2 Aerosols system and Nucleation phenomenon
J.S. Laura
5.1 Introduction
The aerosols are an important part of the atmosphere. The aerosol scatter the radiation from the sun, so impact the Earth’s radiative budget and also act as condensation nuclei (CCN) for formation of cloud droplets. Aerosol particles are responsible for reducing visibility and impact the air quality. A major fraction of this important constituent of atmosphere is formed in the atmosphere through condensation of atmospheric vapours. There are several chemical compounds (nitric acid, organics, ammonia and water etc.) which can exist in the gaseous and aerosol phases in the atmosphere. When particles are formed the vapour is condensed into liquid or solid. The vapor molecules collide constantly with the liquid surface and become part of the liquid. At the same time there is a chance that molecules in the liquid escape from the liquid and become part of the vapor. At equilibrium these two processes balance.
So the concentration and particle properties keep changing with time. These changes can be the result of external forces, such as the loss of larger particles by gravitational settling, or they may be the result of physical and chemical processes that serve to change the size or composition of the particles. These physical and chemical processes involve mass transfer to from a particle. This transfer may be the result of molecular transfer between the particle and the surrounding gas, for example, condensation, evaporation, nucleation, adsorption, absorption, and chemical reaction, or it may result from interparticle mass transfer, such as by coagulation. Processes that cause physical or chemical changes in the particulate phase influence the particle size distribution of nearly all aerosols. These processes contribute in an essential way to the earth’s hydrological cycle. They are involved in the formation of photochemical smog and are the key to shaping the atmospheric aerosol size distribution. Condensation, thermal coagulation, and adsorption are related processes that rely on the diffusion of molecules or particles to a particle surface. Evaporation is the opposite of condensation and is governed by the same laws. Reactions may be non-growth processes that change the composition or density of an aerosol particle with little or no change in particle size. This chapter discusses these processes.
To understand the aerosol system it is necessary to understand some terms and processes, and these are given below.
Partial pressure (p)
In a mixture of gases, each gas has its own partial pressure and it is equal to the pressure the vapour of a substance or gas would exert if it were the only component present at the same temperature. It describes the gas phase concentration of substance in a system.
Vapor pressure (ps)
It’s also known as equilibrium vapor pressure or saturation vapor pressure. It is the pressure exerted by vapor in thermodynamic equilibrium with its condensed phases at a given temperature. It represents the minimum partial pressure of vapour of a liquid required to prevent the evaporation at the gas-liquid interface. So at saturation vapor pressure no net evaporation or condensation takes place.
Saturation ratio (SR)
It is the ratio of the partial pressure of vapor to the saturation vapor pressure.
Saturation ratio is very important for aerosol condensation and evaporation processes. When the saturation ratio is less than one (SR< 1), then situation is subsaturated or unsaturated and evaporation takes place. But when the saturation ratio is greater than one (SR> 1), then situation is supersaturated and condensation takes place. And when the saturation ratio is equal to one (SR= 1), then situation is saturated and process is in equilibrium.
SR < 1(sub saturated): evaporation
SR > 1(supersaturated): condensation
SR = 1(saturated): no net transport between the phases
The Kelvin Effect
The liquid aerosol particles have sharply curved surface so slightly greater partial pressure is required to maintain the mass equilibrium around aerosol as compared to the flat liquid surface at a given temperature. This increase in the partial pressure of vapor required for mass equilibrium, increases with decreasing particle size. This effect is called the Kelvin effect. The saturation ratio for such droplet having diameter dp is given by the Kelvin equation:
Where,
SR = saturation ratio
y= surface tension of liquid
M = molecular weight
p = density of the liquid
R = gas constant
T = temperature
dp = diameter of droplet
Thus for smaller particle higher saturation ratio is required to prevent evaporation. For example, for 0.01 µm water droplets a saturation ratio of 1.24 is required (as compared to 1 for flat water surface) to prevent evaporation.
5.2 Nucleation
Nucleation is the process in which a small number of ions, atoms or molecules are arranged in a characteristic pattern to form a site upon which the additional particles are deposited as the crystal grows. The nucleation is of two types:
5.2.1 Homogenous nucleation
The formation of the droplet from vapours is a complex process. Homogenous nucleation is the process of formation of droplets in the absence of any condensation nuclei. It takes place itself so it is also called self nucleation. Homogenous nucleation needs large saturation ratios (in the range of 2 to 10), which is normally created in special laboratory or chemical process situations. Pure water vapour at 293 °K (200°C) and at a saturation ratio of 3.5 or greater spontaneously forms droplets by homogeneous nucleation. This corresponds to a Kelvin diameter of 0.0017 µm and suggests that molecular clusters of about 90 molecules are necessary for this process.
Figure 1: Homogenous nucleation
5.2.2 Heterogeneous nucleation
The other mechanism of nucleation is condensation or heterogeneous nucleation. This is common process and occurs on the existing submicrometer particles, called condensation nuclei. In the atmosphere there are thousands of these condensation nuclei per cubic centimetre of air which serve as sites for condensation. These nuclei could be insoluble or soluble.
5.2.2.1 Nucleation with insoluble nuclei
These nuclei serve as the passive sites on which condensation occurs. Under supersaturated conditions the vapour molecules get adsorbed on the wettable surface of solid (insoluble) nucleus. Now if the nucleus has a diameter greater than the Kelvin diameter for a given condition of supersaturation, the vapor starts condensing on its surface. Once condensation starts, droplets start growing and rate of growth depends on
-saturation ratio
-particle size and
-rate of arrival of vapor molecules at the droplet surface
In the beginning the droplet size is less than the mean free path of the surrounding gas (dp < λ), so the kinetic theory of gases governs the rate of arrival of vapor molecules at the droplet surface. Growth rate (cm/s) is given by equation:
Where,
c = condensation coefficient (the fraction of arriving molecules that stick)
p∞ = partial pressure of vapor in the neighborhood of the droplet, but away from the droplet surface (dyne/cm2)
pd = partial pressure of vapor at the droplet surface (dyne/cm2)
M = molecular weight (g/mol)
p = density of the liquid (g/cm3)
R = gas constant (8.31 X 107 dyne.cm/K.mol)
T = temperature (°K)
When particle has grown in size more than the mean free path (dp > λ), then the rate of molecular diffusion governs the rate of arrival of vapor molecules to the droplet surface and growth rate is given by equation:
where
This factor can be omitted if the growing or evaporating droplet is > 2 µm and doing so offers a little error.
During rapid condensation (SR > 1.05) the temperature of the droplet Td will be greater than the surrounding air due to the release of heat of vaporization. The droplet temperature due to heating during condensation or cooling during evaporation can be given by equation:
5.2.2.2 Nucleation with soluble nuclei
This process is more complex and important. Our atmosphere contains a large number of droplets containing different soluble material. When water evaporates from these, solid residue left behind. For example the sodium chloride nuclei formed from sea spray. These soluble nuclei have a strong affinity for water which helps in the initial formation and growth of droplets even at lower saturation ratios than that needed for insoluble nuclei. So generally in presence of dissolved salt growth rate increases while evaporation rate decreases in comparison with pure liquid droplets. When a droplet containing dissolved salt grows or evaporates, two opposite effects work on the droplet. For instance, as a droplet evaporates its salt concentration increases, because only water evaporates. So this increases the water holding affinity of the dissolved salt in the droplet. The second effect is the Kelvin effect, i.e. with decrease in droplet size, an increase in the equilibrium vapor pressure (so higher saturation ratio) will be required for the droplet. The relationship between saturation ratio and particles size for droplets containing dissolved salts can be given by Kohler curves, shown below in figure 2.
Figure 2: Saturation ratio versus droplet size for pure water and droplets containing the indicated mass of sodium chloride at 293 K (20 °C).
Figure shows three concentrations of dissolved salt (NaCl) and for droplet of higher concentration of dissolved salt lower saturation ratio is enough for its growth. The region below and the left of the peak for a given curve, represents equilibrium region, where droplet will remain at a given size until the saturation conditions change. Thus, there are a large number of particles in the atmosphere that will experience an increase in their size with an increase in relative humidity and a decrease with a decrease in relative humidity. The line for pure water does not have this type of equilibrium region. It represents only a demarcation between the growth (above) and evaporation (below) regions. As droplets continue to grow the concentration of dissolved salts decreases, eventually reaching the point where the droplets behave the same as pure water and their curves merge with that for pure water.
5.3 Coagulation
The aerosol growth also occurs through the collision of aerosol particles. This collision can be of two types and so is the coagulation i.e. thermal coagulation and kinematic coagulation.
5.3.1 Thermal coagulation
The process where the collisions between the particles occur as a result of Brownian motion is called thermal coagulation. Thermal coagulation seems similar to the condensation, but it differs in many aspects. In thermal coagulation no supersaturation is required, there is no process like evaporation and on particle’s surface other particle diffuses rather than molecule. This results in increase in average particle size and decrease in aerosol number concentration. But volume and mass concentration remain same if there are no addition or removal mechanisms.
Simple Monodisperse Coagulation: Aerosol particles exhibit Brownian motion and diffuse like gas molecules, but their diffusion occurs at a much slower pace; consequently, the diffusion coefficients for aerosol particles are about a million times smaller than those for gas molecules. The derivation developed by Smoluchowski gives the rate of change (decrease) in aerosol number concentration as
Where
N= particle number concentration (particles/m3)
K= coagulation coefficient (m3/s)
For particles larger than the gas mean free path (For dp > λ), K is given by
Where
D= particle diffusion coefficient m2/s,
n= gas viscosity in Pa . s,
k= Boltzmann’s constant, 1.38 X10-23 J/K
Cc= slip correction factor
In the usual situation, the extent of particle size increase is sufficiently limited that the coagulation coefficient can be considered a constant, and the rate of coagulation is proportional only to number concentration squared. Thus, coagulation is a rapid process at high number concentration and a slow one at low concentrations. The change in number concentration over a period of time t is given by
Where
N(t)= number concentration at time t,
N0= initial number concentration
As number concentration decreases, particle size increases, but, for a closed system with no losses, total particle mass will remain constant. If number concentration decreases to one half of its original value, then the same mass (and volume) will be contained in half as many particles, so each particle will have twice its original mass (and volume). For liquid particles, particle size is proportional to the cube root of particle volume and, consequently, it is also proportional to the inverse cube root of number concentration.
Thus an eight-fold reduction in particle number concentration results in a doubling of particle size. Combining above two equations we can give the change in particle size due to coagulation over a period of time t as
Source: Adapted from Hinds (1999)
Table 1 gives the time required for various initial concentrations to reach one half their number concentrations and the time for particle size to double. It is apparent from Table 1 that whether or not coagulation can be neglected depends on the concentration and time scale under consideration. Thus, over a period of a few minutes, coagulation is only important if particle number concentration exceeds 1012/m3.
Polydisperse Coagulation: In the real world, we usually have a polydisperse aerosol, and the situation is more complicated. Because the coagulation process is governed by the rate of diffusion of particles to the surface of each particle, the process is enhanced when small particles with their high diffusion coefficients diffuse to a large particle with its large surface. A ten-fold difference in particle size produces a three-fold increase in coagulation rate. Now since in polydispersed coagulation the size of coagulating particles is different, so there will be a different value of K for them and has to be calculated separately. So average coagulation coefficient (K̅) is be used in place of K to predict the change in number concentration over a period of time.
5.3.2 Kinematic Coagulation
In this type of coagulation the external forces creates the relative motion between the particles rather than the Brownian motion. In this the rate of coagulation increases with the particle number concentration. Because particles of different sizes settle at different rates, there is a relative motion between settling particles of different sizes. When particles travel at different velocities, the faster particles eventually overtake the slower ones, and particle contact occurs by interception if particles are big enough. This coagulation for particles moving in a flow velocity gradient is known as Gradient coagulation.
In turbulent flow, particles follow a complex path having strong velocity gradients. Relative motion between particles arises from these gradients and from inertial projection of the particles. The resulting coagulation is called turbulent coagulation. This mechanism is only important for particles larger than about 1 μm, and depends on the intensity the turbulence.
In acoustic coagulation, the relative motion between particles is created by intense sound waves. The smaller particles are more affected and oscillate with the sound waves. The relative motion that results leads to collisions and the process is called acoustic coagulation. Generally, sound pressure levels exceeding 120 dB are required to produce significant coagulation.
5.4 Types of Interactions
Being very small in size, the aerosol particles have very high surface area to mass ratio. Their high specific surface area facilitates them to participate actively in many kinds of interaction between gas molecules and liquid or solid particles. These interactions are of three kinds-
-reactions between compounds within a particle
-reactions between particles of different chemical composition, and
-reactions between a particle and one or more chemical species in the surrounding gas phase
Chemical kinetics governs the first case reactions. While, the second case is initially controlled by the rate of arrival of other particles (as described by the coagulation) and then reactions proceed by chemical kinetics. The third case may be controlled by the rate of arrival of the appropriate gas molecules at the particle surface. These interactions involves following processes.
Reaction
The chemical reaction between the suspending gas and a particle may involve diffusion of specific gas molecules to the surface of the particle, transfer across the interface or reaction at the interface and diffusion into the solid or liquid particle. For solid particles, diffusion into the interior will be relatively slow even though the distances involved are small. Diffusion into the interior of liquid particles will be more rapid and may be augmented by internal circulation. If the reaction is controlled by the rate of arrival of gas molecules at the particle surface, then the maximum rate of reaction is given by
Where, RR is the rate of reaction in molecules per seconds. This situation is called a diffusion controlled reaction. The process can continue until all molecules of the particle have reacted.
Absorption
The process whereby gas molecules dissolve in a liquid droplet is called absorption. In this process the transfer at the interface is usually not controlling, but diffusion in either the gas phase or liquid phase may be. The process can continue until the limit of solubility of the gas in the liquid is reached. This limit may change with temperature or the presence of other dissolved components.
Adsorption
Adsorption is the transfer of gas molecules from the surrounding gas to a solid surface. It is of two types- physical adsorption and chemical adsorption.
In physical adsorption, gas molecules are held by van der Waals’ forces to particle’s surface. It occurs for all gases when the ambient temperature is below their critical temperature. It is a rapid and readily reversible process. Because the adsorption process is rapid, the diffusion of gas molecules to the particle surface is usually the rate-limiting step. It is usually not significant if the saturation ratio is below 0.05, but can lead to an adsorbed layer several molecules thick when the saturation ratio is 0.8 or greater. For a particle in adsorption equilibrium, a reduction in the partial pressure of the vapor will lead to a transfer of adsorbed vapor molecules from the particle’s surface to the gas.
Chemical adsorption is similar, except that chemical bonds are formed to hold the gas molecules on the particle’s surface. It can occur above or below the critical temperature of the gas. In this only a monolayer can form and, it is not easily reversible because the chemical bonds are much stronger than van der Waals’ forces. Either the rate of gas-phase diffusion or the rate of reaction can control the rate of this process. The rate of transfer slows as a complete monolayer is approached. A physi-sorption layer may also form on top of a chemisorption layer.
Glossary
Partial pressure (p): In a mixture of gases, each gas has its own partial pressure and it is equal to the pressure the vapour of a substance or gas would exert if it were the only component present at the same temperature. It describes the gas phase concentration of substance in a system.
Vapor pressure (ps) or equilibrium vapour pressure or saturation vapor pressure: It is the pressure exerted by vapour in thermodynamic equilibrium with its condensed phases at a given temperature.
Saturation ratio (SR): It is the ratio of the partial pressure of vapor to the saturation vapor pressure.
The Kelvin Effect: The liquid aerosol particles have sharply curved surface so slightly greater partial pressure is required to maintain the mass equilibrium around aerosol as compared to the flat liquid surface at a given temperature. This increase in the partial pressure of vapor required for mass equilibrium, increases with decreasing particle size. This effect is called the Kelvin effect.
Nucleation: Nucleation is the process in which a small number of ions, atoms or molecules are arranged in a characteristic pattern to form a site upon which the additional particles are deposited as the crystal grows.
Homogenous nucleation: It is the process of formation of droplets in the absence of any condensation nuclei.
Heterogeneous nucleation: This is common process and occurs on the existing sub-micrometer particles, called condensation nuclei.
Thermal coagulation: The process where the collisions between the particles occur as a result of Brownian motion is called thermal coagulation.
Suggested links-
- Aerosols. http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap8.html
- Atmospheric nucleation: from molecular to global scale (ATMNUCLE). https://www.atm.helsinki.fi/m/atmnucle/images/project/ATMNUCLE_SciencePlan.pdf
- Correlation of aerosol nucleation rate with sulfuric acid and ammonia in Kent Ohio: An atmospheric observation. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2010JD013942
- Heterogeneous nucleation of a common atmospheric aerosol: Ammonium sulfate. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/1998GL900199