1 Atmospheric aerosol: Size distribution, Lognormal distribution, Surface area, Volume and mass distribution, Dynamics

J.S. Laura

4.1 Introduction

Aerosol is defined as a suspension of solid or liquid particles in a gas or air. They include a wide range of phenomena such as dust, fume, smoke, mist, fog, haze, clouds, and smog. Like the smoke from cigarettes, fumes from chimneys, dust raised by the wind and so on, are all aerosols. Aerosols usually remain suspended in air for at least a few seconds and in some cases a year or more. Particle size of aerosol ranges from about 0.002 µm to more than 100 µm. They are two-phase systems, consisting of the particles and the gas in which they are suspended. The word aerosol was coined in 1920 as an analog to the term hydrosol, which is a stable liquid suspension of solid particles. Aerosols are also referred to as suspended particulate matter, aero colloidal and disperse systems, although the word aerosol is popularly used to refer to pressurized spray-can products, it is the universally accepted scientific term for particulate suspensions in a gaseous medium.

Atmospheric aerosol particles originate from a wide variety of natural and anthropogenic sources. Aerosols are divided into two classes, namely primary aerosols and secondary aerosols, according to the mechanisms of their formation.

Primary aerosol: These particles are emitted directly into the atmosphere as liquid or solid form and come from combustion or fragmentation processes, for example- sea-salt, mineral aerosols (or dust), volcanic dust, smoke and soot, some organics, biological materials (plant fragments, microorganisms, pollen, etc.).

Secondary aerosol: The particles that are formed in the atmosphere by gas-to-particles conversion processes are secondary aerosols. The new particles are formed by nucleation and condensation of gaseous precursors for example- sulphates, nitrates, and some organics.

The aerosols are regularly form and introduced in the earth’s atmosphere, undergo various physical and chemical interactions and transformations (such as coagulation, restructuring, gas uptake and chemical reaction etc.), and play a key role in a number of global processes such as-

They serve as condensation nuclei and help in formation of clouds.
They affect the abundance and distribution of atmospheric trace gases by heterogeneous chemical reactions and other multiphase processes.
They can scatter, absorb and emit electromagnetic radiation.
They serve as media upon which chemical reactions can occur.
Airborne particles play an important role in the spreading of biological organisms, reproductive materials, and pathogens (pollen, bacteria, spores, viruses, etc.), and they can cause or enhance respiratory, cardiovascular, infectious, and allergic diseases.

A significant fraction of the atmospheric aerosols is anthropogenic in origin. Aerosols are responsible for climate change, visibility reduction, acid deposition and affect air quality and human health. Since the aerosols are highly important in the atmospheric phenomenon and affects the mankind in many ways, the study of their size and distribution become very useful to tackle the problems related with them.

4.2 Size distribution

Primary and secondary aerosols are characterized by the size, shape, chemical content, amount and distribution in space and time, and how long they survive in the atmosphere. One of the most of important characteristics of polydisperse aerosol is its particle size distribution, which represents the distribution of a specific aerosol property over the particle size range of interest. To construct a particle size distribution, the particle size is “weighted” by either number, mass, surface area, volume, or other aerosol property of interest. Normally shape of particles is assumed to be spherical for simplification of the mathematical problems related to the behaviour of aerosol particles.

Figure1: Photomicrograph made with a Scanning Electron Microscope (SEM): Fly ash particles

Many aerosols comprise irregularly shaped particles. The non-sphericity of particles creates many problems. There exist also agglomerates of particles. If particle is non-spherical, its equivalent radius is introduced. There are several ways to define particle equivalent radius (for instance, aerodynamic equivalent radius, which is radius of a sphere that experience the same resistance to motion as the nonspherical particle). The diameters of atmospheric aerosol particles span over four orders of magnitude, from a few nanometers to around 100 μm. Particle number concentrations may be as high as 107 to 108 cm-3. Thus, a complete description of the aerosol size distribution may be a challenging problem. Therefore, several mathematical approaches are used to characterize the aerosol size distribution.

First let’s try to understand why normal distribution cannot be used to characterize the particle size distribution. The normal distribution has a fundamental defect related to its use in particle sizing analysis. This is because if the random variable (particle size) is normally distributed, it implies that the values of particle size are at equal distances from the central tendency.

Figure 2: Normal distribution curve

Now suppose the mean particle size or central tendency of the distribution is 20 µm. Then it would be equally probable to find either a 15 or 25 µm particle. One might also find a particle the size of 50 µm in the distribution. And for a normal distribution, it would be equally likely to find a particle the size of minus 10 µm (not physically possible).

Figure 3: A log-normal distribution with original scale (a) and with logarithmic scale (b). Areas under the curve, from the median to both sides, correspond to one and two standard deviation ranges of the normal distribution

In practical application, the size distribution of a typical dust is typically skewed to the right, i.e., skewed to the larger particle size. The central tendency of a skewed frequency distribution is more adequately represented by the median rather than by the mean (Fig.3). Statistically, the particle size distribution can be characterized by three properties: mode, median, and mean. The mode is the value that occurs most frequently. It is a value seldom used for describing particle size distribution. The average or arithmetic mean diameter is affected by all values actually observed and thus is influenced greatly by extreme values. The median particle size is the size that divides the frequency distribution into two equal areas.

When the skewed particle size distribution shown in Fig.3 (a) is replotted using the logarithm of the particle size, the skewed curve is transformed into a symmetrical bell shaped curve (Fig. 3b). This transformation is of great significance and importance in that a symmetrical bell-shaped distribution is amenable to all the statistical procedures developed for the normal or Gaussian distribution. In the log-normal particle size distribution, the mean, median, and mode coincide and have an identical value. This single value is called the geometric median particle size, dg, and the measure of dispersion is geometric standard deviation, σg. Thus the log-normal particle size distribution can be described completely by these two characteristic values. To determine whether the particles have a distribution close to lognormal distribution, the particle cumulative frequency data can be plotted on a logarithmic probability graph paper. If the distribution follows the lognormal relationship, then the plot will result in a straight line.

Figure 4: Log-normal distribution plotted on a logarithmic probability graph paper

The geometric median particle size is the 50% value of the distribution as shown in Fig. 4. The geometric standard deviation is equal to the ratio of 84.1% value divided by the 50% value or 50% value divided by the 15.9% value. Although 68.26% of the particles will lie in the particle size range between (dg+σg) and (dg-σg). If the particle size reduction is due to comminution such as crushing, milling, and grinding, the resulting particle size distribution very often tends to be log-normal distribution. The reason for the use of logarithmic or geometric size scale can be illustrated by considering an example of successive disintegration of a piece of blackboard chalk. For example, a 64 mm-long piece of chalk would break up into two pieces of 32 mm length each. Subsequent breakups yield pieces with lengths 16, 8, 4, 2, 1 mm, and so on, until one reaches molecular length scales. The ratio of adjacent sizes is always two, thus appearing at the same linear distance on a logarithmic or geometric size scale. Because with each breakage step, more and more particles are produced, the distribution is skewed, so that there are many smaller particles than larger ones. This exercise of successive disintegration of a piece of chalk mimics the way particles are produced in many natural as well as industrial systems. Therefore, aerosol particle size is generally plotted on a logarithmic size scale.

4.3 Log normal distribution

As explained above the atmospheric aerosols can be described well with a set of log-normal distribution functions (log-normal = normally distributed in logarithmic scale), which can be given by the following expression.

Ψ can be number, surface area, mass or volume.

Aerosol particle concentrations can be expressed by Number, Surface area, Volume, or Mass per unit volume. Based on particle distributions, different groups of atmospheric particles can be separated as:

Nucleation (Aitken) mode: particle diameter < 0.1 µm

Accumulation mode: particle diameter: 0.1 µm > d > 1 µm

Coarse mode: particle diameter d > 1 µm

Figure 5: Lognormal distribution of Number, Surface area and volume versis particle size

Aitken mode: Aerosol particles below 0.1 µm in diameter constitute the aitken mode. The smallest range of these particles (>0.01 µm) sometimes called ultrafine mode. These particles are produced by homogeneous and heterogeneous nucleation processes. They can form during natural gas-to particle condensation or during condensation of hot vapor in combustion processes. Due to their rapid coagulation or random impaction onto surfaces, the lifetime of these small particles is very short (order of minutes to hours).

Accumulation mode: Larger aerosol particles in the size range 0.1 to 1 µm in diameter can accumulate in the atmosphere because their removal mechanisms are least efficient. Their lifetime in the atmosphere is 7–10 days and during this period they can transported to a long distance from their sources. Particles belonging to this accumulation mode are formed mainly by coagulation of smaller particles or condensation of vapors onto existing particles, and during these mechanisms they growth into this size range. At the same time, they can also be emitted to the atmosphere from different sources, mainly from incomplete combustion. Accumulation particles removed from the atmosphere mainly by wet deposition.

Coarse mode: These contain particles with diameter larger than 1.0μm. These particles mostly emitted to the atmosphere during mechanical processes from both natural and anthropogenic sources (e.g. sea-salt particles from ocean surface, soil and mineral dust, biological materials). Due to their relatively large mass, they have short atmospheric lifetimes because of their rapid sedimentation.

The number concentration is (in most cases) dominated by the ultrafine aerosols. Area concentration is dominated by the accumulation mode. The mass or volume concentration is dominated by the coarse and accumulation aerosols (fig.5).

4.4 Aerosol dynamics

Particles are emitted into the air, or may form in the air. Aerosol dynamics explains the evolution of complete aerosol populations. They spend some time in the air before being deposited from the air either naturally or artificially. 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.

In this section we shall look at some of the fundamental principles that control how particles behave under various conditions. Particles are deposited to surfaces by three main mechanisms: sedimentation, Brownian diffusion and impaction/interception. Each of the three processes operates most effectively in a different particle size range and can be understood in following sections.

4.4.1 Drag force

If a particle is moving through the air, or the air is moving past a particle, then a viscous drag force acts on the particle which acts opposite to its relative motion. Assuming that the flow of the particle is smooth (laminar) and not turbulent, then this drag force FD is given by

Flow starts to become turbulent for Re > 1, otherwise the flow is smooth.

The drag equation assumes that the particle is large compared to the spaces between the molecules in the gas. This distance, known as the mean free path (λ), is about 0.07 μm for standard atmospheric temperature and pressure. As particle diameter decreases, there becomes an increased probability that the particle will move a distance without experiencing a collision, effectively slipping through the gaps between the molecules. Then we must consider the Cunningham slip correction factor CC in calculating drag force. When d > 0.1 µm then Cunningham slip correction factor is given by

4.4.2 Sedimentation

Every particle in the Earth’s gravitational field experiences a force due to gravity towards the centre of mass of the Earth. If, for example, a stationary particle is released into the atmosphere, the gravitational force will accelerate it downwards. As its speed increases, the drag force will increase. The gravitational force acts downward, but the drag forces acts upward. The net force, which is the difference between the two, therefore decreases as the particle accelerates. Since the gravitational force remains constant, a speed will eventually be reached at which the two forces are equal and opposite and no more acceleration can take place. This is called the terminal or sedimentation speed (Vterm). Particles that fall out of the air under the action of gravity do so at their terminal speed. For a spherical particle gravitational force (Fgrav) is given by following expression.

This equation is known as stokes’ law which explains the sedimentation.

4.4.3 Brownian diffusion

All the particles discussed here are very much larger than atmospheric molecules such as nitrogen and oxygen, and are continually bombarded all over their surfaces by such molecules. Brownian diffusion is the irregular movement of a particle immersed in a fluid, caused by its collisions with the surrounding molecules of much smaller size. For very small particles, two effects become important. First, the rate of collisions with molecules becomes small enough that there is a reasonable probability of the collisions from one direction not being instantaneously balanced by collisions from the opposite direction. Second, the particle mass is small enough that the resultant momentum of these colliding molecules can exert a significant impulse in the unbalanced direction. So a small particle deflects slightly when gas molecules impact on them. The transfer of kinetic energy from the fast moving gas molecules to the small particle causes this deflection, which is termed Brownian motion. Diffusivity provides a measure of the extent to which molecular collisions cause these very small particles to move in a random manner across the direction of gas flow. The diffusion coefficient (D) in the equation below represents the diffusivity of a particle at given gas stream conditions.

Where

K= Boltzmann’s constant

T= The absolute temperature

μ= The dynamic viscosity of air

dpa= particle aerodynamic diameter

C= Cunningham slip correction factor

Brownian diffusion becomes the dominant collection mechanism for particles less than 500 nm (0.5mm) and is especially significant as the particles become smaller. Small particles obtain a high diffusion coefficient because it is inversely proportional to particle size. Thus, small particles in a fluid are subject to a random displacement known as the Brownian motion. This occurs in addition to the net motion in a given direction owing to the action of any of the external forces.

4.4.4 Coagulation

When there is relative movement of particles within a cluster by Brownian or turbulent diffusion, there is collision between particles which sometimes result in their combination to form a single new larger particle. This process is called coagulation. The new particle may be spherical if the original particles are liquid (e.g. sulphuric acid aerosol). But more likely it is untidy asymmetric clump of discrete parts, held together by electrostatic and molecular forces. Coagulation is fastest for smaller particles. The denser the particle cloud, the more will be collisions and coagulation. The basic rate equation is given by:

The particle diameter increases correspondingly, although at a slower rate because it takes eight original particles to produce one new particle of double the diameter (table 2). Equation for change in particle diameter is:

So by using above formulas it is possible to predict the change in number and size of particle with time.

Glossary

Aerosol: Aerosol is defined as suspension of solid or liquid particles in a gas or air. They include a wide range of phenomena such as dust, fume, smoke, mist, fog, haze, clouds, and smog.

Secondary aerosol: The particles that are formed in the atmosphere by gas-to-particles conversion processes are secondary aerosols.

Normal distribution: The normal distribution, also known as the Gaussian or standard normal distribution, is the probability distribution that plots all of its values in a symmetrical fashion, and most of the results are situated around the probability’s mean.

log-normal distribution: Normally distributed in logarithmic scale.

Particle-size distribution: It is a list of values or a mathematical function that defines the relative amount, typically by mass, of particles present according to size.

Drag: Drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

Dynamics: It is the branch of applied mathematics (classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes.

Bioaerosol: An aerosol of biological origin, including airborne suspensions of viruses, pollen, bacteria, and fungal spores and their fragments.

Cloud: A high-density suspension of particles in air, often with a well-defined boundary.

Dust: Solid particles formed by crushing or other mechanical breakage of a parent material. These particles generally have irregular shapes and are larger than about 0.5 um.

Fog or Mist: Liquid particle aerosol. These can be formed by condensation of supersaturated vapors or by physical shearing of liquids, such as in nebulization, spraying, or bubbling.

Fume: Particles that are usually the result of condensed vapor with subsequent agglomeration. Solid fume particles typically consist of complex chains of submicrometer-sized particles (usually < 0.05 |im) of similar dimension. Fumes are often the result of combustion and other high temperature processes. Note that the common usage of fume also refers to noxious vapor components.

Haze: A visiblity-reducing aerosol.