statistical Mechanical Formulation. Chem. Eng. Sci. ,19 (8):555–574.
33. ^ Landgrebe, J. D., and Pratsinis, S. E. (1990). A Discrete-Sectional Model for Particulate Production by Gas-Phase Chemical Reaction and Aerosol Coagulation in the Free-Molecular Regime. J. Colloid Interf. Sci. , 139 (1):63–86.
34. ^ R. McGraw, Description of aerosol dynamics by the quadrature method of moments, Aerosol Science and Technology, 1997
35. ^ D Marchisio, R Fox, Solution of population balance equations using the direct quadrature method of moments, Journal of Aerosol Science, 2005.
36. ^ Yu, M., Lin, J., and Chan, T. (2008). A New Moment Method for Solving the Coagulation Equation for Particles in Brownian Motion. Aerosol Sci. Technol. , 42(9):705–713.
37. ^ Yu, M., and Lin, J. (2009). Taylor-Expansion Moment Method for Agglomer- ate Coagulation Due to Brownian Motion in the Entire Size Regime. J. Aerosol Sci. , 40(6):549–562.
38. ^ Kraft, M. (2005). Modelling of Particulate Processes. KONA , 23(23):18–35.
39. ^ Hinds, 1999, 428
40. ^ Hidy, 1984, p 255
41. ^ Hidy, 1984, p 257
42. ^ Hidy, 1984, p 274
43. ^ Hidy, 1984, p 278
44. ^ Yaobo Ding & Michael Riediker (2015), A system to assess the stability of airborne nanoparticle agglomerates under aerodynamic shear, Journal of Aerosol Science 88 (2015) 98–108. doi:10.1016/j.jaerosci.2015.06.001
45. ^ 8. B. Stahlmecke, S. Wagener,C. Asbach,H. Kaminski, H. Fissan & T.A.J. Kuhlbusch (2009). Investigation of airborne nanopowder agglomerate stability in an orifice under various differential pressure conditions. Journal of Nanoparticle Research, 1625-1635.
46. ^ 9. S. Froeschke, S. Kohler, A.P. Weber & G. Kasper (2003). Impact fragmentation of nanoparticle agglomerates. Journal of Aerosol Science, 34(3), 275–287.
47. ^ Hinds, 1999, p.233
48. ^ Hinds, 1999, p. 233
49. ^ Hinds, 1999, p. 249
50. ^ Hinds, 1999, p. 244
51. ^ Hinds, 1999, p. 246
52. ^ Hinds, 1999, p. 254
53. ^ Hinds, 1999, p. 250
54. ^ Hinds, 1999, p. 252
55. ^ "Particulate pollution – PM10 and PM2.5". Recognition, Evaluation, Control. News and views from Diamond Environmental Limited. Retrieved 23 September 2012.
56. ^ "Particulate Matter (PM-10)". Archived from the original on 1 September 2012. Retrieved 23 September 2012.
57. ^ "Basic Information". Retrieved 23 September 2012.
58. ^ "Atmospheric Aerosols: What Are They, and Why Are They So Important?". NASA Langley Research Center. 22 Apr 2008. Retrieved 27 December 2014.
59. ^ a b Allen, Bob. "Atmospheric Aerosols: What Are They, and Why Are They So Important?". NASA. NASA. Retrieved 8 July 2014.
60. ^ a b Kommalapati, Raghava R.; Valsaraj, Kalliat T. (2009). Atmospheric aerosols: Characterization, chemistry, modeling, and climate. 1005. Washington, DC: American Chemical Society. pp. 1–10. doi:10.1021/bk-2009-1005.ch001. ISBN 9780841224827. Retrieved 10 July 2014.
61. ^ Grainger, Don. "Volcanic Emissions". Earth Observation Data Group, Department of Physics, University of Oxford. University of Oxford. Retrieved 8 July 2014.

Works cited

• Colbeck, Ian, Mihalis Lazaridis (editors) (2014). Aerosol Science: Technology and Applications. John Wiley & Sons - Science. ISBN 978-1-119-97792-6.
• Hinds, William C. (1999). Aerosol Technology (2nd ed.). Wiley - Interscience. ISBN 978-0-471-19410-1.
• Hidy, George M. (1984). Aerosols, An Industrial and Environmental Science. Academic Press, Inc. ISBN 978-0-12-412336-6.