Aerosol
An aerosol is a colloid of fine solid particles or liquid droplets, in air or another gas.^{[1]} Aerosols can be natural or not. Examples of natural aerosols are fog, forest exudates and geyser steam. Examples of artifical 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 clearcut. 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]}
Contents
 Definitions 1
 Size distribution 2

Physics 3
 3.1 Terminal velocity of a particle in a fluid
 Aerodynamic diameter 3.2

Dynamics 3.3
 Coagulation 3.3.1
 Dynamics regimes 3.3.2
 Partitioning 3.3.3
 Activation 3.3.4
 Solution to the General Dynamic Equation 3.3.5
 Generation and Applications 4

Detection 5
 In situ observations 5.1
 Remote sensing approach 5.2
 Size selective sampling 5.3
 Atmospheric 6
 Importance of Aerosols 7
 See also 8
 References 9
 Works cited 10
 Further reading 11
 External links 12
Definitions
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 aerosolution, 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 gastoparticle conversion.^{[4]}
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/m^{3}. Also commonly used is the number concentration (N), the number of particles per unit volume with units such as number/m^{3} or number/cm^{3}.^{[5]}
The size of particles has a major influence on their properties, and the aerosol particle radius or diameter (d_{p}) 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.^{[6]} 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.^{[7]} The equivalent volume diameter (d_{e}) is defined as the diameter of a sphere of the same volume as that of the irregular particle.^{[8]} Also commonly used is the aerodynamic diameter.
Size distribution
For a monodisperse aerosol, a single number—the particle diameter—suffices to describe the size of the particles. However, more complicated particlesize distributions describe the sizes of the particles in a polydisperse aerosol. This distribution defines the relative amounts of particles, sorted according to size.^{[9]} 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.^{[10]} If the width of the bins tends to zero, one gets the frequency function:^{[11]}
 \mathrm{d}f = f(d_p) \,\mathrm{d}d_p
where
 d_p is the diameter of the particles
 \,\mathrm{d}f is the fraction of particles having diameters between d_p and d_p + \mathrm{d}d_p
 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:^{[12]}
 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:^{[13]}
 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:^{[13]}
 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:^{[13]}
 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.^{[14]}
A more widely chosen lognormal distribution gives the number frequency as:^{[14]}
 \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:
 \sigma is the standard deviation of the size distribution and
 \bar{d_p} is the arithmetic mean diameter.
The lognormal distribution has no negative values, can cover a wide range of values, and fits many observed size distributions reasonably well.^{[15]}
Other distributions sometimes used to characterise particle size include: the RosinRammler distribution, applied to coarsely dispersed dusts and sprays; the NukiyamaTanasawa 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 KhrgianMazin distribution.^{[16]}
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:^{[17]}
 F_D = \frac {3 \pi \eta V d}{C_c}
where
 F_D is the resisting force on a spherical particle
 \eta is the viscosity of the gas
 V is the particle velocity
 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:^{[18]}
 V_{TS} = \frac{\rho_p d^2 g C_c}{18 \eta}
where
 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:^{[19]}
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 efolding time equal to the relaxation time:^{[20]}
V(t) = V_{f}(V_{f}V_{0})e^{\frac{t}{\tau}}
where:
 V(t) is the particle speed at time t
 V_f is the final particle speed
 V_0 is the initial particle speed
To account for the effect of the shape of nonspherical 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:^{[21]}
\chi = \frac{F_D}{3 \pi \eta V d_e}
where:
 \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/m^{3} and the same settling velocity as the irregular particle.^{[22]}
Neglecting the slip correction, the particle settles at the terminal velocity proportional to the square of the aerodynamic diameter, d_{a}:^{[22]}
 V_{TS} = \frac{\rho_0 d_a^2 g}{18 \eta}
where
 \ \rho_0 = standard particle density (1000 kg/m^{3}).
This equation gives the aerodynamic diameter:^{[23]}
 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.
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.^{[24]}
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.^{[24]}
\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 + gasparticle interactions + coagulation + migration by external forces
Where:
 n_i is number density of particles of size category i
 \mathbf{q} is the particle velocity
 D_p is the particle StokesEinstein diffusivity
 \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 particlesize distribution, with the mode increasing in diameter as total number of particles decreases.^{[25]} 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:
 K_n=\frac{2\lambda}{d}
where \lambda is the mean free path of the suspending gas and d is the diameter of the particle.^{[26]} For particles in the free molecular regime, K_{n} >> 1; particles small compared to the mean free path of the suspending gas.^{[27]} 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:
 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 P_{A} are the pressures far from the droplet and at the surface of the droplet respectively, k_{b} is the Boltzmann constant, T is the temperature, C_{A} is mean thermal velocity and α is mass accommodation coefficient. The derivation of this equation assumes constant pressure and constant diffusion coefficient.
Particles are in the continuum regime when K_{n} << 1.^{[27]} 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.^{[27]} The molecular flux in this regime is:
 I_{cont} \sim \frac{4 \pi a M_A D_{AB}}{RT} \left( P_{A \infty}  P_{AS}\right)
where a is the radius of the particle A, M_{A} is the molecular mass of the particle A, D_{AB} 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 P_{A∞} and P_{AS} are the pressures at infinite and at the surface respectively.
The transition regime contains all the particles in between the free molecular and continuum regimes or K_{n} ≈ 1. The forces experienced by a particle are a complex combination of interactions with individual gas molecules and macroscopic interactions. The semiempirical equation describing mass flux is:
 I = I_{cont} \cdot \frac{1 + K_n}{1 + 1.71 K_n + 1.33 {K_n}^2}
where I_{cont} is the mass flux in the continuum regime. This formula is called the FuchsSutugin interpolation formula. These equations do not take into account the heat release effect.
Partitioning
Aerosol partitioning theory governs condensation on and evaporation from an aerosol surface, respectively. Condensation of mass causes the mode of the particlesize 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:
 Lowering the temperature of the system lowers the vapour pressure.
 Chemical reactions may increase the partial pressure of a gas or lower its vapour pressure.
 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 preexisting aerosol particles, known as heterogeneous nucleation. This process causes the diameter at the mode of particlesize distribution to increase with constant number concentration.^{[28]} With sufficiently high supersaturation and no suitable surfaces, particles may condense in the absence of a preexisting surface, known as homogeneous nucleation. This results in the addition of very small, rapidly growing particles to the particlesize distribution.^{[28]}
Activation
Water coats particles in an aerosols, making them activated, usually in the context of forming a cloud droplet. 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:
 RH = \frac{p_s}{p_0} \times 100\% = S \times 100\%
where p_s is the saturation vapor pressure above a particle at equilibrium (around a curved liquid droplet), p_{0} 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:
 \ln{p_s \over p_0} = \frac{2 \sigma M}{RT \rho \cdot r_p}
where r_{p} 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);^{[29]} common methods used to solve the general dynamic equation include:
 Moment method,
 Modal/sectional method, and
 Quadrature method of moments.
Generation and Applications
People generate aerosols for various purposes, including:
 as test aerosols for calibrating instruments, performing research, and testing sampling equipment and air filters;^{[30]}
 to deliver deodorants, paints, and other consumer products in sprays;^{[31]}
 for dispersal and agricultural application of pesticides;^{[32]}
 for medical treatment of respiratory disease;^{[33]} and
 in fuel injection systems and other combustion technology.^{[34]}
Some devices for generating aerosols are:^{[2]}
 Aerosol spray
 Atomizer nozzle or Nebulizer
 Electrospray
 Vibrating orifice aerosol generator (VOAG)
Detection
Aerosol can either be measured insitu or with remote sensing techniques.
In situ observations
Some available in situ measurement techniques include:
 Aerosol mass spectrometer (AMS)
 Differential mobility analyzer (DMA)
 Aerodynamic particle sizer (APS)
 Wide range particle spectrometer (WPS)
 MicroOrifice Uniform Deposit Impactor(MOUDI)
 Condensation particle counter (CPC)
 Epiphaniometer
 Electrical low pressure impactor (ELPI)
 Aerosol particle massanalyser (APM)
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.^{[35]} The location of deposition of aerosol particles within the in the respiratory system strongly determines the health effects of exposure to such aerosols.^{[36]} This phenomenon led people to invent aerosol samplers that select a subset of the aerosol particles that reach certain parts of the respiratory system.^{[37]} Examples of these subsets of the particlesize 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.^{[38]} 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 particlesize distribution by aerodynamic diameter.^{[39]} The thoracic fraction is the proportion of the particles in ambient aerosol that can reach the thorax or chest region.^{[40]} The respirable fraction is the proportion of particles in the air that can reach the alveolar region.^{[41]} To measure the respirable fraction of particles in air, a precollector is used with a sampling filter. The precollector 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 precollector, but other techniques include impactors, horizontal elutriators, and large pore membrane filters.^{[42]}
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 sizeselective inlet with a 50 % efficiency cutoff at 10 μm aerodynamic diameter. PM10 corresponds to the “thoracic convention” as defined in ISO 7708:1995, Clause 6 and PM2.5 as particles which pass through a sizeselective inlet with a 50 % efficiency cutoff at 2,5 μm aerodynamic diameter. PM2,5 corresponds to the “highrisk respirable convention” as defined in ISO 7708:1995, 7.1.^{[43]} 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^{[44]} and then introduced standards for PM2.5 (also known as fine particulate matter) in 1997.^{[45]}
Atmospheric
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:
 natural inorganic materials: fine dust, sea salt, water droplets.
 natural pollen, spores, bacteria
 anthropogenic products of combustion such as: smoke, ashes or dusts
Aerosols can be found in urban Ecosystems in various forms, for example:
 Dust,
 Cigarette smoke,
 Mist from aerosol spray cans,
 Soot or fumes in car exhaust.
The presence of aerosols in earth's atmosphere can influence Earth's climate, as well as human health.
Importance of Aerosols
 Volcanic eruptions release large amounts of sulphuric acid, hydrogen sulphide and hydrochloric acid into the atmosphere. These gases represent aerosols and eventually return to earth as acid rain, having a number of adverse effects on the environment and human life.^{[46]}
 Aerosols interact with the Earth's energetic 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.^{[47]}

 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.^{[46]}
 When aerosols absorb or adsorb pollutants, it facilitates the deposition of pollutants to the surface of the earth as well as to bodies of water.^{[47]} 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,^{[48]} which can be hazardous to human health.
See also
 Nebulizer
 Aerogel
 Aerosol spray, the spraying device
 Bioaerosol
 Atmospheric particulate matter
 Deposition (Aerosol physics)
 Cloud
References
 ^ ^{a} ^{b} ^{c} ^{d} Hinds, 1999, p. 3
 ^ ^{a} ^{b} Hidy, 1984, p. 254.
 ^ Hidy, 1984, p. 5
 ^ Hinds, 1999, p. 8
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 ^ Hinds, 1999, p. 8.
 ^ Hinds, 1999, p. 10.
 ^ Hinds, 1999, p. 51.
 ^ Jillavenkatesa, A; Dapkunas, SJ; LinSien, Lum (2001). "Particle Size Characterization". NIST Special Publication. 9601.
 ^ Hinds, 1999, pp. 7577.
 ^ Hinds, 1999, p. 79
 ^ Hinds, 1999, p. 79.
 ^ ^{a} ^{b} ^{c} Hidy, 1984, p. 58
 ^ ^{a} ^{b} Hinds, 1999, p 90.
 ^ Hinds, 1999, p 91.
 ^ Hinds, 1999, p 1045
 ^ Hinds, 1999, p. 4449
 ^ Hinds, 1999, p. 49
 ^ Hinds, 1999, p. 47
 ^ Hinds, 1991, p 115.
 ^ Hinds, 1991, p. 51
 ^ ^{a} ^{b} Hinds, 1999, p. 53.
 ^ Hinds, 1999, p. 54.
 ^ ^{a} ^{b} Hidy, 1984, p. 60
 ^ Hinds, 1999, p. 260
 ^ Baron, P. A., and Willeke , K. (2001). "Gas and Particle Motion". Aerosol Measurement: Principles. Techniques. and Applications.
 ^ ^{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).
 ^ ^{a} ^{b} Hinds, 1999, p.288
 ^ Hidy, 1984, p62
 ^ Hinds, 1999, 428
 ^ Hidy, 1984, p 255
 ^ Hidy, 1984, p 257
 ^ Hidy, 1984, p 274
 ^ Hidy, 1984, p 278
 ^ Hinds, 1999, p.233
 ^ Hinds, 1999, p. 233
 ^ Hinds, 1999, p. 249
 ^ Hinds, 1999, p. 244
 ^ Hinds, 1999, p. 246
 ^ Hinds, 1999, p. 254
 ^ Hinds, 1999, p. 250
 ^ Hinds, 1999, p. 252
 ^ "Particulate pollution – PM10 and PM2.5". Recognition, Evaluation, Control. News and views from Diamond Environmental Limited. Retrieved 23 September 2012.
 ^ "Particulate Matter (PM10)". Retrieved 23 September 2012.
 ^ "Basic Information". Retrieved 23 September 2012.
 ^ ^{a} ^{b} Allen, Bob. "Atmospheric Aerosols: What Are They, and Why Are They So Important?". NASA. NASA. Retrieved 8 July 2014.
 ^ ^{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.
 ^ Grainger, Don. "Volcanic Emissions". Earth Observation Data Group, Department of Physics, University of Oxford. University of Oxford. Retrieved 8 July 2014.
Works cited
 Hinds, William C. (1999). Aerosol Technology (2nd ed.). Wiley  Interscience.
 Hidy, George M. (1984). Aerosols, An Industrial and Environmental Science. Academic Press, Inc.
Further reading
 Friedlander, Sheldon K. (2000). Smoke, Dust and Haze (2nd ed.).
 Kulkarni, Pramod; Baron, Paul A.; Willeke, Klaus, Aerosol Measurement  Principles, Techniques, and Applications, 2011 John Wiley & Sons, ISBN 9780470387412.
 Preining, Othmar and E. James Davis (eds.), History of Aerosol Science, Österreichische Akademie der Wissenschaften, ISBN 3700129157 (pbk.)
 Aerosol Education Resources
 Pruppacher, H. R.; J. D. Klett. Microphysics of Clouds and Precipitation (2nd ed.). Springer.
 Seinfeld, John; Spyros Pandis (1998). Atmospheric Chemistry and Physics: From Air Pollution to Climate Change (2nd ed.). Hoboken, New Jersey: John Wiley & Sons, Inc.
External links
 American Association for Aerosol Research