For a monodisperse aerosol, a single number - the particle diameter - suffices to describe the size of the particles. However, for a polydisperse aerosol, we describe the size of the aerosol by use of the particle-size distribution. This defines the relative amounts of particles present, sorted according to size. One approach to defining the particle size distribution is to use a list of the size of all particles in a sample. However, this approach is awkward to use so other solutions have been found. Another approach is to split the complete size range into intervals and find the number of particles in each interval. This data can then be visualised using a histogram where the area of each bar represents the total number of particles in that size bin, usually normalised by dividing the number of particles in an interval by the width of the interval and by the total number of particles so that the total area is equal to 1 and the area of each bar is equal to the proportion of all particles in that size range. If the width of the bins tends to zero we get the frequency function:
- is the diameter of the particles
- is the fraction of particles having diameters between and +
- 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:
It can also be formulated in terms of the total number density N:
If we assume the aerosol particles are spherical, we then find that the aerosol surface area per unit volume (S) is given by the second moment:
and the third moment gives the total volume concentration (V) of the particles:
It can also be useful to approximate the particle size distribution using a mathematical function. The normal distribution is not usually suitable as most aerosols have a skewed distribution 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 clearly not physically realistic. However, the normal distribution can be suitable for some aerosols, such as test aerosols, certain pollen grains and spores.
A more widely chosen distribution is the log-normal distribution where the number frequency is given as:
- is the standard deviation of the size distribution and
- is the arithmetic mean diameter.
The log-normal distribution has no negative values, can cover a wide range of values and fits observed size distributions reasonably well.
Other distributions which can be used to characterise particle size are: the Rosin-Rammler distribution, applied to coarsely dispersed dusts and sprays; the Nukiyama-Tanasawa distribution, for sprays having extremely broad size ranges; the power function distribution, which has been applied to atmospheric aerosols; the exponential distribution, applied to powdered materials and for cloud droplets the Khrgian-Mazin distribution.
Read more about this topic: Aerosol
Other articles related to "size distribution, distributions, sizes, size, distribution":
... The model assumes that bubble nuclei are always present in a specific size distribution, and that a certain number are induced to grow by compression and decompression ... of helium, nitrogen, and oxygen contain bubble distributions of different sizes, but the same phase volume limit is used ... nuclei with aqueous and/or lipid skin structure, in a number and size distribution quantified by an equation-of-state ...
... measurements on the two-dimensional sectioning plane and estimating the amount, size, shape or distribution of the microstructure in three dimensions ... a phase or constituent, measurement of the grain size in polycrystalline metals and alloys, measurement of the size and size distribution of particles, assessment of the shape of particles, and ... that is, its volume fraction, is defined in ASTM E 562 manual grain size measurements are described in ASTM E 112 (equiaxed grain structures with a single size ...
... fine powders, the irregular particle sizes and shapes in a typical powder often lead to non-uniform packing morphologies that result in packing ... rate at which the solvent can be removed, and thus highly dependent upon the distribution of porosity ... particles, however even their non-aggreated deposits have lognormal size distribution, which is typical with nanoparticles ...
... - the particle diameter - suffices to describe the size of the particles ... However, for a polydisperse aerosol, we describe the size of the aerosol by use of the particle-size distribution ... This defines the relative amounts of particles present, sorted according to size ...
Famous quotes containing the words distribution and/or size:
“There is the illusion of time, which is very deep; who has disposed of it? Mor come to the conviction that what seems the succession of thought is only the distribution of wholes into causal series.”
—Ralph Waldo Emerson (18031882)
“O hideous little bat, the size of snot,
With polyhedral eye and shabby clothes,”
—Karl Shapiro (b. 1913)