BSA Flow Software Installation and User's Guide - CSI

Three further factors are however important:
− particle diameter
− particle trajectory
− validation criteria
Size dependent detection area (X-Y)
In particular it is the latter three, which are briefly discussed in the following
three sub-sections, after which some final expressions for size distribution,
fluxes and concentration are given.
This is the effect, which has been treated previously by Saffman (1987),
accounting for the larger effective measurement volume size for larger
particles. The algorithm introduced by Saffman is adequate for onedimensional
particle trajectories in the X- direction. Additional
considerations must be made for arbitrary particle trajectories in the XYplane.
If flux measurements are performed in both coordinate directions, it
is necessary to consider the measurement volume cross section in both the X-
and Y-directions.
The area measurement is based on the concept of an effective measurement
volume diameter, d e , which is particle size dependent. Knowing this size, the
cross section in the X- and Y-direction are given by the following relations
respectively, as is shown diagrammatically in Figure 7-75:
A D d D Ls
x( i) = e( i)
sinφ
A D d D Ls
π
y( i) = e( i)
+ d
sinφ
4
2
e
cot φ
( 7-42)
( 7-43)
Accordingly an on-line measurement of d e is required. This will be derived
below, following an approach analog to Saffman, but taking into account
both velocity components of the particle in the XY-plane.
To begin, it is assumed that the ellipticity of the measurement volume can be
disregarded, since the half-intersection angle of the laser beams (ϑ/2) is
generally small. The amplitude of the signal envelope can then be expressed
as:
V ( d , x ', y ') = V ( d ) e
p max p
8 2 2
− ( x ' + y ' )
2
d o
( 7-44)
BSA Flow Software:Reference guide 7-113