Environmental Engineering Reference
In-Depth Information
Eficiency
E
i
of the
I
-ilter in the package equals to
(
)
−
∏
i
1
*
*
(17.32)
E
=
E
1
−
E
i
i
j
j
=
1
where
E
j
*
is the eficiency of the
j
-ilter.
Functions
E
i
(
r
) are equation kernels in the system of
n
Fredholm integral equations of irst kind.
A system of ill-conditioned equation appears after replacing of integrals by a inite sum.
Some authors [122,123] have analyzed the size distribution of sub-micron radioactive aerosols
using a package of several ibrous ilters by solving a reverse task (17.31) without any additional
presumptions. Naturally, such an approach turned out to be inconvenient in praxis.
In this work [124] authors managed to reduce the task (31) to a correctly posed one thanks to
introduction of priory information about size distribution spectrum and to determine size distribu-
tion of alpha-active submicron aerosols in the surface air layer.
It is known that the sizes of the majority of natural and artiicial aerosols can be well approxi-
mated by logarithmically normal distribution (LND), whose density equals to
⎧
⎨
⎩
2
⎫
⎬
⎭
1
(ln
r
ln )
(ln )
−
r
0
f r
( )
=
exp
−
(17.33)
2
2
σ
2
π σ
ln
⋅
r
where
r
is the radius of particles
r
0
and σ are the LND parameters (median radius and standard geometrical deviation)
So, if to assume that aerosol particle sizes are subject to LND then the task to determine their dis-
tribution is reduced to determination of LND parameters from a system of equations:
R
2
⎧
⎨
⎩
2
⎫
⎬
⎭
E r
( )
ln
(ln
r
−
ln )
r
dr
r
∫
i
0
(17.34)
N
=
⋅
exp
−
i
2
2
ln
σ
2
π σ
R
1
To ind LND parameters it is suficient to have three ilters, at that the third one is to be highly effec-
tive (to capture practically all aerosol particles).
Task (17.34) is solved by minimizing the deiciency functional
2
⎛
R
⎞
2
2
∑
=
∫
⎜
⎜
⎟
⎟
Q
=
N
−
E r f r dr
( ) ( )
(17.35)
i
i
⎝
⎠
i
1
R
1
As it was mentioned before ilter eficiency at inertial capturing mechanism is proportional to the
particle size raised to the second power. Quantitative correlations of effectiveness of FP iltering
materials with Stokes numbers in the range of 0.2-5 [125] were received to solve the task (17.34),
calculation algorithms and programming realization for the search of required parameters [126,127]
were proposed, a range of method use was widened, optimal composition of a ilter package and
characteristics of ilters [125] were determined. The process for production of FP ibrous ilter-
ing materials and analytical ilter kits intended for aerosol particles size distribution analysis was
upgraded, which lead to production of very thin layers of uniform and moldable iltering materials.
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