## 3 Results
### Characterization of Technical Solutions
#### 3.1.3 Electrofilter (EF)  
Figure 4a summarizes the results of the EF penetration measurements. The EF removed all singly charged particles smaller than 17 nm. The penetration of singly charged 23, 30 and 50 nm particles was 11%, 42% and 88%, respectively, and reached 98% at 70 nm. Since particle collection in the EF depends on the electrical mobility, the penetration will depend on the actual charge state of the particles. Multiple charged particles will exhibit the same electrical mobility as smaller singly charged  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Diameter (nm)**} & \multicolumn{2}{c}{**Experimental**} & \multicolumn{2}{c}{**Fuchs 2 \(\times\) 10\({}^{12}\) m\({}^{-3}\)s**} & \multicolumn{2}{c}{**Fuchs 3 \(\times\) 10\({}^{12}\) m\({}^{-3}\)s**} \\  & **+1** & **+2** & **+1** & **+2** & **+1** & **+2** \\ \hline
23 & 27\%(\(\pm\)7\%) & noise \({}^{1}\) & 18\% & 26\% & 4\% & 5\% \\
30 & 8\%(\(\pm\)2\%) & 23\%(\(\pm\)  
particles and therefore the penetration curve will be shifted towards larger particle sizes. The shift can be calculated from the measured penetrations for singly charged particles through [41]:  
\[Z(d^{n})=Z\Big{(}d^{1}\Big{)}\ \Rightarrow\ \frac{d^{n}}{nC_{c}(d^{n})}=\frac{d^{1}}{ C_{c}(d^{1})}, \tag{2}\]  
where \(d^{n}\) is the diameter of a particle carrying \(n\) charges, having the same electrical mobility with a particle carrying one charge (having diameter \(d^{1}\)), while \(C_{c}\) is the Cunningham correction factor and \(Z\) the electrical mobility. The calculated penetrations for particles carrying up to two charges are shown as dashed curves in Figure 4a.  
For bipolarly charged particles being on average neutral, like typical engine exhaust [18], only the charged fractions will be affected by the EF. Accordingly, the interference of the EF with such particles will be limited since the uncharged fractions are expected to increase with decreasing size. For example, the dotted curve in Figure 4a illustrates the calculated penetration of neutralized particles based on the commonly assumed charging probability distribution of Wiedensohler [42].  
To better illustrate the performance of the EF some numerical calculations were performed with the Fuchs model for the \(N_{i}t\) product of 2.5 \(\times\) 10\({}^{12}\) m\({}^{-3}\)s of the corona on which the EF was installed. Figure 4b illustrates the effect of the EF on the average charge exiting the corona for neutralized, singly charged and doubly charged particles. The percentage differences on the average acquired charges between singly or doubly charged and neutralized particles for this configuration are summarized in Table 2 for selected sizes. The installation of the EF will introduce a small (maximum 20%) reduction in the baseline charging efficiencies of neutralized particles at sizes below 50 nm. In the case of singly charged particles, the EF can effectively constrain the change in the average particle charge to less than \(\pm\)30% over the regulated size range (>23 nm). Doubly charged particles are more efficiently removed leading to a complete removal of charges below 30 nm. Since the EF is targeting the small size range, the performance of this technical solution at large sizes can only be improved by increasing the \(N_{i}t\) product (Figure 3a).  
Figure 4: **(a)** Particle penetration through the EF as a function of mobility diameter and particle charge. Experimental results for singly charged particles are shown in circles. The dashed curves correspond to extrapolation of the experimental results for neutralized and multiply charged particles; **(b)** Average particle charge downstream of a corona charger operating at \(N_{i}t\) products of 2.5 \(\times\) 10\({}^{12}\) m\({}^{-3}\)/s with (dashed lines) and without (solid lines) an EF.