The output signals from the Nanoparticle Spectrometer’s electrometers in response to a given aerosol sample can be modelled by combining the charging model described in section 5.1 and the particle tracks model described in section 5.2.
5.4.1 Model Structure Electrometer Mobility Limits
The boundary representing the ground electrode in the defined instrument cross section (section 5.3) is divided into 16 equal sections representing 16 channels for the electrom- eters. The numerical particle tracking model described in section 5.2 is used to find the mobilities of particles that would land at the intersections of these sections, thus the mobility limits of each channel are defined. Now if a particle’s electrical mobility is known, then the channel where it will land is also known.
Input Distribution
Combustion generated aerosols are nearly always log-normally distributed [Kittelson, 1998]. A sample with a lognormal size distribution can be input by the user specifying the mean particle diameter and the geometric standard deviation. The concentration is normalized because the shape of the signal is dependant only on size distribution.
The program then divides the lognormal intonnumber of discrete strips along the
xaxis. Each strip is treated as a mono-disperse sample with diameter equal to that at the centre of the strip. The fraction of area occupied by the strip is retained for later calculation.
Charge Distribution
The charge distribution is calculated using the “birth and death model”, described in section 5.1. AnNitvalue of 1×1013is used in the data presented in this section as this
Nit produced predicted results with good resolution, and appears to be a reasonable assumption for a diffusion charger according to available literature [Pui, 1976, Biskos et al, 2005].
For each particle size, the fraction of particles with 0,1,2,· · ·50 elementary charges is calculated. This fraction is multiplied by the fraction of the area occupied by the strip of the lognormal. And finally the combined fraction is multiplied by the number of elementary charges on the particle. This gives number of elementary charges per unit volume, which is proportional to the current that would be induced by the particles
5.4. MODEL OF THE INSTRUMENT OUTPUT 71 landing on an electrometer. This is done for all n mono-disperse samples relating to the strips of the original log-normal distribution
Classification
Finally for each combination of particle size and number of charges the electrical mo- bility is calculated.
Knowing the mobility for a specific particles size allows the charge per unit volume for that size to be added to a running total for the corresponding channel in which a particle of that mobility will land.
The final output of the program is a bar graph showing the charge per unit volume in each channel, this is proportional to the current reading on the electrometers for an aerosol sample with the input distribution.
5.4.2 Examples of Modelled Instrument Output
This section presents some examples of outputs produced by the model. For simplicity, the first examples considered are the outputs for aerosol samples where the particles are all the same diameter (monodisperse). Figures 5.10 and 5.11 show graphs of the modelled instrument output and the modelled charge distribution for six particle sizes. In the case of 10nmparticles it can be seen that the model predicts that the particles will attain a maximum of one charge and a large proportion of the particles will be uncharged. These uncharged particles will not be classified. The NPS output shows that the singly charged particles are expected to land in channel five.
For 20,39, and 76nm particles the effects of multiple charging can clearly be seen. The charge distribution for 20nm shows singly charged particles and a small amount of doubly charged particles. The NPS output shows singly charged particles landing in channel 9, and doubly charged particles landing in channel 7. The size of the signal in channel 7 is about twice as large (relative to the singly charged signal) as the predicted fraction of doubly charged, compared to singly charged. This is expected because doubly charged particles induce twice the current per particle of singly charged particles. Similarly the plots for 39nm, and 76nm particles show distinct signals in separate channels representing the 1, 2, 3...etc elementary charges.
In the case of 150nmthe charge distribution predicts particles with 4-9 elementary charges. However signals are only predicted in channels 14, 15, and 16. This is because particles with different levels of charge are predicted to land in the same channels. There are two reasons for this: The higher numbered channels in the instrument cover a larger mobility range than the lower, and the difference in mobility between two
particle of the same size with n, and n+ 1 charges reduces, as nincreases. The same effect is observed for 296nm.
Observing the outputs for monodisperse samples is useful for the purpose of eval- uating the model. However, in general monodisperse samples will not be presented for classification. Figures 5.12 and 5.13 show the predicted NPS output signals for a selection of narrow log-normal distributions (GSD = 1.1). Importantly a unique signal can be seen for each of the lognormals evaluated, and they can be easily differentiated. Between 10nm and 39nm mean diameter, the spread of channels in which signals are predicted broadens with increasing diameter. Between 39nm and 269nm the signals narrow again as the wider mobility limits of the channels becomes the dominant factor. These graphs would seem to indicate that, as predicted by the analytical classifier approximation (section 5.3.1), that resolution will be better for samples landing in the middle of the classifier.