## 3 Results and Discussion
### Particle Number Size Distribution (PNSD)  
The normalized PNSD of smoke particle could be best fitted with lognormal functions [27]:  
\[\frac{\mathrm{d}N}{\mathrm{d}D}=\sum_{n}\frac{1}{\sqrt{2\pi}D\ln\sigma_{g}}\exp \left[-\frac{1}{2}\left(\frac{\ln D-\ln D_{g}}{\ln\sigma_{g}}\right)^{2}\right], \tag{2}\]  
in which \(N\) is the total number concentration of particles per volume, \(D\) is size diameter of particles, \(D_{g}\) is geometry mean diameter (GMD) of particles, \(\sigma_{g}\) is geometric standard deviation (GSD), and \(n\) stands for the number of modes. If \(n=1\), it means there is a unimodal lognormal distribution; it is a bimodal lognormal distribution when \(n=2\); \(n=3\) means a trimodal lognormal distribution; and so on. The PNSDs of aerosols are influenced by short fluctuations in different kinds of emission sources [41], which can be a part of data set in source apportionment of aerosol particles. In the PNSDs, two modes were identified with \(D_{g}\) about 20 nm and 100 nm from transit traffic and household heating, respectively [42; 43]. As a major source of fine particles in the atmosphere, the size distributions of freshly emitted smoke particles from biomass burning resided mainly within the accumulation mode, with \(D_{g}\) at 50-200 nm [2]. The discrepancy of \(D_{g}\) and distribution pattern related to fuel type, combustion environment and conditions, and the aging process [44]. For different kinds of biomass samples, the PNSDs of smoke from smoldering burning were quite different with each other and from results from other researchers [45; 46; 47; 48; 15; 49]. As shown in Figure 4, the PNSD of soya has two modes, which can be fitted with a bimodal lognormal distribution. Meanwhile, the PNSD of P2 can be fitted with a trimodal lognormal distribution, which has three modes. Figure 3: Correlation between the contents of volatile matter (VM) and ash from the proximate analysis results of biomass samples on dry basis. The PNSDs of aerosol from biomass burning can be fitted with bimodal or trimodal lognormal functions [30; 50]. The PNSDs of smoke from smoldering burning of agricultural straw are similar and can be fitted with a bimodal lognormal distribution, with the average values of mode size are 12.71 nm \(\pm\) 0.71 nm and 58.42 nm \(\pm\) 8.64 nm, respectively. The PNSD of wood sawdust can be fitted with a trimodal lognormal distribution, with the average values of mode size at 10.25 nm \(\pm\) 2.18 nm, 19.81 nm \(\pm\) 5.50 nm, and 66.70 nm \(\pm\) 11.18 nm, respectively. The fit parameters of multimodal lognormal distribution are shown in Table 2. The majority of particles by number are mainly in the nucleation (\(D_{p}\) < 30 nm) and Aitken modes (30 nm \(<D_{p}\) < 100 nm) [49]. The two modes of agricultural straw are around 10 nm (nucleation mode) and 60 nm (Aitken mode). The two modes of wood sawdust are in nucleation mode, and one is in Aitken mode. The \(D_{g}\) of mode 1 for Ph and Po are similar, while that of mode 2 for Ph, Pi, P1, and P2 are similar. However, the \(D_{g}\) of mode 2 for Po is similar to that of  
Figure 4: Two kinds of particle size distributions and their fitted curves in the well-mixed stage after burning out. (**a**) Particle size distribution of soya which has two modes; (**b**) particle size distribution of P2 which has three modes. mode 1 for Pi, P1, and P2. The characteristic modes are similar to the characteristics of particle size distributions in lab scale biomass fires of southwestern United States fuels [47] in which the major modes of PNSD of smoldering smoke ranged from 10 nm to 40 nm, but the PNSDs were slightly different because they showed bimodal distributions. During the biomass burning events [44; 51], the PNSDs of aerosol showed trimodal distributions, with nucleation (\(D_{g}\) = 16 nm or 9.0 nm), Aitken (\(D_{g}\) = 52 nm or 31.0 nm), and accumulation (\(D_{g}\) = 130 nm or 102 nm). The results were similar to our results in the nucleation and Aitken modes, except for the accumulation modes.