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SCATMECH > Classes and Functions >
Property Models
> Size Distributions
Abstract class Distribution
class VolumeParticleSizeDistribution
class SurfaceParticleSizeDistribution
This page describes models for particle size distributions and number densities. The class Distribution describes the size distribution, while
the classes VolumeParticleSizeDistribution and SurfaceParticleSizeDistribution define the particle size distributions and the number densities
together. The two latter classes are defined separately, because the units for volume number density are different than those for surface number density.
These distributions are used by a number of models that average over particle size in SCATMECH.
The following models are available:
- Abstract class Distribution
- Abstract class VolumeParticleSizeDistribution
- Abstract class SurfaceParticleSizeDistribution
Instantiable Models for Distribution and Their Parameters:
| Parameter |
Data
Type |
Description |
Default |
Log_Normal_Distribution:
This distribution specifies a log-normal distribution in particle diameter $D$, with its probability density function (PDF) given by
\begin{equation}
{\rm PDF}(D)=\frac{1}{D\sigma\sqrt{2\pi}}\exp\left[{-\frac{(\log D-\log\mu)^2}{2\sigma^2}}\right].
\end{equation}
|
| sigma |
double |
The parameter $\sigma$, which is the standard deviation of $\log D$. |
0 |
| median |
double |
The parameter $\mu$, which is the median of diameter $D$ [µm]. |
10 |
Modified_Gamma_Distribution:
This distribution specifies the distribution described by Deirmendjian [in Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969)].
The probability density function (PDF) is given by
\begin{equation}
{\rm PDF}(D)=\frac{1}{A} r^\mu \exp\left(-\Lambda r^\gamma\right)
\end{equation}
where
\begin{equation}
A = \frac{\Lambda^{-(1+\mu)/\gamma}\Gamma[(1+\mu)/\gamma]}{\gamma}
\end{equation}
and $r=D/2$ is the radius.
|
| mu |
double |
The parameter $\mu$. |
8 |
| Lambda |
double |
The parameter $\Lambda$. |
0.0417 |
| gamma |
double |
The parameter $\gamma$. |
3 |
Normal_Distribution:
This distribution specifies the normal distribution.
The probability density function (PDF) is given by
\begin{equation}
{\rm PDF}(D)=\frac{1}{\sigma\sqrt{2\pi}}\exp\left[-\frac{(D-\mu)^2}{2\sigma^2}\right].
\end{equation}
|
| mean |
double |
The mean $\mu$ [µm]. |
10 |
| sigma |
double |
The standard deviation $\sigma$ [µm]. |
5 |
Weibull_Distribution:
This distribution given by Weibull [J. Appl. Mech.-Trans. ASME 18, 293-297 (1951)].
The probability density function (PDF) is given by
\begin{equation}
{\rm PDF}(D)=\frac{k}{\lambda}\left(\frac{D}{\lambda}\right)^{k-1}\exp[-(D/\lambda)^k].
\end{equation}
|
| scale |
double |
The parameter $\lambda$ [µm]. |
10 |
| exponent |
double |
The parameter $k$. |
4 |
Bimodal_Distribution:
This distribution given by the sum of any two partial distributions.
The probability density function (PDF) is given by
\begin{equation}
{\rm PDF}(D)=f_{\rm A} {\rm PDF}_{\rm A}(D) + (1-f_{\rm A}) {\rm PDF}_{\rm B}(D).
\end{equation}
|
| distributionA |
Distribution_Ptr |
The distribution ${\rm PDF}_{\rm A}(D)$. |
Log_Normal_Distribution |
| distributionB |
Distribution_Ptr |
The distribution ${\rm PDF}_{\rm B}(D)$. |
Log_Normal_Distribution |
| fractionA |
double |
The fraction of distribution A, $f_A$. |
0.5 |
Instantiable Models for VolumeParticleSizeDistribution and Their Parameters:
| Parameter |
Data
Type |
Description |
Default |
Regular_VolumeParticleSizeDistribution:
This volume particle diameter distribution specifies a distribution and the number of particles in a volume.
|
| distribution |
Distribution_Ptr |
The diameter distribution ${\rm PDF}(D)$. |
Log_Normal_Distribution |
| numberdensity |
double |
The volume number density [µm-3]. |
0.00001 |
Instantiable Models for SurfaceParticleSizeDistribution and Their Parameters:
| Parameter |
Data
Type |
Description |
Default |
Regular_SurfaceParticleSizeDistribution:
This surface particle diameter distribution specifies a distribution and the number of particles per area on a surface.
|
| distribution |
Distribution_Ptr |
The diameter distribution ${\rm PDF}(D)$. |
Log_Normal_Distribution |
| numberdensity |
double |
The surface number density [µm-2]. |
0.001 |
CC1246E_SurfaceParticleSizeDistribution:
The distribution given by IEST-STD-CC1246E, which specifies the number of particles on an area 0.1 m2
having diameter greater than $D$ (in micrometers) given by
\begin{equation}
N(D) = 10^{0.926[(\log_{10} L)^2-(\log_{10} D)^2]}.
\end{equation}
where $L$ is the cleanliness level.
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| cleanliness |
double |
The cleanliness level $L$.
| 1000 |
| slope |
double |
The slope parameter, which is defined by IEST-STD-CC1246E to be 0.926, but which can be changed for this model.
When the slope is not 0.926, the distribution is adjusted so that the total area coverage of particles is the same as it would
be for a slope of 0.926, cleanliness level $L$, and where the particles have diameters between 1 µm and 1000 µm.
See M. G. Dittman, "Contamination scatter functions for stray-light analysis," Proc. SPIE 4774, 99-110 (2002).
|
0.926 |
See also:
SCATMECH Home, Conventions, Polydisperse_Sphere_BRDF_Model
Include file:
#include "sizedistribution.h"
Source code:
sizedistribution.cpp
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Current SCATMECH version: 7.22 (April 2021)
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