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Particle counters all measure a signal, for example, electrical resistance or intensity of scattered light, originating from a small but finite sensing zone with volume greater than that of the smallest particle they can sense. Ideally, it is expected that the sensing zone contains 0 or 1 particle. However, given that the number of particles in a volume of dispersion is a random variable, there is a finite probability that more particles than one are simultaneously present in the sensing zone. This is referred to as coincidence.
In the case of monodispersed particles the phenomenon of coincidence causes simply a loss of counts. Given that the probability of finding k particles in a volume V of dispersion, which on average contains N particles, is Poisson-distributed:
| p(k) = e-N N k / k! | (1) |
the observed particle count, N ' can be expressed as follows (for example, Wales and Wilson 1961):
| N ' = L [1 - exp(-N / L)] | (2) |
where L is the number of sensing zone volumes in the sample volume, V, and one assumes that the presence of one particle in the sensing zone "hides" other particles that are simultaneously present there. The true particle concentration, N, can thus be calculated from Eq. 2, given the observed particle count N '.
The coincidence theory of Wales and Wilson (1961) is based on modeling a continuous flow of fluid with particles through the sensing zone of a particle counter as a string of sensing zone volumes, some of which contain more than one particles in unspecified configuration. Princen and Kwolek (1965) recognized the importance of a distance between any two conciding particles and arrived at a modified coincidence formula for the particle-hiding case in the limit of N / L << 1:
| N ' = N - (1 / 2) N 2 / L | (3) |
Pisani and Thompson (1971) extended the theory of Princen and Kwolek (1965) to large N:
| N ' = N exp( -N / L ) | (4) |
In the limit of N / L << 1, these coincidence corrections provide similar results. However for the large particle concentrations, N, only the two latter equations account for a decline in the observed particle count, N ' when the particle concentration increases, with Eq. 4 providing a better fit (for example, Pisani and Thompson 1971).
| CITATION: Jonasz M. 2006. Coincidence correction: Monodispersions (www.tpdsci.com/Tpc/ERMCoincM.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 22-Feb-2006 Modified: 20-Jun-2006 Peer-reviewed: PENDING |
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