# A Review of Experimental Techniques for Measuring Micro- to Nano-Particle-Laden Gas Flows
## 3 Specific Measurement Methods
### Optical Particle Characterization
#### 3.1.3 Scattering Intensity Measurements  
Particle characterization (e.g., particle size and concentration) using scattering intensity measurements is a long-standing technology for multiphase flow, which was well known and widely used before the emergence of either LDA/PDA or PIV. Recently, scattering intensity measurements combined with laser or fluorescence illumination have extended the particle characteristics able to be detected in this technique, e.g., particle velocity [PERSON] (1986); [PERSON] (1987), temperature [PERSON] (1987); [PERSON] (1988) and chemical species [PERSON] (1988). It is used not only to detect micro- or larger particles, but also to measure nano-particle concentrations, e.g., in condensation particle counters, and a practical result obtained using this technique is shown in Figure 8b. The optical principles behind scattering intensity measurements are shown in Figure 8a. The signal received from the optical measurement system is usually equal to the integral of the scattering intensity on the receiving aperture of the optical sensor. In this case, \(\varphi\) is the scattering angle (the receiving angle of the photoelectric detection system), and \(\Delta\delta\) is the receiving solid aperture angle. Under parallel and monochromatic light, with a scattering angle \(\varphi\), the scattering intensity is equal to:  
\[Q\big{(}\lambda,d_{p},m_{0},\kappa,\Delta\delta\big{)}=I_{0}\frac{\lambda^{2}} {8\pi^{2}}\int_{0}^{2\pi}\int_{\Delta\delta}I\big{(}\lambda,\gamma,\varphi,d_ {p},m_{0},\kappa\big{)}\sin\varphi d\varphi d\gamma \tag{10}\]  
where \(Q\) is the scattering intensity received by the detector, \(\kappa\) and \(m_{0}\) are the particle complex refractive index coefficients and \(I_{0}\) is the incident light intensity. This equation indicates that the scattering intensity depends on the optical arrangement constants, as well as the particle refractive index. Figure 7: Optical configuration of the standard (three detector) phase Doppler analyzer. There are three fundamental scattering mechanisms for a water droplet in air: Rayleigh scattering, Mie scattering and geometric optics, depending on the particle size and its related scattering intensity, as shown in Figure 9. Here, \(X_{M}\) is the Mie parameter \(X_{M}=d_{p}\pi/\lambda\), which is equivalent to the dimensionless particle diameter for Mie scattering, for parallel polarized light and complex refractive index \(m=1.333+i0.313\). This relationship indicates that particle scattering intensity is basically proportional to the dimensionless particle diameter (\(X_{M}\)) for Rayleigh scattering and geometric optics. This yields values of \(X_{M}^{6}\) and \(X_{M}^{10}\) for scattering angles of \(30^{\circ}\) and \(90^{\circ}\), respectively, under Rayleigh scattering; but \(X_{M}^{2}\) for both scattering angles under geometric optics. This linear relationship is critical for determining particle diameter from scattering intensity measurements, although it is difficult to do this for Mie scattering, because of its non-monotonic and highly fluctuating relationship between \(X_{M}\) and \(I\). However, there are modifications available to deal with this problem, such as expanding  
Figure 8: Schematic of scattering intensity measurements and results: (**a**) optical arrangement constants; (**b**) particle size distribution with different multiple charged correction (MCC) methods [39]. the receiving aperture area, using a white light source or setting the scattering angle to 0\({}^{\circ}\) to smooth Mie scattering, as particle size increases [1]. For \(d_{p}\gg\lambda\), the particle scattering intensity is strongest at a 0\({}^{\circ}\) scattering angle, because diffracted light is dominant, compared with the other two scattered light components (externally-reflected and internally-refracted light), and is highly concentrated in a forward scattering direction. This regime of geometrical optics is termed the Fraunhofer diffraction regime.