# Decay of High-Concentration Aerosol in a Chamber

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## Abstract

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 10^{4} cm^{−3}, and the DSMC results are consistent to the experimental data for concentration ranging from 10^{4} cm^{−3} to more than 10^{6} cm^{−3}.

## Keywords

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 10^{4} 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

*C*

_{d}is the concentration of aerosol with a diameter of

*d*, m

^{−3};

*K*is the coagulation coefficient, m

^{3}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.

*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)

*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}(m

^{3}) 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*

_{d}(s), can be derived as shown in Eq. (5) as the same principle as Eq. (3).

*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)

Otherwise, deposition is selected.

*t*(s), can be determined by:

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

*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).

*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.

*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.

*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.

## 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 m^{3}, a surface area of 3.8 m^{2}, 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

^{9}m

^{3}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*

_{s}–

*d*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.

### 5.2 Aerosol Concentration Decay and Wall-Loss Correction

^{4}cm

^{−3}. When the initial concentration is higher than 10

^{4}cm

^{−3}, the subsequent aerosol concentration can be overestimated if only wall-loss correction was considered.

### 5.3 Aerosol Concentration Simulation by DSMC

^{−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 10

^{4}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 10

^{4}cm

^{−3}.

## 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 10^{4} 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 10^{6} cm^{−3}.

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