BSA Flow Software Installation and User's Guide - CSI

d
e
ln
2
max
2 V
do
∗
Vt
= ( 7-48)
An expression for ln(V max /V t ) must therefore be found. This is possible in
terms of the burst length:
Ld ( , y')
=
p
⎡
⎢
⎣
V
V
ln max
t
⎤
⎥∗do−8y ⎦
2
2 2
( 7-49)
If this expression is squared and integrated over all possible values of y’
between 0 and d e /2, then normalized by d e /2, which is denoted as L 2 , the
following expression can be derived:
V
ln
V
max
t
2 ( 3L
( d ) )
1
= 2
p
( 7-50)
d
o
It leads to a final expression for d e :
2 ( )
3
d e = L
( 7-51)
2
Therefore, for each size class, the quantity L 2 must be measured. There are
considerable difficulties with this approach however. For one, there may
exist only a few particles in a particle size class, thus the statistical certainty
of the estimation is not good. This is particularly the case for larger particle
size classes where the measured mean square burst length is therefore
completely unreliable.
For this reason, it is necessary to devise a more robust method of estimating
the mean square burst length, especially at larger particle sizes, since these
will be more influential for the derived mass flux measurements of the
instrument. The approach adopted here is to assume that the signal amplitude
is proportional to the square of the particle diameter. It can be deduced from
the above equations that L 2 is linearly correlated to the logarithm of
particle diameter, i.e.:
2
L = A∗ d + B
ln ( 7-52)
p
BSA Flow Software:Reference guide 7-115