Aerosol Science and Engineering

, Volume 1, Issue 4, pp 155–159 | Cite as

Decay of High-Concentration Aerosol in a Chamber

  • Longbo Liu
  • Zhihong Zhang
  • Yanmin Wu
  • Wen Yang
  • Shan Wu
  • Lixing Zhang
Original Paper


High-concentration aerosol is supposed to be crucial in some air pollution events. Aerosol always decays due to such mechanisms as coagulation, gravitational settling and diffusion deposition in a chamber; so its concentration needs to be calibrated in chamber experiments, especially for high-concentration aerosol. Two methods including the wall-loss correction and the direct simulation Monte Carlo (DSMC) were used to describe decay of the aerosol concentration. The parameters of diffusion deposition were fitted by experimental data. The results by both methods were compared to the experimental results of high-concentration aerosol decay process. The results show that the wall-loss correction under the present conditions is valid when the initial total aerosol concentration is less than 104 cm−3, and the DSMC results are consistent to the experimental data for concentration ranging from 104 cm−3 to more than 106 cm−3.


Aerosol decay High-concentration aerosol Wall loss Numerical simulation 

1 Introduction

Air pollution events such as haze and release of fireworks usually cause notable visibility impairment and serious health hazards (Zhang et al. 2010; Kang et al. 2013). Emission of fireworks including gaseous pollutants such as nitrogen oxides and aerosols such as carbon black and dust has a complex impact on air quality. These gaseous and aerosol mixture can evolute in air via both physical and chemical processes, so they need be investigated in chambers, as smoke-chamber experiments in atmospheric photochemistry research (Wu et al. 2007; Pierce et al. 2008; Jia et al. 2011; Geng et al. 2012). In chamber experiments, aerosol yields or growth from chemical reactions of gaseous pollutants can be determined.

A major complication in the experiments is that aerosols loss due to walls of chamber (Crump and Seinfeld 1981; McMurry and Rader 1985). Wall-loss correction, a linear correction accounting for diffusion deposition, gravitational sedimentation and sometimes electrostatic deposition, is a popular method to correct aerosol loss in a chamber (Crump et al. 1983; McMurry and Rader 1985; Bunz and Dlugi 1986; Okuyama et al. 1986). The wall-loss correction can be regarded as independent of components and chemical reactions; so it is convenient to be applied. However, there are still some diverge between the experimental results and correction until recently (Pierce et al. 2008).

Aerosol coagulation, one of the most important mechanisms in aerosol dynamics, is usually not included in the wall-loss correction since it has no direct influence on aerosol mass concentration (Schnell et al. 2006). However, coagulation can cause aerosol diameters to increase and hence has influence on aerosol loss to a certain extent. According to more recent researches (Hussein et al. 2009; Yu et al. 2013), for aerosol with number concentration more than 104 cm−3, coagulation can have more impact on aerosol number concentration than deposition, though the threshold shifts to some degree as diameter and size distribution differ.

If coagulation cannot be neglected, the general dynamic equation (GDE), also called the population balance equation (PBE), should be applied to describe change of aerosol rather than the wall-loss correction. GDE can include all mechanisms such as coagulation, deposition, condensation and so on. Since the GDE can hardly be solved analytically, many methods were developed to solve it in the last century. Among them, the moment method (Hulburt and Katz 1964; Lee and Chen 1984; Yu et al. 2008; Xie 2014; Yu et al. 2015), the sectional method (Gelbard and Seinfeld 1980; Landgrebe and Pratsinis 1990; Friedlander 2000) and the direct simulation Monte Carlo (DSMC) method (Kruis et al. 2000; Loyalka 2003; Sheng and Shen 2007) are the most important ones. The DSMC is high efficient for multi-component aerosol dynamics and easy to couple with chemical or nuclear reactions; so it has been applied in many fields such as aerosol reactors and nuclear reactor safety (Efendiev and Zachariah 2002; Loyalka 2003). However, DSMC has not been reported in smoke-chamber researches.

In the present study, we examined the decay of high-concentration aerosol in a chamber experimentally, and then tried describing the decay by both the wall-loss correction and DSMC. The better method for high-concentration aerosol was recommended finally based on comparison with the experimental results.

2 DSMC Simulation

Aerosol dynamic in a chamber can be described by the GDE (Friedlander 2000)
$$\frac{{\partial C_{\text{d}} }}{\partial t} = \frac{1}{2}\sum {K(d_{i} ,d_{j} )C_{{{\text{d}},i}} C_{{{\text{d}},j}} } - C_{\text{d}} \sum {K(d,d_{i} )C_{{{\text{d}},i}} } - \beta_{\text{d}} C_{\text{d}} ,$$
where C d is the concentration of aerosol with a diameter of d, m−3; K is the coagulation coefficient, m3 s−1; β d is the decay coefficient of aerosol with a diameter of d, s−1.The subscript i and j refer to different sections (i.e., diameters, volumes or mass, etc.) of aerosol.

In the right hand of Eq. (1), the first two terms refer to the coagulation and the third term refers to the deposition. The coagulation coefficient K can be calculated by the classical formula by Fuchs (Friedlander 2000). The decay coefficient β d would be determined experimentally (see section below). The DSMC with Metropolis sampling algorithm (Palaniswaamy and Loyalka 2008) was adopted and improved in the present research because of its simplicity and high efficiency.

Coagulation in Eq. (1) can be simulated by DSMC as follows: the collision pair is chosen in an N × N collision matrix by the Metropolis sampling algorithm. Let i and j be the particles sampled for the current collision with the coagulation coefficient given as K (d i , d j ). Let i′ and j′ be the previous samples with the coagulation coefficient, K(d i′ , d j′ ). The criterion for sampling is given by Eq. (2) (Palaniswaamy and Loyalka 2008)
$${\text{RAND}} \le \frac{{K(d_{i} ,d_{j} )}}{{K(d_{i'} ,d_{j'} )}},$$
where RAND is a random number distributed uniformly between 0 and 1.
The same steps are repeated for another new pair of particles, i and j randomly chosen for collision. After every collision, the collision time or the time per collision, t c (s) is calculated as shown in Eq. (3), where N refers to the total number of particles before collision, V s (m3) refers to the simulation volume, and the factor 2 in the numerator eliminates the double counting of collisions occurring between two particles (Palaniswaamy and Loyalka 2008).
$$t_{\text{c}} = \left( {\frac{1}{N - 1} - \frac{1}{N}} \right)\frac{{2V_{\text{s}} }}{{K(d_{i} ,d_{j} )}}.$$
Deposition in Eq. (1) can also be simulated by the Metropolis sampling algorithm. The particle that deposits can be chosen by Eq. (4) and the time interval between two deposited particles, t d (s), can be derived as shown in Eq. (5) as the same principle as Eq. (3).
$${\text{RAND}} \le \frac{{\beta (d_{i} )}}{{\beta (d_{i'} )}}$$
$$t_{\text{d}} = \frac{{\ln \left[ {N/\left( {N - 1} \right)} \right]}}{{\beta (d_{i} )}}.$$
After coagulation and deposition are found, the corresponding time t c and t d are calculated to decide whether the event occurring is coagulation or deposition. The probability of coagulation (Sheng and Shen 2007)
$$P_{\text{c}} = \frac{{1/t_{\text{c}} }}{{1/t_{\text{c}} + 1/t_{\text{d}} }} = \frac{{t_{\text{d}} }}{{t_{\text{c}} + t_{\text{d}} }}.$$
Coagulation is selected by generating a random number RAND, if
$${\text{RAND}} \le P_{\text{c}} .$$

Otherwise, deposition is selected.

Because coagulation and deposition do not depend on each other, each of these events is statistically independent with a known probability. As a result, the time needed for an event, t (s), can be determined by:
$$t = \frac{{ - \ln \left( {\text{RAND}} \right)}}{{1/t_{\text{c}} + 1/t_{\text{d}} }}.$$

After each successful event, the time is incremented by t. The above steps are repeated until the desired extent of the processing time has been reached. It should be noted that both the coagulation and the deposition lead to a continuous decrease of the particle number in the simulated volume. In order to avoid the increase in statistical error associated with decreasing N, the simulated volume V s and the particle number N are doubled when N has dropped by half. The new particles in the added volume copy the properties of the old particles so as to conserve the statistical properties.

3 Wall-Loss Correction

If the first two terms about coagulation in Eq. (1) are neglected and the decay coefficient is constant, Eq. (1) could have an analytical solution. Deposition mainly includes gravitational settling and diffusion deposition. As a result, the decay coefficient β d can be divided into the gravitational settling decay coefficient β d,G (s−1) and the diffusion deposition decay coefficient β d,D (s−1), as shown in Eq. (9).
$$C_{\text{d}} (t) = C_{\text{d}} (0){\text{EXP}}\left[ { - \beta_{\text{d}} t} \right] = C_{\text{d}} (0){\text{EXP}}\left[ { - \left( {\beta_{{{\text{d}},{\text{D}}}} + \beta_{{{\text{d}},{\text{G}}}} } \right)t} \right].$$
The gravitational settling decay coefficient is usually calculated by Eq. (10) (Hinds 1999).
$$\beta_{\text{d ,G}} = \frac{{V_{\text{TS}} }}{H},$$
where V TS is the terminal settling velocity, m s−1 and H is the height of settling, m.

On the other hand, however, there are many opinions about the diffusion deposition decay coefficient in literatures, which can be classified into three forms: The first method is based on the thickness of boundary layer (Okuyama et al. 1986; Bunz and Dlugi 1986), and the second on the coefficient of the eddy diffusivity (Crump and Seinfeld 1981; Lai and Nazaroff 2000), while the third is simply obtained by fitting experimental data (Pierce et al. 2008). Among them, the first method is adopted in this work due to its clearer physical meaning though two parameters still need to be determined by experimental data.

$$\beta_{\text{d,D}} = \frac{D}{{\delta R_{\text{VS}} }},$$
$$\delta = aD^{b} ,$$
where D refers to diffusion coefficient of the aerosol, m s−2; δ is boundary layer thickness, m; R VS is the ratio of volume of the chamber to its surface area, m; a and b are parameters of data fitting.
The decay coefficient β d is taken place by deposition velocity u s (m s−1) in the following section for convenience of comparing with data in literatures.
$$u_{\text{d}} = \beta_{\text{d}} R_{\text{VS}} = \left( {\frac{{D^{1 - b} }}{{aR_{\text{VS}} }} + \frac{{V_{\text{TS}} }}{H}} \right)R_{\text{VS}}$$

4 Experimental

A stainless-steel cylinder container was used for experiments since it can resist blast of fireworks. It has a volume of 0.54 m3, a surface area of 3.8 m2, and a settling height of 0.55 m. Three kinds of aerosols were included in the experiments: Carbon black aerosol with diameter of 10–30 nm generated by Model GFG aerosol generator (Palas Inc. Germany), aerosol with diameter of 0.1–0.7 μm generated by fireworks (its main components are supposed to include carbon black and dust), and loess aerosol with diameter of 0.5–3 μm generated by a fluidized bed aerosol generator. Aerosol number concentration was measured by SMPS (Model 3936, TSI Inc., USA) and APS (Model 3310, TSI Inc., USA).

The initial pressure of the chamber was controlled to be lower than the ambient pressure. The generated aerosol was pumped into the chamber and let mixing well for half an hour. Subsequently, the aerosol concentrations were measured by SMPS and APS after some time. The sampling flowrate is lower than 1 L/min by using dilutor, and the total sampling volume for each time was controlled to be lower than 10% of volume of the chamber. After sampling for each time, clean air was charged into the chamber to keep the internal pressure consistent with the ambient pressure. The intervals between two samplings are longer than half an hour to keep the internal aerosol uniform. Dilution of aerosol concentration by charging clean air was then adjusted in data treatment.

5 Results and Discussion

5.1 The Decay Coefficient

Aerosol concentration in the chamber was measured as function of diameter and decay time. The number concentrations of aerosol were controlled below 109 m3 to avoid the effects of turbulent and coagulation (Okuyama et al. 1986; Hussein et al. 2009; Yu et al. 2013). The parameters a and b were fitted by the data to Eq. (9)–(12) and compared to those in literatures (as shown in Table 1). The corresponding deposition velocity u s of the experimental values and the calculated values were illustrated in Fig. 1. The u s for diameter around 1 μm was in consistent with the fitted curve and the curves from literatures. It implies that gravitational settling could be described well by Eq. (10). The main diverge comes from diffusion deposition when diameter is less than 0.8 μm. The fitted curve with a = 136 and b = 0.64 was in consistent with the experimental data well and showed obvious difference from those recommended by Okuyama et al. (1986) or Bunz and Dlugi (1986). The shape of the u sd curve fitted by the experimental data was much flatter than those from others, which was also found by Pierce et al. (2008). It implies that the boundary layer thickness δ may be sensitive to the experimental facilities and procedure, and must be determined experimentally.
Table 1

Comparison of the parameters in Eq. (3) in this paper with those in literatures








Okuyama et al. (1986)




Bunz and Dlugi (1986)




This paper

Fig. 1

Comparison of the fitted u d with the experimental data. Exp 1, Exp 2 and Exp 3 are three aerosols with different diameters. The curves follow the Eq. (9) and the parameters in Table 1

5.2 Aerosol Concentration Decay and Wall-Loss Correction

Aerosol concentration change was observed when aerosol was generated by firework which can produce a high-concentration aerosol rapidly. The concentration versus time was shown in Fig. 2 (square points). The concentration decay by wall loss was calculated by Eq. (9) using every experimental data as the initial value (see straight lines in Fig. 2). It is obvious that the wall-loss correction is valid when the aerosol concentration is lower than 104 cm−3. When the initial concentration is higher than 104 cm−3, the subsequent aerosol concentration can be overestimated if only wall-loss correction was considered.
Fig. 2

Comparison of the experimental aerosol concentrations with the calculated ones by the wall-loss correction. The square points with the dashed line are the experimental values; the solid lines are the calculated ones by Eq. (9) and using every experimental data as the initial value

5.3 Aerosol Concentration Simulation by DSMC

The aerosol concentration in the chamber was simulated by the DSMC with Metropolis sampling as described in the Sect. 1. The measured data in the first experimental were used as the initial concentration and size distribution in simulation. Particle density was assumed as 2300 kg m−3, and temperature and pressure were measured to be 299 K and 96 kPa, respectively. The simulated concentration and count median diameter (CMD) were compared to the experimental ones as shown in Fig. 3. The simulated values are in consistent with the experimental ones. The concentration showed a tendency of decreasing rapidly firstly and then slowly. The CMD increased at first and later was close to a steady value. It could be drawn that coagulation is the main mechanism controlling aerosol number concentration decay when the aerosol number concentration is high, and gravitational settling and diffusion deposition show their effect when the concentration is low. According to the results above mentioned, the wall-loss correction is valid when the aerosol number concentration is lower than 104 cm−3, which is consistent with Hussein et al. (2009) and Yu et al. (2013). Meanwhile, DSMC can predict the aerosol decay when the aerosol number concentration is higher than 104 cm−3.
Fig. 3

Comparison of the measured aerosol concentrations and CMD with the results by DSMC

6 Conclusions

The main mechanisms of wall loss were analyzed and the parameters for the diffusion deposition were determined experimentally. The wall-loss correction under the present conditions was validated with aerosol number concentration lower than 104 cm−3. If the concentration is higher, coagulation must be taken into consideration, as consistent with Hussein et al. (2009) and Yu et al. (2013). A DSMC with metropolis sampling was established to describe aerosol dynamics in a chamber, which gives results in consistent with experimental data even the aerosol number concentration is as high as 106 cm−3.


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Copyright information

© Institute of Earth Environment, Chinese Academy Sciences 2017

Authors and Affiliations

  1. 1.Northwest Institute of Nuclear TechnologyXi’anChina
  2. 2.Atmospheric Environment InstituteChinese Research Academy of Environmental SciencesBeijingChina

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