Editing Aerosol

{{Short description|Suspension of fine solid particles or liquid droplets in a gas}}
{{Distinguish|aerosil}}
{{For|the spray can|Aerosol spray dispenser}}
[[File:Heavy mist.jpg|thumb|upright=1.4|[[Mist]] and [[fog]] are aerosols|alt=photograph of heavy mist]]

An '''aerosol''' is a [[suspension (chemistry)|suspension]] of fine [[solid]] [[particle]]s or [[liquid]] [[Drop (liquid)|droplets]] in [[air]] or another [[gas]].{{sfn|Hinds|1999|p=3}} Aerosols can be generated from natural or [[Human impact on the environment|human causes]]. The term ''aerosol'' commonly refers to the mixture of [[particulates]] in air, and not to the particulate matter alone.<ref>{{cite book |url=https://archive.org/details/atmosphericchemi0000sein/page/97 |title=Atmospheric Chemistry and Physics: From Air Pollution to Climate Change |vauthors=Seinfeld J, Pandis S |publisher=[[John Wiley & Sons]] |year=1998 |isbn=978-0-471-17816-3 |edition=2nd |location=Hoboken, New Jersey |page=[https://archive.org/details/atmosphericchemi0000sein/page/97 97] |url-access=registration}}</ref> Examples of natural aerosols are [[fog]], [[mist]] or [[dust]]. Examples of human caused aerosols include [[particulate]] [[air pollutants]], mist from the discharge at [[hydroelectric dam]]s, irrigation mist, perfume from [[Spray nozzle|atomizers]], [[smoke]], [[dust]], [[Pesticide|sprayed pesticides]], and medical treatments for respiratory illnesses.{{sfn|Hidy|1984|p=254}}

Several types of atmospheric aerosol have a significant effect on Earth's climate: volcanic, desert dust, sea-salt, that originating from biogenic sources and human-made. Volcanic aerosol forms in the stratosphere after an eruption as droplets of [[sulfuric acid]] that can prevail for 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 aerosol]]s, primarily from burning oil and coal, affect the behavior of clouds.<ref name=":0" /> When aerosols absorb pollutants, it facilitates the deposition of pollutants to the surface of the earth as well as to bodies of water.<ref name="kommalapati" /> This has the potential to be damaging to both the environment and human health.

[[Ship tracks]] are [[cloud]]s that form around the [[Exhaust gas|exhaust]] released by ships into the still ocean air. Water [[molecule]]s collect around the tiny particles ([[Particulate|aerosols]]) from exhaust to form a [[cloud seed]]. More and more water accumulates on the seed until a visible cloud is formed. In the case of ship tracks, the cloud seeds are stretched over a long narrow path where the wind has blown the ship's exhaust, so the resulting clouds resemble long strings over the ocean.

The warming caused by human-produced greenhouse gases has been somewhat offset by the cooling effect of human-produced aerosols. In 2020, regulations on fuel significantly cut sulfur dioxide emissions from international shipping by approximately 80%, leading to an unexpected global geoengineering termination shock.<ref name=":1" />

The liquid or solid particles in an aerosol have diameters typically less than [[micrometre|1&nbsp;μm]]. Larger particles with a significant settling speed make the mixture a [[Suspension (chemistry)|suspension]], but the distinction is not clear. In everyday language, ''aerosol'' often refers to a [[aerosol spray|dispensing system]] that delivers a consumer product from a [[spray can]].

[[Airborne disease|Diseases can spread]] by means of small droplets in the [[breath]],<ref>{{Cite journal|last=Hunziker|first=Patrick|date=2021-10-01|title=Minimising exposure to respiratory droplets, 'jet riders' and aerosols in air-conditioned hospital rooms by a 'Shield-and-Sink' strategy|url=https://bmjopen.bmj.com/content/11/10/e047772|journal=BMJ Open|language=en|volume=11|issue=10|pages=e047772|doi=10.1136/bmjopen-2020-047772|pmid=34642190|pmc=8520596|issn=2044-6055}}</ref> sometimes called [[bioaerosols]].<ref>{{Cite book|url=https://books.google.com/books?id=e3INDgAAQBAJ&q=%C2%A0Diseases+can+also+spread+by+means+of+small+droplets+in+the+breath+called+aerosols&pg=PA129|title=Surgical Technology – E-Book: Principles and Practice|last=Fuller|first=Joanna Kotcher|date=2017-01-31|publisher=Elsevier Health Sciences|isbn=978-0-323-43056-2|language=en}}</ref>

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== Definitions ==
{{See also|Particulates}}
[[File:Fly Ash FHWA dot gov.jpg|thumb|[[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.|alt=Fly ash particles shown at 2,000 times magnification]]
[[Image:Aerosol.png|thumb|[[Aerosol spray dispenser|Aerosol spray can]]]]
Aerosol is defined as a suspension system of solid or liquid particles in a gas. An aerosol includes both the particles and the suspending gas, which is usually air.{{sfn|Hinds|1999|p=3}} Meteorologists and climatologists often refer to them as particle matter, while the classification in sizes ranges like PM2.5 or PM10,<ref>PM2.5 refers to the mass of particles with sizes between 0 and 2.5 micrometers, and PM10 for sizes between 0 and 10 micrometers.</ref><ref name="auto">{{cite web |title=Aerosols: Tiny Particles, Big Impact |url=https://earthobservatory.nasa.gov/features/Aerosols |website=earthobservatory.nasa.gov |language=en |date=2 November 2010}}</ref> is useful in the field of atmospheric pollution as these size range play a role in ascertain the harmful effects in human health.<ref>{{Cite web |last=US EPA |first=OAR |date=2016-04-19 |title=Particulate Matter (PM) Basics |url=https://www.epa.gov/pm-pollution/particulate-matter-pm-basics |access-date=2024-11-04 |website=www.epa.gov |language=en}}</ref> [[Frederick G. Donnan]] presumably first used the term ''aerosol'' during [[World War I]] to describe an aero-[[Solution (chemistry)|solution]], clouds of microscopic particles in air. This term developed analogously to the term [[Sol (colloid)|hydrosol]], a [[colloid]] system with water as the dispersed medium.{{sfn|Hidy|1984|p=5}} ''Primary aerosols'' contain particles introduced directly into the gas; ''[[Secondary organic aerosol|secondary aerosols]]'' form through gas-to-particle conversion.{{sfn|Hinds|1999|p=8}}

Key aerosol groups include sulfates, organic carbon, black carbon, nitrates, mineral dust, and sea salt, they usually clump together to form a complex mixture.<ref name="auto"/> Various types of aerosol, classified according to physical form and how they were generated, include dust, fume, mist, smoke and fog.{{sfn|Colbeck|Lazaridis|2014|p= Ch. 1.1}}

There are several measures of aerosol concentration. [[Environmental science]] and [[environmental health]] often use the ''[[Mass concentration (chemistry)|mass concentration]]'' (''M''), defined as the mass of particulate matter per unit volume, in units such as μg/m<sup>3</sup>. Also commonly used is the ''[[Number density|number concentration]]'' (''N''), the number of particles per unit volume, in units such as number per m<sup>3</sup> or number per cm<sup>3</sup>.{{sfn|Hinds|1999|pp=10-11}}

Particle size has a major influence on particle properties, and the aerosol particle radius or diameter (''d<sub>p</sub>'') 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.{{sfn|Hinds|1999|p=8}} Liquid droplets are almost always nearly spherical, but scientists use an ''equivalent diameter'' to characterize the properties 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.{{sfn|Hinds|1999|p=10}} The ''equivalent volume diameter'' (''d<sub>e</sub>'') is defined as the diameter of a sphere of the same volume as that of the irregular particle.{{sfn|Hinds|1999|p=51}} Also commonly used is the [[#Aerodynamic diameter|aerodynamic diameter]],&nbsp; ''d<sub>a</sub>''.

== Generation and applications ==
People generate aerosols for various purposes, including:
* as test aerosols for [[calibration|calibrating]] instruments, performing research, and testing sampling equipment and air filters;{{sfn|Hinds|1999|p=428}}
* to deliver [[deodorant]]s, [[paint]]s, and other consumer products in sprays;{{sfn|Hidy|1984|p=255}}
* for dispersal and agricultural application
* for medical treatment of [[respiratory disease]];{{sfn|Hidy|1984|p=274}} and
* in [[fuel injection]] systems and other [[combustion]] technology.{{sfn|Hidy|1984|p=278}}

Some devices for generating aerosols are:{{sfn|Hidy|1984|p=254}}
* [[Aerosol spray]]
* [[Atomizer nozzle]] or [[nebulizer]]
* [[Electrospray]]
* [[Electronic cigarette]]
* Vibrating orifice aerosol generator (VOAG)

== In the atmosphere ==
[[File:Aerosol-India.jpg|thumb|Aerosol pollution over northern [[India]] and [[Bangladesh]]|alt=Satellite photo showing aerosol pollution visible from space]]
[[File:Portrait of global aerosols.jpg|thumb|upright=1.6|Overview of large clouds of aerosols around Earth (green: smoke, blue: salt, yellow: dust, white: sulfuric)]]

{{main|Particulates}}

Several types of atmospheric aerosol have a significant effect on Earth's climate: volcanic, desert dust, sea-salt, that originating from biogenic sources and human-made. Volcanic aerosol forms in the stratosphere after an eruption as droplets of [[sulfuric acid]] that can prevail for 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 aerosol]]s, primarily from burning oil and coal, affect the behavior of clouds.<ref name=":0">{{cite web |date=22 Apr 2008 |title=Atmospheric Aerosols: What Are They, and Why Are They So Important? |url=http://www.nasa.gov/centers/langley/news/factsheets/Aerosols.html |access-date=27 December 2014 |publisher=NASA Langley Research Center}}</ref>

Although all [[Precipitation#Hydrometeor definition|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.<ref>The water in atmospheric modelling has an important role with a particular behavior: their different phases (vapor, liquid and solid) are mostly conditioned by temperature which differentiate in practical terms the hydrometeors from other atmospheric particles.</ref> The [[atmosphere of Earth]] contains aerosols of various types and concentrations, including quantities of:
* natural [[Inorganic chemistry|inorganic]] materials: fine dust, sea salt, or water droplets
* natural [[Organic chemistry|organic]] materials: smoke, [[pollen]], [[spore]]s, or [[bacteria]]
* [[human impact on the environment|anthropogenic]] products of combustion such as: smoke, [[fly ash|ashes]] or dusts

Aerosols can be found in urban [[ecosystem]]s in various forms, for example:
* Dust
* Cigarette smoke
* Mist from [[aerosol spray]] cans
* [[Soot]] or fumes in car exhaust

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

=== Effects ===
{{See also|Particulates#Climate effects}}
[[File:20231206 Radiative forcing (warming influence) - global warming.svg |thumb|Aerosols have a cooling effect that is small compared to the radiative forcing (warming effect) of greenhouse gases.<ref name=ESSD_2022>{{cite journal |last1=Forster |first1=Piers M. |last2=Smith |first2=Christopher J. |last3=Walsh |first3=Tristram |last4=Lamb |first4=William F. |last5=Lamboll |first5=Robin |display-authors=4 |title=Indicators of Global Climate Change 2022: annual update of large-scale indicators of the state of the climate system and human influence |url=https://essd.copernicus.org/articles/15/2295/2023/essd-15-2295-2023.pdf |journal=Earth System Science Data |date=2023 |volume=15 |issue=6 |pages=2295–2327 |publisher=Copernicus Programme |doi=10.5194/essd-15-2295-2023 |bibcode=2023ESSD...15.2295F |doi-access=free }} Fig. 2(a).</ref>]]
[[File:1750- Radiative forcing - greenhouse gases and aerosols.svg|thumb| Hansen ''et{{nbsp}}al.'' (2025) wrote that the IPCC had underestimated aerosols' cooling effect, causing it to also underestimate [[climate sensitivity]] (Earth's responsiveness to increases in greenhouse gas concentrations).<ref name=Envt_Hanson_20250203/> In what Hansen called a [[Deal with the Devil|Faustian bargain]], regulation of aerosols improved air quality, but aerosols' cooling effect became inadequate to temper the increasing warming effect of greenhouse gases—explaining unexpectedly large global warming in 2023-2024.<ref name=Envt_Hanson_20250203>{{cite journal |last1=Hansen |first1=James E. |last2=Kharecha |first2=Pushker |last3=Sato |first3=Makiko |last4=Tselioudis |first4=George |last5=Kelly |first5=Joseph |last6=Bauer |first6=Susanne E. |last7=Ruedy |first7=Reto |last8=Jeong |first8=Eunbi |last9=Jin |first9=Quijian |last10=Rignot |first10=Eric |last11=Velicogna |first11=Isabella |last12=Schoeberl |first12=Mark R. |last13=von Schuckmann |first13=Karina |last14=Amponsem |first14=Joshua |last15=Cao |first15=Junji |last16=Keskinen |first16=Anton |last17=Li |first17=Jing |last18=Pokela |first18=Anni |display-authors=4 |title=Global Warming Has Accelerated: Are the United Nations and the Public Well-Informed? |journal=Environment |date=3 February 2025 |volume=67 |issue=1 |pages=6-44 |doi=10.1080/00139157.2025.2434494|doi-access=free }} Figure 3.</ref>]]

Volcanic eruptions release large amounts of [[sulphuric acid]], [[hydrogen sulfide]] and [[hydrochloric acid]] into the atmosphere. These gases represent aerosols and eventually return to earth as [[acid rain]], having a number of [[Acid rain#Adverse effects|adverse effects]] on the environment and human life.<ref name="nasa">
{{cite web |last1=Allen |first1=Bob |title=Atmospheric Aerosols: What Are They, and Why Are They So Important? |url=http://www.nasa.gov/centers/langley/news/factsheets/Aerosols.html |access-date=8 July 2014 |website=NASA }}</ref>

When aerosols absorb pollutants, it facilitates the deposition of pollutants to the surface of the earth as well as to bodies of water.<ref name="kommalapati" /> This has the potential to be damaging to both the environment and human health.

Aerosols interact with the [[Earth's energy budget]] in two ways, directly and indirectly.
:* E.g., a ''direct'' effect is that aerosols scatter and absorb incoming solar radiation.<ref>{{Cite web |last=Highwood |first=Ellie |date=2018-09-05 |title=Aerosols and Climate |url=https://www.rmets.org/resource/aerosols-and-climate |access-date=2019-10-07 |website=Royal Meteorological Society |language=en}}</ref> This will mainly lead to a cooling of the surface (solar radiation is scattered back to space) but may also contribute to a warming of the surface (caused by the absorption of incoming solar energy).<ref>{{Cite web |title=Fifth Assessment Report - Climate Change 2013 |url=https://www.ipcc.ch/report/ar5/wg1/ |access-date=2018-02-07 |website=www.ipcc.ch}}</ref> This will be an additional element to the [[greenhouse effect]] and therefore contributing to the global climate change.<ref name="kommalapati">{{cite book |last1=Kommalapati |first1=Raghava R. |title=Atmospheric aerosols: Characterization, chemistry, modeling, and climate |last2=Valsaraj |first2=Kalliat T. |date=2009 |publisher=American Chemical Society |isbn=978-0-8412-2482-7 |volume=1005 |location=Washington, DC |pages=1–10 |doi=10.1021/bk-2009-1005.ch001}}</ref>
:* The ''indirect'' effects refer to the aerosol 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.<ref name="nasa" />
:* There is evidence to suggest that anthropogenic aerosols actually offset the effects of greenhouse gases in some areas, which is why the Northern Hemisphere shows slower surface warming than the Southern Hemisphere, although that just means that the Northern Hemisphere will absorb the heat later through ocean currents bringing warmer waters from the South.<ref>Anthropogenic Aerosols, Greenhouse Gases, and the Uptake, Transport, and Storage of Excess Heat in the Climate System {{cite journal |last1=Irving |first1=D. B. |last2=Wijffels |first2=S. |last3=Church |first3=J. A. |year=2019 |title=Anthropogenic Aerosols, Greenhouse Gases, and the Uptake, Transport, and Storage of Excess Heat in the Climate System |journal=Geophysical Research Letters |volume=46 |issue=9 |pages=4894–4903 |bibcode=2019GeoRL..46.4894I |doi=10.1029/2019GL082015 |doi-access=free|hdl=1912/24327 |hdl-access=free }}</ref> On a global scale however, aerosol cooling decreases greenhouse-gases-induced heating without offsetting it completely.<ref>GIEC AR6 WG1 - Figure SPM.2 https://www.ipcc.ch/report/sixth-assessment-report-working-group-i/</ref>
[[Ship tracks]] are [[cloud]]s that form around the [[Exhaust gas|exhaust]] released by ships into the still ocean air. Water [[molecule]]s collect around the tiny particles ([[Particulate|aerosols]]) from exhaust to form a [[cloud seed]]. More and more water accumulates on the seed until a visible cloud is formed. In the case of ship tracks, the cloud seeds are stretched over a long narrow path where the wind has blown the ship's exhaust, so the resulting clouds resemble long strings over the ocean.<ref>{{Cite web |last=Wellock |first=Bill |date=2024-01-17 |title=Changing the sky: FSU researchers examine how aerosols from ships affect cloud formation, climate change |url=https://news.fsu.edu/news/science-technology/2024/01/17/changing-the-sky-fsu-researchers-examine-how-aerosols-from-ships-affect-cloud-formation-global-warming/ |access-date=2024-07-15 |website=Florida State University News |language=en-US}}</ref>

The warming caused by human-produced greenhouse gases has been somewhat offset by the cooling effect of human-produced aerosols. In 2020, regulations on fuel significantly cut [[sulfur dioxide]] emissions from international shipping by approximately 80%, leading to an unexpected global geoengineering termination shock.<ref name=":1">{{Cite journal |last1=Yuan |first1=Tianle |last2=Song |first2=Hua |last3=Oreopoulos |first3=Lazaros |last4=Wood |first4=Robert |last5=Bian |first5=Huisheng |last6=Breen |first6=Katherine |last7=Chin |first7=Mian |last8=Yu |first8=Hongbin |last9=Barahona |first9=Donifan |last10=Meyer |first10=Kerry |last11=Platnick |first11=Steven |date=2024-05-30 |title=Abrupt reduction in shipping emission as an inadvertent geoengineering termination shock produces substantial radiative warming |journal=Communications Earth & Environment |language=en |volume=5 |issue=1 |page=281 |doi=10.1038/s43247-024-01442-3 |issn=2662-4435 |pmc=11139642 |pmid=38826490|bibcode=2024ComEE...5..281Y }}</ref>

Aerosols in the 20&nbsp;μm range show a particularly long persistence time in air conditioned rooms due to their "jet rider" behaviour (move with air jets, gravitationally fall out in slowly moving air);<ref>{{Cite medRxiv |medrxiv=10.1101/2020.12.08.20233056v1 |first=Patrick |last=Hunziker |title=Minimizing exposure to respiratory droplets, 'jet riders' and aerosols in air-conditioned hospital rooms by a 'Shield-and-Sink' strategy |date=2020-12-16 |language=en}}</ref> as this aerosol size is most effectively adsorbed in the human nose,<ref>{{Cite journal |last1=Kesavanathan |first1=Jana |last2=Swift |first2=David L. |year=1998 |title=Human Nasal Passage Particle Deposition: The Effect of Particle Size, Flow Rate, and Anatomical Factors |journal=Aerosol Science and Technology |volume=28 |issue=5 |pages=457–463 |bibcode=1998AerST..28..457K |doi=10.1080/02786829808965537 |issn=0278-6826}}</ref> the primordial infection site in [[COVID-19]], such aerosols may contribute to the pandemic.<ref name="McNeill">{{cite journal |vauthors=McNeill VF |date=June 2022 |title=Airborne Transmission of SARS-CoV-2: Evidence and Implications for Engineering Controls |journal=Annual Review of Chemical and Biomolecular Engineering |volume=13 |issue=1 |pages=123–140 |doi=10.1146/annurev-chembioeng-092220-111631 |pmid=35300517 |s2cid=247520571}}</ref>

Aerosol particles with an effective diameter smaller than 10&nbsp;μm can enter the bronchi, while the ones with an effective diameter smaller than 2.5&nbsp;μm can enter as far as the gas exchange region in the lungs,<ref name="volcanic_emissions">
{{cite web |last1=Grainger |first1=Don |title=Volcanic Emissions |url=http://eodg.atm.ox.ac.uk/eodg/research_ve.html |access-date=8 July 2014 |website=Earth Observation Data Group, Department of Physics, University of Oxford |publisher=University of Oxford}}</ref> which can be hazardous to human health.

==Size distribution==
{{See also|Particulates#Size, shape, and solubility matter}}
[[File:Synthetic aerosol distribution in number area and volume space.png|thumb|upright=1.3|The same hypothetical log-normal (bi-modal) 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 shown at the top. Each distribution is normalized so that the total area is 1000.|alt=graph showing the size distribution of aerosols over different variables]]
For a monodisperse aerosol, a single number—the particle diameter—suffices to describe the size of the particles. However, more complicated [[particle-size distribution]]s describe the sizes of the particles in a polydisperse aerosol. This distribution defines the relative amounts of particles, sorted according to size.<ref>{{cite journal| last1 = Jillavenkatesa | first1 = A | last2 = Dapkunas | first2 = SJ |last3 = Lin-Sien |first3 = Lum| title = Particle Size Characterization | journal = NIST Special Publication | volume = 960-1 | date = 2001}}</ref> 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 size range into intervals and finds the number (or proportion) of particles in each interval. These data can be presented 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.{{sfn|Hinds|1999|pp=75-77}} If the width of the bins [[Limit (mathematics)|tends to zero]], the frequency function is:{{sfn|Hinds|1999|p=79}}

:<math> \mathrm{d}f = f(d_p) \,\mathrm{d}d_p</math>
where
:<math> d_p </math> is the diameter of the particles
:<math> \,\mathrm{d}f </math> is the fraction of particles having diameters between <math>d_p</math> and <math>d_p</math> + <math>\mathrm{d}d_p</math>
:<math>f(d_p)</math> 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:{{sfn|Hinds|1999|p=79}}
:<math> f_{ab}=\int_a^b f(d_p) \,\mathrm{d}d_p</math>

It can also be formulated in terms of the total number density ''N'':{{sfn|Hidy|1984|p=58}}
:<math> dN = N(d_p) \,\mathrm{d}d_p</math>

Assuming spherical aerosol particles, the aerosol surface area per unit volume (''S'') is given by the second [[Moment (mathematics)|moment]]:{{sfn|Hidy|1984|p=58}}
:<math> S= \pi/2 \int_0^\infty N(d_p)d_p^2 \,\mathrm{d}d_p</math>

And the third moment gives the total volume concentration (''V'') of the particles:{{sfn|Hidy|1984|p=58}}
:<math> V= \pi/6 \int_0^\infty N(d_p)d_p^3 \,\mathrm{d}d_p</math>

The particle size distribution can be approximated. The [[normal distribution]] usually does not suitably describe particle size distributions in aerosols because of the [[skewness]] associated with 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, which is not physically realistic. However, the normal distribution can be suitable for some aerosols, such as test aerosols, certain [[pollen]] grains and [[spore]]s.{{sfn|Hinds|1999|p=90}}

A more widely chosen [[log-normal distribution]] gives the number frequency as:{{sfn|Hinds|1999|p=90}}

:<math> \mathrm{d}f = \frac{1}{d_p \sigma\sqrt{2\pi}} e^{-\frac{(ln(d_p) - \bar{d_p})^2}{2 \sigma^2} }\mathrm{d}d_p</math>

where:

:<math> \sigma</math> is the [[standard deviation]] of the size distribution and
:<math> \bar{d_p}</math> 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.{{sfn|Hinds|1999|p= 91}}<ref>There is also a practical advantage of modelling the aerosols size distributions with a log-normal distribution, as the n-th moment of a log-normally distributed variable X has a simple analytical expression using the two parameters <math>\sigma</math> and <math>\mu</math> which simplifies the model.</ref>

Other distributions sometimes used to characterise particle size include: the [[Weibull distribution|Rosin-Rammler distribution]], applied to coarsely dispersed dusts and sprays; the Nukiyama–Tanasawa distribution, for sprays of extremely broad size ranges; the [[Power law#Power-law probability distributions|power function distribution]], occasionally applied to atmospheric aerosols; the [[exponential distribution]], applied to powdered materials; and for cloud droplets, the Khrgian–Mazin distribution.{{sfn|Hinds|1999|pp=104-5}}

== 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&nbsp;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:{{sfn|Hinds|1999|p=44–49}}
:<math>F_D = \frac {3 \pi \eta V d}{C_c}</math>
where
:<math>F_D</math> is the resisting force on a spherical particle
:<math>\eta</math> is the dynamic [[viscosity]] of the gas
:<math>V</math> is the particle velocity
:<math>C_c</math> 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:{{sfn|Hinds|1999|p=49}}
:<math>V_{TS} = \frac{\rho_p d^2 g C_c}{18 \eta}</math>
where
:<math>V_{TS}</math> 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:{{sfn|Hinds|1999|p=47}}

:<math>B = \frac{V}{F_D} = \frac {C_c}{3 \pi \eta d}</math>

A particle traveling at any reasonable initial velocity approaches its terminal velocity [[Exponential decay|exponentially]] with an ''e''-folding time equal to the relaxation time:{{sfn|Hinds|1999|p=115}}

:<math>V(t) = V_{f}-(V_{f}-V_{0})e^{-\frac{t}{\tau}}</math>

where:
:<math>V(t)</math> is the particle speed at time t
:<math>V_f</math> is the final particle speed
:<math>V_0</math> 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:{{sfn|Hinds|1999|p=51}}

:<math>\chi = \frac{F_D}{3 \pi \eta V d_e}</math>

where:
:<math>\chi</math> 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&nbsp;kg/m<sup>3</sup> and the same settling velocity as the irregular particle.{{sfn|Hinds|1999|p=53}}

Neglecting the slip correction, the particle settles at the terminal velocity proportional to the square of the [[aerodynamic]] diameter, ''d<sub>a</sub>'':{{sfn|Hinds|1999|p=53}}

:<math>V_{TS} = \frac{\rho_0 d_a^2 g}{18 \eta}</math>

where
:<math>\ \rho_0</math> = standard particle density (1000&nbsp;kg/m<sup>3</sup>).

This equation gives the aerodynamic diameter:{{sfn|Hinds|1999|p=54}}
:<math>d_a=d_e\left(\frac{\rho_p}{\rho_0 \chi}\right)^{\frac{1}{2}} </math>

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|date=August 2012}}

=== Dynamics ===
The previous discussion focused 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 charge]]s 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.{{sfn|Hidy|1984|p=60}}

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.{{sfn|Hidy|1984|p=60}}

: <math>\frac{\partial{n_i}}{\partial{t}} = -\nabla \cdot n_i \mathbf{q} +\nabla \cdot D_p\nabla_i n_i+ \left(\frac{\partial{n_i}}{\partial{t}}\right)_\mathrm{growth} + \left(\frac{\partial{n_i}}{\partial{t}}\right)_\mathrm{coag} -\nabla \cdot \mathbf{q}_F n_i</math>

Change in time = Convective transport + [[Brownian motion|brownian diffusion]] + gas-particle interactions + coagulation + migration by external forces

Where:
:<math>n_i</math> is number density of particles of size category <math>i</math>
:<math>\mathbf{q}</math> is the particle velocity
:<math>D_p</math> is the particle [[Einstein relation (kinetic theory)|Stokes-Einstein]] [[Mass diffusivity|diffusivity]]
:<math>\mathbf{q}_F</math> is the particle velocity associated with an external force

==== Coagulation ====
[[File:Aerosol 1.png|thumb|]]
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.{{sfn|Hinds|1999|p=260}} 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:

:<math>K_n=\frac{2\lambda}{d}</math>

where <math>\lambda</math> is the [[mean free path]] of the suspending gas and <math>d</math> is the diameter of the particle.<ref name="Baron&Willeke">{{cite book|last=Baron |first=P. A.|author2=Willeke, K.|name-list-style=amp|date=2001|section=Gas and Particle Motion|title=Aerosol Measurement: Principles, Techniques, and Applications}}</ref> For particles in the ''free molecular regime'', ''K<sub>n</sub>'' >> 1; particles small compared to the mean free path of the suspending gas.<ref name="DeCarlo2004">{{cite journal|doi=10.1080/027868290903907|last=DeCarlo |first=P.F.|date=2004|title=Particle Morphology and Density Characterization by Combined Mobility and Aerodynamic Diameter Measurements. Part 1: Theory|journal= Aerosol Science and Technology|volume=38|issue=12|pages=1185–1205|bibcode=2004AerST..38.1185D|doi-access=free}}</ref> 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:

:<math> I = \frac{\pi a^2}{k_b} \left( \frac{P_\infty}{T_\infty} - \frac{P_A}{T_A} \right) \cdot C_A \alpha </math>

where ''a'' is the particle radius, ''P''<sub>∞</sub> and ''P<sub>A</sub>'' are the pressures far from the droplet and at the surface of the droplet respectively, ''k<sub>b</sub>'' is the Boltzmann constant, ''T'' is the temperature, ''C<sub>A</sub>'' is mean thermal velocity and ''α'' is mass accommodation coefficient.{{citation needed|date=August 2012}} The derivation of this equation assumes constant pressure and constant diffusion coefficient.

Particles are in the ''continuum regime'' when K<sub>n</sub> << 1.<ref name="DeCarlo2004"/> 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.<ref name="DeCarlo2004"/> The molecular flux in this regime is:

:<math> I_{cont} \sim \frac{4 \pi a M_A D_{AB}}{RT} \left( P_{A \infty} - P_{AS}\right)</math>

where ''a'' is the radius of the particle ''A'', ''M<sub>A</sub>'' is the molecular mass of the particle ''A'', ''D<sub>AB</sub>'' 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<sub>A∞</sub>'' and ''P<sub>AS</sub>'' are the pressures at infinite and at the surface respectively.{{citation needed|date=August 2012}}

The ''transition regime'' contains all the particles in between the free molecular and continuum regimes or ''K<sub>n</sub>'' ≈ 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:

:<math> I = I_{cont} \cdot \frac{1 + K_n}{1 + 1.71 K_n + 1.33 {K_n}^2}</math>

where ''I''<sub>cont</sub> is the mass flux in the continuum regime.{{citation needed|date=August 2012}} This formula is called the Fuchs-Sutugin interpolation formula. These equations do not take into account the heat release effect.

==== Partitioning ====
[[Image:Cond n evap.svg|thumb|Condensation and evaporation|alt=graph showing the process of condensation and evaporation on a molecular level]]
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 [[vapor]]. Net condensation of the vapor requires supersaturation, a [[partial pressure]] greater than its [[vapor pressure]]. This can happen for three reasons:{{citation needed|date=August 2012}}
# Lowering the temperature of the system lowers the vapor pressure.
# Chemical reactions may increase the partial pressure of a gas or lower its vapor pressure.
# The addition of additional vapor to the system may lower the equilibrium vapor 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.{{sfn|Hinds|1999| p=288}} 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.{{sfn|Hinds|1999| p=288}}

====Activation====
Water coats particles in aerosols, making them ''activated'', usually in the context of forming a cloud droplet (such as natural cloud seeding by aerosols from trees in a forest).<ref>{{Cite journal|last1=Spracklen|first1=Dominick V|last2=Bonn|first2=Boris|last3=Carslaw|first3=Kenneth S|date=2008-12-28|title=Boreal forests, aerosols and the impacts on clouds and climate|url=https://royalsocietypublishing.org/doi/10.1098/rsta.2008.0201|journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|language=en|volume=366|issue=1885|pages=4613–4626|doi=10.1098/rsta.2008.0201|pmid=18826917|bibcode=2008RSPTA.366.4613S|s2cid=206156442|issn=1364-503X}}</ref> 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:

:<math> RH = \frac{p_s}{p_0} \times 100\% = S \times 100\%</math>

where <math>p_s</math> is the [[saturation vapor pressure]] above a particle at equilibrium (around a curved liquid droplet), ''p''<sub>0</sub> 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:

:<math> \ln{p_s \over p_0} = \frac{2 \sigma M}{RT \rho \cdot r_p} </math>

where ''r<sub>p</sub>'' 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 [[Equation solving|solutions]] to the general dynamic equation (GDE);{{sfn|Hidy|1984|p=62}} common methods used to solve the general dynamic equation include:{{sfn|Friedlander|2000}}
* Moment method<ref>{{Cite journal | doi = 10.1016/0009-2509(64)85047-8 | title = Some problems in particle technology | journal = Chemical Engineering Science | volume = 19 | issue = 8 | pages = 555–574 | year = 1964 | last1 = Hulburt | first1 = H.M. | last2 = Katz | first2 = S. }}</ref>
* Modal/sectional method,<ref>{{Cite journal | doi = 10.1016/0021-9797(90)90445-T | title = A discrete-sectional model for particulate production by gas-phase chemical reaction and aerosol coagulation in the free-molecular regime | journal = Journal of Colloid and Interface Science | volume = 139 | issue = 1 | pages = 63–86 | year = 1990 | last1 = Landgrebe | first1 = James D. | last2 = Pratsinis | first2 = Sotiris E. | bibcode = 1990JCIS..139...63L }}</ref> and
* Quadrature method of moments<ref>{{Cite journal | doi = 10.1080/02786829708965471 | title = Description of Aerosol Dynamics by the Quadrature Method of Moments | journal =  Aerosol Science and Technology| volume = 27 | issue = 2 | pages = 255–265 | year = 1997 | last1 = McGraw | first1 = Robert | bibcode = 1997AerST..27..255M | doi-access = free }}</ref><ref>{{Cite journal | doi = 10.1016/j.jaerosci.2004.07.009 | title = Solution of population balance equations using the direct quadrature method of moments | journal = [[Journal of Aerosol Science]] | volume = 36 | issue = 1 | pages = 43–73 | year = 2005 | last1 = Marchisio | first1 = Daniele L. | last2 = Fox | first2 = Rodney O. | bibcode = 2005JAerS..36...43M }}</ref>/Taylor-series expansion method of moments,<ref>{{Cite journal | doi = 10.1080/02786820802232972 | title = A New Moment Method for Solving the Coagulation Equation for Particles in Brownian Motion | journal = Aerosol Science and Technology | volume = 42 | issue = 9 | pages = 705–713 | year = 2008 | last1 = Yu | first1 = Mingzhou | last2 = Lin | first2 = Jianzhong | last3 = Chan | first3 = Tatleung | bibcode = 2008AerST..42..705Y | hdl = 10397/9612 | s2cid = 120582575 | hdl-access = free }}</ref><ref>{{Cite journal | doi = 10.1016/j.jaerosci.2009.03.001 | title = Taylor-expansion moment method for agglomerate coagulation due to Brownian motion in the entire size regime | journal = Journal of Aerosol Science | volume = 40 | issue = 6 | pages = 549–562 | year = 2009 | last1 = Yu | first1 = Mingzhou | last2 = Lin | first2 = Jianzhong | bibcode = 2009JAerS..40..549Y }}</ref> and
* Monte Carlo method.<ref>{{Cite journal | doi = 10.14356/kona.2005007 | title = Modelling of Particulate Processes | journal = KONA Powder and Particle Journal | volume = 23 | pages = 18–35 | year = 2005 | last1 = Kraft | first1 = Murkus | doi-access = free }}</ref>

== Detection ==
Aerosols can either be measured [[In-situ#Earth and atmospheric sciences|in-situ]] or with [[remote sensing]] techniques either ground-based on airborne-based.

=== ''In situ'' observations ===
Some available in situ measurement techniques include:
* [[Aerosol mass spectrometer]] (AMS)
* [[Differential mobility analyzer]] (DMA)
* [[Electrical aerosol spectrometer]] (EAS)
* [[Aerodynamic particle sizer]] (APS)
* [[Aerodynamic aerosol classifier]] (AAC)
* [[Wide range particle spectrometer]] (WPS)
* [[Micro-Orifice Uniform Deposit Impactor]](MOUDI)
* [[Condensation particle counter]] (CPC)
* [[Epiphaniometer]]
* [[Electrical low pressure impactor]] (ELPI)
* [[Particle mass analyser|Aerosol particle mass-analyser]] (APM)
* [[Particle mass analyser|Centrifugal Particle Mass Analyser]] (CPMA)

=== Remote sensing approach ===
Remote sensing approaches include:
* [[Sun photometer]]
* [[Lidar]]
* [[Imaging spectroscopy]]

=== Size selective sampling ===
Particles can deposit in the [[Human nose|nose]], [[Human mouth|mouth]], [[Human pharynx|pharynx]] and [[larynx]] (the head airways region), deeper within the respiratory tract (from the [[Vertebrate trachea|trachea]] to the [[terminal bronchioles]]), or in the [[Pulmonary alveolus|alveolar region]].{{sfn|Hinds|1999|p=233}} The location of deposition of aerosol particles within the respiratory system strongly determines the health effects of exposure to such aerosols.{{sfn|Hinds|1999|p=233}} This phenomenon led people to invent aerosol samplers that select a subset of the aerosol particles that reach certain parts of the respiratory system.{{sfn|Hinds|1999|p=249}}

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.{{sfn|Hinds|1999|p=244}} 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.{{sfn|Hinds|1999|p=246}} The thoracic fraction is the proportion of the particles in ambient aerosol that can reach the thorax or chest region.{{sfn|Hinds|1999|p=254}} The respirable fraction is the proportion of particles in the air that can reach the alveolar region.{{sfn|Hinds|1999|p=250}} 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 [[elutriator]]s, and large pore [[membrane filter]]s.{{sfn|Hinds|1999|p=252}}

Two alternative size-selective criteria, often used in atmospheric monitoring, are PM<sub>10</sub> and PM<sub>2.5</sub>. PM<sub>10</sub> is defined by [[International Organization for Standardization|ISO]] as ''particles which pass through a size-selective inlet with a 50% efficiency cut-off at 10&nbsp;μm aerodynamic diameter'' and PM<sub>2.5</sub> as ''particles which pass through a size-selective inlet with a 50% efficiency cut-off at 2.5&nbsp;μm aerodynamic diameter''. PM<sub>10</sub> corresponds to the "thoracic convention" as defined in ISO 7708:1995, Clause 6; PM<sub>2.5</sub> corresponds to the "high-risk respirable convention" as defined in ISO 7708:1995, 7.1.<ref>{{cite web|url=http://diamondenv.wordpress.com/2010/12/10/particulate-pollution-pm10-and-pm2-5/|title=Particulate pollution – PM10 and PM2.5|work=Recognition, Evaluation, Control. News and views from Diamond Environmental Limited|access-date=23 September 2012|date=2010-12-10}}</ref> The [[United States Environmental Protection Agency]] replaced the older standards for particulate matter based on Total Suspended Particulate with another standard based on PM<sub>10</sub> in 1987<ref>{{cite web|url=http://www.epa.gov/airtrends/aqtrnd95/pm10.html |title=Particulate Matter (PM-10) |access-date=23 September 2012 |archive-url=https://web.archive.org/web/20120901140447/http://www.epa.gov/airtrends/aqtrnd95/pm10.html |archive-date=1 September 2012 }}</ref> and then introduced standards for PM<sub>2.5</sub> (also known as fine particulate matter) in 1997.<ref>{{cite web|url=http://www.epa.gov/pmdesignations/basicinfo.htm|title=Basic Information|access-date=23 September 2012}}</ref>

== See also ==
* [[Aerogel]]
* [[Aeroplankton]]
* [[Aerosol transmission]]
* [[Bioaerosol]]
* [[Deposition (Aerosol physics)]]
* [[Global dimming]]
* [[Nebulizer]]
* [[Monoterpene]]
* [[Stratospheric aerosol injection]]

== References ==
{{Reflist}}

=== Sources ===
{{refbegin}}
* {{cite book |editor1-last = Colbeck |editor1-first = Ian |editor2-first = Mihalis |editor2-last = Lazaridis |title = Aerosol Science: Technology and Applications |publisher = John Wiley & Sons - Science |year = 2014 |isbn = 978-1-119-97792-6 }}
* {{cite book |last = Friedlander |first = S. K. |year = 2000 |title = Smoke, Dust and Haze: Fundamentals of Aerosol Behavior |edition = 2nd |publisher = Oxford University Press |location = New York |isbn = 0-19-512999-7 }}
* {{cite book |last = Hinds |first = William C. |title = Aerosol Technology |publisher = Wiley - Interscience |edition = 2nd |year = 1999 |isbn = 978-0-471-19410-1 }}
* {{cite book |last = Hidy |first = George M. |title = Aerosols, An Industrial and Environmental Science |publisher = Academic Press, Inc. |year = 1984 |isbn = 978-0-12-412336-6 }}
{{refend}}

==External links==
{{Commons category}}
* [http://www.iara.org/index.html International Aerosol Research Assembly] {{Webarchive|url=https://web.archive.org/web/20200121010501/http://www.iara.org/index.html |date=2020-01-21 }}
* [http://www.aaar.org American Association for Aerosol Research]
* [https://www.cdc.gov/niosh/nmam/chapters.html NIOSH Manual of Analytical Methods] (see chapters on aerosol sampling)

{{Aerosol terminology|state=expanded}}
{{pollution}}
{{Authority control}}

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