# A Review of Experimental Techniques for Measuring Micro- to Nano-Particle-Laden Gas Flows
## 3 Specific Measurement Methods
### Experimental Methods for Sub-micro- and Nano-particle Laden Gas Flow
\right]} \tag{14}\]  
under the conditions of 1 nm \(\leq D_{p}\leq\) 1000 nm, \(N=-1\), 0, 1; or 20 nm \(\leq D_{p}\leq\) 1000 nm, \(N=-2\), +2; and:  
\[f_{c}(N)=\frac{e}{\sqrt{4\pi^{2}\epsilon_{0}D_{p}KT}}\exp\frac{-\left[N-\frac{2 \pi\epsilon_{0}D_{p}KT}{e^{2}}\ln\left(\frac{Z_{i+}}{Z_{i-}}\right)\right]^{2} }{2\times\frac{2\pi\epsilon_{0}D_{p}KT}{e^{2}}} \tag{15}\]  
for the fraction of particles carrying three or more charges. Here, \(N\) is the number of elementary charges on a particle; \(a_{i}\) is a coefficient related to \(N\); \(T\) is the temperature; and all other physical constants are listed in Table 3.  
The sampled particles are classified according to their differential electrical mobility in both the SMPS and the FMPS or their characteristic aerodynamic diameter in the ELPI. Because particle density clearly has a huge influence on ELPI measurements, particle density needs to be known to use this technique. The DMA in a SMPS, used to classify the particles, usually consists of two cylindrical electrodes made of polished stainless steel [54], in which the resulting drag force on the charged particle can quickly increase and become equal to the electrical force. According to the Stokes law, the neutralized particles following a steady-state charge distribution will achieve different terminal velocities related  
Figure 11: Time-averaged particle number density and its root mean square at different positions in flow around a circular cylinder using FMPS [50]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Physical Constants** & **Definition** & **Value** & **Units** \\ \hline \(\epsilon\) & elementary charge units & \(e=1.60217733\times 10^{-19}\) & C \\ \(\epsilon_{0}\) & Dielectric constant & \(\epsilon_{0}=8.854187817\times 10^{-12}\) & (F/m) \\ \(K\) & [PERSON]’s constant & \(K=1.380658\times 10^{-23}\) & (J/k) \\ \(z_{i+}/z_{i-}\) & ion mobility ratio & \(z_{i+}/z_{i-}=0.875\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relevant physical constants for modeling the charge distribution of submicron- to nanometer-sized particles. to their experience of the electrical force and the drag force in the annular electrical field. This produces a specific electrical mobility in the particle that determines whether it meets the conditions outlined in Equation (16) and enters the DMA, as the presupposed particle size to be measured. \[\frac{d_{p}}{C_{c}(d_{p})}=\frac{2 NeVL}{3\mu q_{sh}\ln\frac{R_{1}}{R_{2}}} \tag{16}\]  
where \(d_{p}\) is the particle electrical mobility equivalent diameter, \(q_{sh}\) is given by \(q_{sh}=(Q_{sh}+Q_{ex})/2\), \(Q_{sh}\) is the sheath air flow rate, \(Q_{ex}\) is the excess flow rate, \(V\) is the average voltage on the inner central rod, \(L\) is the length between the exit slit and the polydisperse aerosol inlet, \(R_{1}\) is the inner radius of the annular space, \(R_{2}\) is the outer radius of the annular space, \(C_{c}\) is Cunningham slip correction and \(\mu\) is the gas dynamic viscosity. Equation (16) also indicates that monodisperse particles of a defined diameter can be attained by accurately adjusting \(V\). These monodisperse aerosols are transported into a concentration detector, e.g., a concentration particle counter [55] or electrometer [56; 57], to characterize particle concentration. It usually takes an SMPS several minutes to analyze each size distribution, with sizes ranging from 2.5 nm to 1000 nm, because it needs to scan through all size channels. The size resolution of an SMPS has increased to cover up to 64 channels, making its size resolution one of the highest among these three techniques. In contrast to an SMPS, the outer cylinder in an FMPS classifier is divided into several electrically isolated segments, which are monitored using individual electrometers [58].