An aerosol is a suspension of fine solid particles or liquid droplets in air or another gas. [1] Aerosols can be generated from natural or human causes. The term aerosol commonly refers to the mixture of particulates in air, and not to the particulate matter alone. [2] Examples of natural aerosols are fog, mist or dust. Examples of human caused aerosols include particulate air pollutants, mist from the discharge at hydroelectric dams, irrigation mist, perfume from atomizers, smoke, dust, sprayed pesticides, and medical treatments for respiratory illnesses. [3]
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 aerosols, primarily from burning oil and coal, affect the behavior of clouds. [4] When aerosols absorb pollutants, it facilitates the deposition of pollutants to the surface of the earth as well as to bodies of water. [5] This has the potential to be damaging to both the environment and human health.
Ship tracks are clouds that form around the exhaust released by ships into the still ocean air. Water molecules collect around the tiny particles (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. [6]
The liquid or solid particles in an aerosol have diameters typically less than 1 μm. Larger particles with a significant settling speed make the mixture a suspension, but the distinction is not clear. In everyday language, aerosol often refers to a dispensing system that delivers a consumer product from a spray can.
Diseases can spread by means of small droplets in the breath, [7] sometimes called bioaerosols. [8]
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. [1] Meteorologists and climatologists often refer to them as particle matter, while the classification in sizes ranges like PM2.5 or PM10, [9] [10] is useful in the field of atmospheric pollution as these size range play a role in ascertain the harmful effects in human health. [11] 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 dispersed medium. [12] Primary aerosols contain particles introduced directly into the gas; secondary aerosols form through gas-to-particle conversion. [13]
Key aerosol groups include sulfates, organic carbon, black carbon, nitrates, mineral dust, and sea salt, they usually clump together to form a complex mixture. [10] Various types of aerosol, classified according to physical form and how they were generated, include dust, fume, mist, smoke and fog. [14]
There are several measures of aerosol concentration. Environmental science and environmental health often use the mass concentration (M), defined as the mass of particulate matter per unit volume, in units such as μg/m3. Also commonly used is the number concentration (N), the number of particles per unit volume, in units such as number per m3 or number per cm3. [15]
Particle size has a major influence on particle 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. [13] 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. [16] The equivalent volume diameter (de) is defined as the diameter of a sphere of the same volume as that of the irregular particle. [17] Also commonly used is the aerodynamic diameter, da.
People generate aerosols for various purposes, including:
Some devices for generating aerosols are: [3]
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 aerosols, primarily from burning oil and coal, affect the behavior of clouds. [4]
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. [22] The 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.
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 adverse effects on the environment and human life. [24]
When aerosols absorb pollutants, it facilitates the deposition of pollutants to the surface of the earth as well as to bodies of water. [5] 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.
Ship tracks are clouds that form around the exhaust released by ships into the still ocean air. Water molecules collect around the tiny particles (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. [29]
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. [6]
Aerosols in the 20 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); [30] as this aerosol size is most effectively adsorbed in the human nose, [31] the primordial infection site in COVID-19, such aerosols may contribute to the pandemic. [32]
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, [33] which can be hazardous to human health.
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. [34] 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. [35] If the width of the bins tends to zero, the frequency function is: [36]
where
Therefore, the area under the frequency curve between two sizes a and b represents the total fraction of the particles in that size range: [36]
It can also be formulated in terms of the total number density N: [37]
Assuming spherical aerosol particles, the aerosol surface area per unit volume (S) is given by the second moment: [37]
And the third moment gives the total volume concentration (V) of the particles: [37]
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 spores. [38]
A more widely chosen log-normal distribution gives the number frequency as: [38]
where:
The log-normal distribution has no negative values, can cover a wide range of values, and fits many observed size distributions reasonably well. [39] [40]
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. [41]
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: [42]
where
This allows us to calculate the terminal velocity of a particle undergoing gravitational settling in still air. Neglecting buoyancy effects, we find: [43]
where
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: [44]
A particle traveling at any reasonable initial velocity approaches its terminal velocity exponentially with an e-folding time equal to the relaxation time: [45]
where:
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: [17]
where:
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. [46]
Neglecting the slip correction, the particle settles at the terminal velocity proportional to the square of the aerodynamic diameter, da: [46]
where
This equation gives the aerodynamic diameter: [47]
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 ]
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 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. [48]
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. [48]
Change in time = Convective transport + brownian diffusion + gas-particle interactions + coagulation + migration by external forces
Where:
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. [49] On occasion, particles may shatter apart into numerous smaller particles; however, this process usually occurs primarily in particles too large for consideration as aerosols.
The Knudsen number of the particle define three different dynamical regimes that govern the behaviour of an aerosol:
where is the mean free path of the suspending gas and is the diameter of the particle. [50] For particles in the free molecular regime, Kn >> 1; particles small compared to the mean free path of the suspending gas. [51] 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:
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. [51] 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. [51] The molecular flux in this regime is:
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:
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.
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 ]
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. [52] 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. [52]
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). [53] 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:
where 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:
where rp droplet radius, σ surface tension of droplet, ρ density of liquid, M molar mass, T temperature, and R molar gas constant.
There are no general solutions to the general dynamic equation (GDE); [54] common methods used to solve the general dynamic equation include: [55]
Aerosols can either be measured in-situ or with remote sensing techniques either ground-based on airborne-based.
Some available in situ measurement techniques include:
Remote sensing approaches include:
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. [63] The location of deposition of aerosol particles within the respiratory system strongly determines the health effects of exposure to such aerosols. [63] This phenomenon led people to invent aerosol samplers that select a subset of the aerosol particles that reach certain parts of the respiratory system. [64]
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. [65] 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. [66] The thoracic fraction is the proportion of the particles in ambient aerosol that can reach the thorax or chest region. [67] The respirable fraction is the proportion of particles in the air that can reach the alveolar region. [68] 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. [69]
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. [70] 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 [71] and then introduced standards for PM2.5 (also known as fine particulate matter) in 1997. [72]
In physics, the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann.
The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. It treats a gas as composed of numerous particles, too small to see with a microscope, which are constantly in random motion. Their collisions with each other and with the walls of their container are used to explain physical properties of the gas—for example, the relationship between its temperature, pressure, and volume. The particles are now known to be the atoms or molecules of the gas.
Cyclonic separation is a method of removing particulates from an air, gas or liquid stream, without the use of filters, through vortex separation. When removing particulate matter from liquid, a hydrocyclone is used; while from gas, a gas cyclone is used. Rotational effects and gravity are used to separate mixtures of solids and fluids. The method can also be used to separate fine droplets of liquid from a gaseous stream.
The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up that fluid. In the modern literature the term Boltzmann equation is often used in a more general sense, referring to any kinetic equation that describes the change of a macroscopic quantity in a thermodynamic system, such as energy, charge or particle number.
In plasma physics, the Vlasov equation is a differential equation describing time evolution of the distribution function of collisionless plasma consisting of charged particles with long-range interaction, such as the Coulomb interaction. The equation was first suggested for the description of plasma by Anatoly Vlasov in 1938 and later discussed by him in detail in a monograph. The Vlasov equation, combined with Landau kinetic equation describe collisional plasma.
The Weber number (We) is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It is named after Moritz Weber (1871–1951). It can be thought of as a measure of the relative importance of the fluid's inertia compared to its surface tension. The quantity is useful in analyzing thin film flows and the formation of droplets and bubbles.
In physics, the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is
In statistical physics, the Smoluchowski coagulation equation is a population balance equation introduced by Marian Smoluchowski in a seminal 1916 publication, describing the time evolution of the number density of particles as they coagulate to size x at time t.
In the physics of aerosols, deposition is the process by which aerosol particles collect or deposit themselves on solid surfaces, decreasing the concentration of the particles in the air. It can be divided into two sub-processes: dry and wet deposition. The rate of deposition, or the deposition velocity, is slowest for particles of an intermediate size. Mechanisms for deposition are most effective for either very small or very large particles. Very large particles will settle out quickly through sedimentation (settling) or impaction processes, while Brownian diffusion has the greatest influence on small particles. This is because very small particles coagulate in few hours until they achieve a diameter of 0.5 micrometres. At this size they no longer coagulate. This has a great influence in the amount of PM-2.5 present in the air.
The Stokes number (Stk), named after George Gabriel Stokes, is a dimensionless number characterising the behavior of particles suspended in a fluid flow. The Stokes number is defined as the ratio of the characteristic time of a particle to a characteristic time of the flow or of an obstacle, or
In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve some form of multiphase flow. It is also prevalent in many natural phenomena.
The Kelvin equation describes the change in vapour pressure due to a curved liquid–vapor interface, such as the surface of a droplet. The vapor pressure at a convex curved surface is higher than that at a flat surface. The Kelvin equation is dependent upon thermodynamic principles and does not allude to special properties of materials. It is also used for determination of pore size distribution of a porous medium using adsorption porosimetry. The equation is named in honor of William Thomson, also known as Lord Kelvin.
The Twomey effect describes how additional cloud condensation nuclei (CCN), possibly from anthropogenic pollution, may increase the amount of solar radiation reflected by clouds. This is an indirect effect by such particles, as distinguished from direct effects (forcing) due to enhanced scattering or absorbing radiation by such particles not in clouds.
Sediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and the movement of the fluid in which the sediment is entrained. Sediment transport occurs in natural systems where the particles are clastic rocks, mud, or clay; the fluid is air, water, or ice; and the force of gravity acts to move the particles along the sloping surface on which they are resting. Sediment transport due to fluid motion occurs in rivers, oceans, lakes, seas, and other bodies of water due to currents and tides. Transport is also caused by glaciers as they flow, and on terrestrial surfaces under the influence of wind. Sediment transport due only to gravity can occur on sloping surfaces in general, including hillslopes, scarps, cliffs, and the continental shelf—continental slope boundary.
In granulometry, the particle-size distribution (PSD) of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amount, typically by mass, of particles present according to size. Significant energy is usually required to disintegrate soil, etc. particles into the PSD that is then called a grain size distribution.
The vapor–liquid–solid method (VLS) is a mechanism for the growth of one-dimensional structures, such as nanowires, from chemical vapor deposition. The growth of a crystal through direct adsorption of a gas phase on to a solid surface is generally very slow. The VLS mechanism circumvents this by introducing a catalytic liquid alloy phase which can rapidly adsorb a vapor to supersaturation levels, and from which crystal growth can subsequently occur from nucleated seeds at the liquid–solid interface. The physical characteristics of nanowires grown in this manner depend, in a controllable way, upon the size and physical properties of the liquid alloy.
In fluid dynamics, the Reynolds number is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation.
The vaporizing droplet problem is a challenging issue in fluid dynamics. It is part of many engineering situations involving the transport and computation of sprays: fuel injection, spray painting, aerosol spray, flashing releases… In most of these engineering situations there is a relative motion between the droplet and the surrounding gas. The gas flow over the droplet has many features of the gas flow over a rigid sphere: pressure gradient, viscous boundary layer, wake. In addition to these common flow features one can also mention the internal liquid circulation phenomenon driven by surface-shear forces and the boundary layer blowing effect.
Quadrature-based moment methods (QBMM) are a class of computational fluid dynamics (CFD) methods for solving Kinetic theory and is optimal for simulating phases such as rarefied gases or dispersed phases of a multiphase flow. The smallest "particle" entities which are tracked may be molecules of a single phase or granular "particles" such as aerosols, droplets, bubbles, precipitates, powders, dust, soot, etc. Moments of the Boltzmann equation are solved to predict the phase behavior as a continuous (Eulerian) medium, and is applicable for arbitrary Knudsen number and arbitrary Stokes number . Source terms for collision models such as Bhatnagar-Gross-Krook (BGK) and models for evaporation, coalescence, breakage, and aggregation are also available. By retaining a quadrature approximation of a probability density function (PDF), a set of abscissas and weights retain the physical solution and allow for the construction of moments that generate a set of partial differential equations (PDE's). QBMM has shown promising preliminary results for modeling granular gases or dispersed phases within carrier fluids and offers an alternative to Lagrangian methods such as Discrete Particle Simulation (DPS). The Lattice Boltzmann Method (LBM) shares some strong similarities in concept, but it relies on fixed abscissas whereas quadrature-based methods are more adaptive. Additionally, the Navier–Stokes equations(N-S) can be derived from the moment method approach.
The raindrop size distribution (DSD), or granulometry of rain, is the distribution of the number of raindrops according to their diameter (D). Three processes account for the formation of drops: water vapor condensation, accumulation of small drops on large drops and collisions between sizes. According to the time spent in the cloud, the vertical movement in it and the ambient temperature, drops have a very varied history and a distribution of diameters from a few micrometers to a few millimeters.