N(r þ Dr) À N(r). Let’s turn to mean concentration i.e. to the value [N(r þ Dr) À
N(r)]/Dr for ability to compare particle concentration in different intervals Dr. Let
Dr decrease towards zero and obtain, according to the derivative definition, the
function of particle size distribution n(r) ¼ dN(r)/dr. The distribution function n(r)
completely describes the aerosol particle ensemble considering its dispersivity and
allows finding the concentration of any radius range (in particular the total aerosols
concentration)
N ¼
ð
1
0
nðrÞdr
(10.1)
The function f(r) ¼ n(r)/N is the normalizing function of aerosol particles
distribution, which is convenient because allows considering particle dispersivity
independently of specific concentration N. Often it is called just the distribution
function without the refinement normalizing. We will use this terminology in
further consideration. The normalizing condition for the function f(r) with the
Eq. 10.1 is the following
ð
1
0
f ðrÞdr ¼ 1
(10.2)
The function f(r) offers also a sense of probability: it is the probability density of
aerosol particle has the radius r.
The experimental data of aerosol concentration versus particle radius N(r) are
used for describing size distribution function of real atmospheric particles
ensembles. For convenience the experimentally obtained distribution function f(r)
is approximated with analytical formulas. The normal logarithmic (lognormal)
distribution is the mostly used approximation:
f ðrÞ ¼
1
ffiffiffiffiffi ffi
2p
p
rs
exp À
1
2s 2 ln
2
ðr=r 0 Þ
(10.3)
Lognormal distribution (10.3) is the distribution of the value that logarithm
changes according to normal (Gaussian) law. It is fully characterized with two
parameters: the mean radius r 0 (as a logarithm value) and the dispersion s. The
mean radius describes particle sizes in total (the larger the radius r 0 ) the greater are
in average particles of the ensemble. The dispersion s represents the scatter of
radiuses (the larger the parameter s, the greater the difference between
concentrations of particles with various radiuses). We use the lognormal distribution (10.3) in the consideration.
10.3 Ensemble of Aerosol Particles
101
N(r)]/Dr for ability to compare particle concentration in different intervals Dr. Let
Dr decrease towards zero and obtain, according to the derivative definition, the
function of particle size distribution n(r) ¼ dN(r)/dr. The distribution function n(r)
completely describes the aerosol particle ensemble considering its dispersivity and
allows finding the concentration of any radius range (in particular the total aerosols
concentration)
N ¼
ð
1
0
nðrÞdr
(10.1)
The function f(r) ¼ n(r)/N is the normalizing function of aerosol particles
distribution, which is convenient because allows considering particle dispersivity
independently of specific concentration N. Often it is called just the distribution
function without the refinement normalizing. We will use this terminology in
further consideration. The normalizing condition for the function f(r) with the
Eq. 10.1 is the following
ð
1
0
f ðrÞdr ¼ 1
(10.2)
The function f(r) offers also a sense of probability: it is the probability density of
aerosol particle has the radius r.
The experimental data of aerosol concentration versus particle radius N(r) are
used for describing size distribution function of real atmospheric particles
ensembles. For convenience the experimentally obtained distribution function f(r)
is approximated with analytical formulas. The normal logarithmic (lognormal)
distribution is the mostly used approximation:
f ðrÞ ¼
1
ffiffiffiffiffi ffi
2p
p
rs
exp À
1
2s 2 ln
2
ðr=r 0 Þ
(10.3)
Lognormal distribution (10.3) is the distribution of the value that logarithm
changes according to normal (Gaussian) law. It is fully characterized with two
parameters: the mean radius r 0 (as a logarithm value) and the dispersion s. The
mean radius describes particle sizes in total (the larger the radius r 0 ) the greater are
in average particles of the ensemble. The dispersion s represents the scatter of
radiuses (the larger the parameter s, the greater the difference between
concentrations of particles with various radiuses). We use the lognormal distribution (10.3) in the consideration.
10.3 Ensemble of Aerosol Particles
101