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Molecular dynamics simulation on agglomeration and growth behavior of dust particles during flue gas filtration
Journal Pre-proof Molecular dynamics simulation on agglomeration and growth behavior of dust particles during flue gas filtration Yinsheng Yu, Yubing Tao, Jie Sun, Ya-Ling He PII:
S0032-5910(19)30863-0
DOI:
https://doi.org/10.1016/j.powtec.2019.10.029
Reference:
PTEC 14777
To appear in:
Powder Technology
Received Date: 24 September 2018 Revised Date:
22 April 2019
Accepted Date: 9 October 2019
Please cite this article as: Y. Yu, Y. Tao, J. Sun, Y.-L. He, Molecular dynamics simulation on agglomeration and growth behavior of dust particles during flue gas filtration, Powder Technology (2019), doi: https://doi.org/10.1016/j.powtec.2019.10.029. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Time-lapse images of the agglomeration of dust particles and growth behaviors of dust clusters
Molecular dynamics simulation on agglomeration and growth behavior of dust particles during flue gas filtration Yinsheng Yua, Yubing Taoa,* , Jie Sunb, Ya-Ling Hea 1
(a. Key Laboratory of Thermo-fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China; b. School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China)
Abstract: High efficiency purification of dust particles contained in industrial flue gas is urgently needed to mitigate environmental pollution and improve waste heat recovery efficiency. The agglomeration and growth behavior of dust particles has significant effects on filtration efficiency of industrial flue gas. In this paper, in order to reveal the microscopic mechanism of dust particles agglomeration and growth, three kinds of typical components in industrial flue gas, such as steam (H2O), PAHs (naphthalene) and dust particles (SiO2) were selected to establish a molecular dynamics (MD) simulation system. The agglomeration behavior of dust particles and the formation and growth process of dust clusters were characterized by MD simulation. The effects of temperature, channel width, cooling rate and gas composition on the agglomeration behavior of dust particles and the growth of dust clusters were investigated. It is found that the formation and growth of dust clusters are driven by agglomeration of dust particles. The decrease of gas temperature, cooling rate and channel width can accelerate the agglomeration of dust particles and the growth of dust clusters, which is beneficial to dust particles filtration. In addition, the hydrogen bonds formed between the H2O molecules and SiO2 particles can promote the adsorption of SiO2 particles to the H2O molecules, which is also beneficial to the formation and growth of dust clusters. So increasing the content of
*
Corresponding author. Tel.: +86 29 82664349; fax: +86 29 82665445. E-mail address: [email protected] (Y.B. Tao)
steam in industrial flue gas is helpful to the growth of dust clusters and the filtration of dust particles. Keywords: Flue gas; Dust particles; Agglomeration; Molecular dynamics simulation
1 Introduction Coal has been playing a major role in the world energy consumption structure for a long time, because of its low cost, abundance and broad distribution etc. It has been widely used in many industrial fields including electricity generation, steel production, winter heating and conversion to gaseous fuels [1-4]. However, the industrial flue gas discharged from the coal-fired power plants and steel plants has been considered to be the main source of a large number of pollutants, such as particulate matter (PM), NOx, SOx, heavy metals, organic pollutants, and polycyclic aromatic hydrocarbons (PAHs) [5-7]. In addition, the industrial flue gas usually has high temperature, so a lot of energy will be wasted if the industrial flue gas emissions into the atmosphere directly. In order to recover the waste heat from the industrial flue gas, heat exchangers have been widely used. However, the deposition of dust particles accompanied by condensation, solidification and adhesion of condensable gases on the surface of the heat exchangers has made serious performance deterioration of the heat exchangers [8-11]. Therefore, the filtration of dust particles contained in industrial flue gas has received widespread concern. Granular bed filter (GBF) is considered as an excellent candidate for dust particles filtration because of its low cost and high efficiency. In recent years, GBF has been widely used in the purification of industrial flue gas with complex composition and high temperature [12-14]. When the industrial flue gas flows through a GBF, the suspended dust particles will be captured and deposited on the surface of filter granules under the influence of various forces. Furthermore, the filter granules can be
cleaned and regenerated for continuous operation. Over the past few years, a variety of studies have been carried out to evaluate and improve the performance of GBF based on experimental and numerical simulation methods. The parameters that determine the filtration efficiency are concluded: superficial velocity, bed depth, granular size, dust particles size and thickness of the dust cake etc. [15]. Guan et al. [14] found that increasing the superficial velocity of the industrial flue gas could improve the filtration efficiency for dust particles greater than 7 µm while it is useless for the particles smaller than 5 µm. The filtration efficiency is also approximately linearly correlates with the granule diameter. Chen et al. [16] experimentally investigated the filtration and resistance characteristics of the moving GBF used for filtration of dust particles. The flow patterns of the filter granules, filtration efficiency and pressure drop under different filtration operating conditions at room temperature were studied. It was found that the decrease of the GBF porosity leads to the increase of both the filtration efficiency and the filtration resistance when the amount of smaller filter granules increased. Chen et al. [17] developed an experimental method to understand the formation and growth of dust cakes and found that the thickness of the dust cake could be controlled. Although researchers have done a lot of experiments and simulation studies on the improvement of the filtration performance of GBF, the filtration mechanism of dust particles is still unclear. Because there are diverse compositions (e.g. solid particles, condensable gases etc.) and complicated interactions (e.g. the collision and agglomeration of solid particles, the condensation of condensable gases and the adsorption between the solid particles and condensable gases) in industrial flue gas. To achieve better filtration performance, the microscopic filtration mechanism, such as the interactions between the solid particles and condensable gases, and their effects
on dust particles agglomeration, dust clusters formation and growth are required. Unfortunately, the microscopic behaviors are difficult to be observed in detail by macroscopic experimental methods. Thus, the investigations from the microscopic point of view is urgently needed to develop filtration theory for dust particles and guide the design of GBF. Molecular dynamics (MD) simulation has been proved to be powerful tools to gain insight into behaviors of systems and provides ultimate detail for addressing specific questions concerning inherent mechanism at nanoscale. To understand the failure mechanisms of the asphalt concrete resulted from the moisture damage, Dong et al. [18] carried out MD simulations to characterize the nanostructure of the asphaltaggregate interface. The simulation results indicate that at the asphalt-aggregate interface, the nanostructure is constructed by periodical molecular bulgy boundaries and central cavities. Besides, it was found that the intermolecular gaps can be filled by naphthene aromatics, and molecular micelles can be lubricated by saturates. Lu et al. [19] studied the mechanical properties and failure behavior of asphalt-aggregate interface using the MD method. Ding et al. [20] carried out MD simulations to investigate the diffusion between virgin and aged asphalt binders. The model of aged binder was constructed by increasing the asphaltenes ratio on the basis of virgin binder. The simulation results show that the diffusion of large molecules in asphalt was a critical factor for the binder’s diffusion, where it was more susceptible to the changes of temperature. The formation of nanoparticles is an important issue for environment assessments. However, the exact mechanism of the diffusion process between virgin and aged asphalt binders is still unclear. Sergio et al. [21] carried out a set of MD simulations to study the nanoparticle-formation from bioethanol-gasoline blend emissions and found that phenanthrene and acetaldehyde quickly generate
nanoparticles with dimensions of 2-5 nm in vacuum. Furthermore, acetaldehyde appears to localize on the surface of the formed nanoparticles, and seemingly acts with the planar geometry of phenanthrene as a facilitator for CO2 absorption. Zhao et al. [22] performed MD simulations to obtain the transport diffusion coefficient from self-diffusion coefficient via thermodynamic factor based on the Wiser bituminous coal model, the properties of CO2 and CH4 diffusion in coal micropores were obtained. Zhou et al. [23] proposed a novel MD workflow to generate organic pores on residuetype kerogen molecules and to simulate the gas adsorption in the pores. Zhang et al. [24] carried out MD simulations to investigate the adsorption behavior of different surfactants-water-oil mixture on quartz surfaces. Wu et al. [25] studied and revealed the mechanisms about adsorption and displacement of methane in carbon nanochannels using MD simulations. They found that as the width of slit pore increases, the structure of adsorbed methane transforms from single adsorption layer to four adsorption layers. From the above literature review, it can be found that MD simulation is well suited to describe the behaviors of diffusion, agglomeration and growth from microscopic point of view. Consequently, in this paper, MD simulations were performed on a flue gas system to reveal the agglomeration behavior of dust particles and the formation and growth process of dust clusters in nanochannel, and analyze the effects of temperature, channel width, cooling rate and gas composition on them. The results are expected to be useful to understand the filtration mechanism and improve the filtration efficiency of dust particles contained in industrial flue gas.
2 Simulation models and methods MD simulations provide the methodology for detailed microscopic modeling on molecular scale. In MD simulations, the motion of atoms is dominated by the second
law of Newton. Firstly, the classical Newton’s equation is applied and solved, then the molecular positions, velocities and trajectories are obtained, finally thermodynamic properties are estimated from the molecular trajectories. Hence, MD is a kind of method which describes the movement, structure and geometry of molecules to reveal the micro/nano-mechanisms at molecular scale. 2.1 Simulation model The schematic for a GBF is shown in Fig. 1 (a). The industrial flue gas flows through the GBF, where the dust particles contained in industrial flue gas are captured by the filter granules. To simulate the agglomeration process of dust particles at molecular scale, MD models are developed. Based on the in-depth analysis of the industrial flue gas components and the filtering process of GBF, three kinds of typical components: steam (H2O), PAHs (naphthalene) and dust particles (SiO2) which are shown in Fig. 1(b) were selected to establish a MD system, as shown in Fig. 1(c). The configurations of atoms are visualized by the Material Studio platform [26]. The surface of silica (-1 0 0) was selected to build layers with different channel widths. The scales in the direction of X and Y are expressed in L and H respectively. While T, W and D represent the thickness of the surface, the width of the channel and diameter of SiO2 particles respectively. N1, N2 and N3 represent the number of SiO2 particles, H2O molecules and naphthalene molecules in each system respectively. The values of the above parameters are shown in Tab. 1. Three models with different channel widths are established to evaluate the effect of channel width on the agglomeration of dust particles and formation and growth of dust clusters, which are named model A, model B and model C respectively. Similarly, the model E, model F and model G with different components are used to study the effect of gas composition on the agglomeration process. In all simulation models, the values of the lattice
parameters α, β and γ which determine the relative orientation of the lattice vectors are all 90°. 2.2 Force field All MD calculations were carried out using the Materials Studio software package including Discover and Amorphous modules that have already been successfully used to explore diffusion, agglomeration and adsorption processes in different fields [20, 27, 28]. The total potential energy is based on the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field, which is a general all-atom force field and first ab initio force field. The COMPASS force field has been parameterized, tested and validated, which is applicable for simulation of biological, organic and main-group inorganic molecules to determination of structures and dynamics. The COMPASS potential energy function is shown as follows [29]:
Etotal =
∑ E ( b ) + ∑ Eθ (θ ) + ∑ b
bond
angle
Eϕ (ϕ ) +
dihedral
+ ∑ E ( b,θ , ϕ ) + Ecoulomb + Evdw
∑ out -of -plane
Eχ ( χ ) (1)
cross
Where the terms of Eb ( b ) , Eθ (θ ) , Eϕ (ϕ ) , Eχ ( χ ) and E ( b, θ , ϕ ) represent the contributions of bond stretching, angle bending, torsion angle, out-of-plane angle coordinates and cross-coupling interactions respectively. The items Ecoulomb and Evdw represent non-bond interactions, which can be expressed as:
Ecoulomb = ∑ i> j
Evdw
qi q j rij
6 r 0 9 rij0 ij = ∑ ε ij 2 + 3 r rij ij
(2)
(3)
Where qi and qj are the charges of atoms i and j with a distance rij, ε is the potential well depth for the interaction between the two atoms.
2.3 Simulation details In the present study, MD simulations are performed by Materials Studio. Some of the properties are analyzed by our homemade PERL scripts. Periodic boundary conditions are applied in X, Y and Z directions. Nose Hoover thermostat and barostat were applied to control the temperature and pressure of systems. All the simulations were performed with a time step of 1 fs. The cutoff distance of each system was set as 12.5 Å. The van der Waals and Coulomb interactions were calculated by Atom based [30] and Eward [31] method. Besides, the equations of motion were integrated by the Velocity Verlet algorithm. Initially, the Forcite module was used to geometrically optimize the simulation systems, so that the total energy of the system was minimized. In the process of geometric optimization, smart minimizer algorithm with an iterative step of 1000 was used to refine the conformation, which starts with the steepest descent method, followed by the conjugate gradient method and ends with a Newton method. Then, the systems were equilibrated at 998 K for 100 ps in constant-volume, constant-temperature NVT ensemble. Next, the system is cooled with a temperature interval of 100 K until the temperature of the system reaches 298 K. The system runs 100 ps at each temperature to achieve the equilibrium state, and runs another 50 ps to calculate the physical quantities. Finally, in order to study the effects of the width and cooling rate on the agglomeration process, different cooling rates (e.g. 3.5 K/ps, 1.75 K/ps and 0.875 K/ps) were used to cool the system down to 298 K respectively. After the system reaches the equilibrium state, the system runs 100 ps again. In this way, the physical quantity of the system was calculated.
3 Results and discussion
3.1 Evolutions of dust particles agglomeration and dust clusters growth process Typical coordinate snapshots of the cooling process from 998 K to 298 K with a cooling rate of 3.5 K/ps in the system of model A are shown in Fig. 2. At the initial state, the system has experienced sufficient relaxation, therefore it can be seen from Fig. 2 that steam (H2O), PAHs (naphthalene) and dust particles (SiO2) are all distributed evenly in the nanoscale channel at 0 ps. During the cooling process, the H2O molecules and naphthalene molecules are observed to be adsorbed on the surface of nanoscale SiO2 particles at 20 ps and then agglomerate with other SiO2 particles, so that the dust clusters are formed and then they grow further. This phenomenon indicates that the formation and growth of dust clusters are driven by agglomeration of SiO2 particles. As the cooling process continues, more H2O molecules and naphthalene molecules are adsorbed, which subsequently leads to agglomeration of the SiO2 particles. According to the time-lapse images, the phase transition of H2O molecules and naphthalene molecules has occurred successively with the decrease of temperature, which thus strengthen the adsorption of H2O molecules and naphthalene molecules on the surface of nanoscale SiO2 particles and promote the formation of dust clusters. The dust cluster structure is more stable, and the growth process is clearly observed at 80 ps and 100 ps, which is roughly in line with few results of similar simulations and experiments [32-35].
3.2 Effect of temperature on agglomeration of dust particles According to the viewpoint of classical statistical mechanics, the dynamic behavior of the atom is closely related to temperature. The agglomeration of SiO2 particles in this study is also closely related to the dynamic behavior of the atoms, which means temperature has important effect on the agglomeration and growth of the
dust clusters. Therefore, the mean square displacement (MSD) and self-diffusion coefficient of the system were calculated to investigate the effects of temperature, and the radial distribution function (RDF) was also calculated to reflect the microstructures of the system.
3.2.1 Diffusion characteristics Indeed, for a given material, the self-diffusion coefficient is generally a singlevalued function of temperature when the material is in a single phase. Besides when the state of the substance changes from gaseous state to liquid state and then to solid state, the diffusion ability of the system is gradually weakened. Therefore, during the cooling process, the self-diffusion coefficient can reflect the physical state of the H2O molecules and naphthalene molecules and affect the agglomeration of SiO2 particles. Thus the self-diffusion coefficient was calculated to describe the movement ability of the molecules in the channel. According to the Einstein equation, the self-diffusion coefficient (D), related to the MSD function, can be expressed as follows [36]: 1 d N (4) lim ∑ MSD 6 t → ∞ dt i =1 Where MSD is the mean square displacement of the system, which means a D=
measure of the average distance of a given particle in a system travels, t is the simulation time. MSD is a typical dynamic parameter, which can be defined as:
r r 2 MSD = R ( t ) − R ( 0 )
(5)
r Where R ( t ) is the position of atom at time t. The value of self-diffusion
coefficient can be calculated by the slope of the MSD curve. The MSD of H2O molecules and naphthalene molecules for different temperatures from 998 K to 298 K are plotted in Fig. 3. The MSD increases with the simulation time and the relationships between the MSD and simulation time are almost linear after sufficient simulation time, e.g. 20 ps in our simulations. Thus, the
diffusion coefficient is defined as the slope of the MSD-simulation time curves for the simulation time larger than 20 ps. Besides, the MSD increases as temperature increases, which is because the atoms have higher degree of mobility for higher temperature. Moreover, the variation trend of MSD of H2O molecules with temperature is consistent with few available results [34, 35], which further implies the reliability of our calculation method. As mentioned before, the agglomeration and growth behavior of SiO2 particles surrounded by H2O molecules and naphthalene molecules are different during the cooling process at different time and temperature, which are closely related to the diffusion coefficient of molecules. Therefore, to give a comprehensive understanding of diffusion of the H2O molecules and naphthalene molecules in the system, the self-diffusion coefficients as a function of temperature were calculated and presented in Fig. 4. It is found that the self-diffusion coefficients of naphthalene molecules are much lower than that of H2O molecules when the temperature is higher than 640 K. For example, when the temperature is 998 K, the self-diffusion coefficient of H2O molecules and naphthalene molecules are 39.052×10-8 m2/s and 11.698×10-8 m2/s respectively, the self-diffusion coefficient of naphthalene molecules was 70.045% lower than that of H2O molecules. However, as the temperature continues to decrease, the self-diffusion coefficient of naphthalene molecules begins to be higher than that of H2O molecules. When the temperature is 598K, the corresponding self-diffusion coefficient are 0.046×10-8 m2/s and 0.410×10-8 m2/s respectively, which means the self-diffusion coefficient of H2O molecules was 88.915% lower than that of naphthalene molecules. The results are attributed to the difference between H2O molecules and naphthalene molecules microstructure. On the one hand, due to the strong polar oxygen atoms, it is easier to form hydrogen bonds between H2O molecules, which are absent in naphthalene molecules; on the other
hand, when the H2O molecules are in liquid state, the distance between molecules is close, which lead to the increase of hydrogen bond number density, so the effect of hydrogen bond on the ability of diffusion is obvious, which limits the diffusion of H2O molecules. With the increase of temperature, the kinetic energy of molecules increased, which weakened the role of hydrogen bonds, the effect of temperature become the dominant factor, and significantly enhance the ability of molecular diffusion.
3.2.2 Radial distribution function The radial distribution function (RDF) represents the atomic density varies as a function of the distance from one designated atom, which is donated by g(r). Usually, RDF is used to analyze the phase state of particles in a system. The result of g(r) is given by the expression [37]:
1 χα χ β ρ gαβ ( r ) = N
Nα N β
∑∑ δ ( r − r − r ) i =1 i =1
i
j
(6)
Where, χα and χβ are the mole fraction of chemical type α and β, ρ is the overall number density, N is the total number of atoms, Nα and Nβ is the number of atoms of chemical type α and β. Here, the RDFs of H2O molecules and naphthalene molecules in the systems are plotted in Fig. 5. The curves of RDF under different agglomeration states are different. So the agglomeration states of the system roughly determined according to the corresponding RDF curves at different temperatures. For H2O molecules, at the condition of 998 K, the first peak of the RDF is 0.95 Å, and from 898 K to 298 K, the first peak of the RDFs is all at 0.97 Å. Similarly, for naphthalene molecules, at temperatures of 998 K and 898 K, the first peak of the RDF is 1.11 Å, and from 898 K to 298 K, the first peak of the RDFs is all at 1.09 Å. The peaks of radial distribution
functions of the H2O molecules and naphthalene molecules are slightly higher and steeper at lower temperatures. It was indicated that as the temperature decreases, more molecules will be adsorbed on the surface of the SiO2 particles, which makes the agglomeration more significant and contributes to the growth of dust clusters.
3.3 Effect of channel width on agglomeration of dust particles As pointed out by many researchers [38-40], cooling rate is an important factor in many thermo-physical processes, e.g., nucleation, agglomeration and dissolution. The few macroscopic experimental results also show that cooling rate would affect the filtration of dust particles. However, the discussion about the effect of cooling rate on agglomeration mechanism from microscopic point of view is especially rare. Consequently, MD is employed hereby to study the agglomeration of SiO2 particles with different cooling rates of 3.5 K/ps, 1.75 K/ps and 0.875 K/ps. In addition, the channel width affects the distribution of the SiO2 particles, H2O molecules and naphthalene molecules, which means the interaction between atoms was significantly affected by the channel width, thus the agglomeration process was also affected. Therefore, considering the factor of channel width, the models A, B, and C with different channel widths as shown in Tab. 1, have been simulated at different cooling rates, and the simulation results are compared to reveal the effect of cooling rate and channel width on the agglomeration process. The time-lapse images for the agglomeration of dust particles and the growth behavior of dust clusters under different channel widths and cooling rates are presented in Fig. 6. The systems are divided into 50 layers along the Z-axis and the density distributions of SiO2 particles, H2O molecules and naphthalene molecules along the direction of the Z-axis were calculated to accurately reflect the size of the dust clusters, which are shown in Fig. 7. It was found that in the initial state of
simulation, SiO2 particles, H2O molecules and naphthalene molecules distributed evenly in the channel, as shown in Fig.6 (a), (e) and (i). This phenomenon can also be reflected from the density distribution curves, as shown in Fig. 7, where the curves are almost parallel to the X-axis. Then with time ongoing, the agglomeration occurs and a peak of the density distribution curve appears when a dust cluster is formed due to agglomeration. It is worth noting that at the same cooling rate, the size of dust clusters decreases gradually as the channel width increases. For model A, B and C, the peak value of density for SiO2 particles at the end of the simulations are 0.44 g/cm3, 0.27 g/cm3 and 0.15 g/cm3 respectively. As the width of the channel increases, the peak value of the density is reduced by 38.6% and 65.9% respectively. This can be explained that with the increase of the channel width, the distribution of molecules within the channel becomes looser, the average distance between atoms increases, which weakens the interaction between atoms, so the molecules collide with molecules nearby, and the smaller dust clusters are formed because of the agglomeration.
3.4 Effect of cooling rate on agglomeration of dust particles However, in the same channel width, the size of dust clusters increases with the decrease of cooling rate. In order to study the effect of cooling rate on the dust particles agglomeration and dust cluster growth, the density distribution of SiO2 particles along Z-axis was calculated based on the model A and it is shown in Fig. 8. As shown in Fig. 8, the initial configuration is consistent and it can be seen that the SiO2 particles fluctuates up and down near the average density in the channel at the initial time, which indicates that the distribution of SiO2 particles is basically uniform. When the system is cooled at different cooling rates, all density curves have a peak value. This implies the occurrence of agglomeration and the growth of dust clusters.
When the cooling rate is 0.875 K/ps, 1.75 K/ps and 3.5 K/ps, the peak values are 0.47 g/cm3 (z=66.84 Å), 0.43 g/cm3 (z=80.67 Å) and 0.33 g/cm3 (z=71.45 Å) respectively. With the cooling rate increasing from 0.875 K/ps to 3.5 K/ps, the peak values are reduced about 8.51% and 23.26%. In this study, the temperature difference is fixed, so the cooling rate is mainly reflected in the simulation cooling time. With the decrease of cooling rate, the cooling process proceeds slowly, and the longer it takes to reach the equilibrium state at the target temperature. So the growth time of dust cluster during the cooling process increases, it is helpful to the formation of large dust clusters. To further study this phenomena, the average number of hydrogen bonds in the system is calculated and shown in Fig. 9. In the MD simulation, the concept of hydrogen bonds has been proposed by many researchers [41-43]. In this study, the hydrogen bonds calculation tool creates a hydrogen bond between two atoms if the following criteria are met. One atom is a hydrogen atom, the hydrogen atom is single bonded and the attached atom may act as a hydrogen bond donor. The other atom may act as a hydrogen bond acceptor and has at least one lone electron pair. The distance between the hydrogen atom and the acceptor is less than or equal to the maximum hydrogen-acceptor distance which specifies the maximum distance (in Å) between the hydrogen and the acceptor atom with a range of 0 to 4 Å. Similarly, the value of the angle formed by the donor, hydrogen and acceptor atoms is at least the minimum donor-hydrogen-acceptor angle, which specifies the minimum angle between the donor, hydrogen and acceptor atom in degrees with a range of 0 to 180°. If both the hydrogen and acceptor atom are within the same molecule, they are separated by at least four nearest neighbor shells [26]. As shown in Fig. 9, the number of the average hydrogen bonds is greatly reduced because of the formation of dust clusters. For the
model A, B and C, the numbers of hydrogen bonds in the initial state are 2.14, 2.17, 2.12 respectively, as the cooling process proceeds, the number of hydrogen bonds decreases. With the cooling rate decreasing from 3.5 K/ps to 0.875 K/ps, the numbers of hydrogen bonds are reduced about 13.79%, 14.99% and 16.51% for model A. Therefore, the reduction of the number of hydrogen bonds increases with the decrease of cooling rate. For each cooling rate, the existence of hydrogen bonds at the beginning of cooling process accelerated the formation of large dust clusters. As the cooling process goes on, the molecular diffusion capacity slows down and the larger dust clusters begin to form, which reduces the average contact surface area between the molecules, thus the number of hydrogen bonds is reduced. Hence the decrease of cooling rate is beneficial to the formation of larger size dust clusters.
3.5. Effect of gas composition on the agglomeration of dust particles In order to study the influence of gas composition on particle agglomeration, cases based on the model E, F and G (as described in Tab. 1) were investigated. The snapshots of the systems at the initial and the end states are shown in Fig. 10. The systems are divided into 50 layers along the Z-axis, the density distributions of SiO2 particles in each layer are calculated, in particular, the calculation results in the range of 70.77 Å to 223.63 Å along the Z-axis are shown in Fig. 11. It can be seen from the density distribution curves in Fig. 11(a) that in the initial state (0 ps), SiO2 distributes uniformly along the Z-axis in the systems. However, in the final state (100 ps), the density distribution curves of model E, F and G appear a significant peak value which means the formation of dust clusters, as mentioned earlier. It is worth noting that the peak value of the curves of model F and model G are significantly higher than that of model E, which indicates both the adsorption of H2O molecules and naphthalene molecules on the surface of Si2O particles are beneficial to the agglomeration of Si2O
particles and the formation of larger size dust clusters. It can also be seen from Fig. 11(b) that the peak value of density distribution curve for model F is obviously higher than that for model G, the peak values are 0.31g/cm3 for model F at z=121.72 Å and 0.22g/cm3 for model G at z=195.32 Å respectively. It can be concluded that the H2O molecules are more beneficial to the agglomeration of SiO2 particles than the naphthalene molecules. As mentioned above, the phenomenon can be explained that the formation of hydrogen bonds between H2O molecules and SiO2 particles in model F but inexistent in model E and G will promote the interaction between atoms, which is beneficial to the formation and growth of dust clusters.
4. Conclusion In order to reveal the mechanism of dust particles agglomeration and dust clusters formation and growth during flue gas filtration, in this paper, MD simulations were carried out on molecular point of view. Three kinds of typical components, which consist of steam (H2O), PAHs (naphthalene) and dust particles (SiO2), were selected to establish a system. The agglomeration behavior of dust particles and growth of dust clusters were characterized. And the effects of temperature, channel width, cooling rate and gas composition on the agglomeration of dust particles and growth of dust clusters were investigated. The conclusions can be summarized as follows: (1) With the decrease of temperature, the diffusion ability of both H2O molecules and naphthalene molecules are significantly reduced, so it is helpful to the adsorption of molecules on the surface of dust particles. Thus, the decrease of temperature contributes to the formation and growth of dust clusters. (2) With the increase of the channel width, the distribution of molecules within the channel become looser, the average distance between atoms increases, which weakens the interaction between atoms. It is unfavorable to the growth of dust clusters.
(3) The decrease of cooling rate is beneficial to the formation of larger size of dust clusters. (4) H2O molecules are more beneficial to the agglomeration and growth of SiO2 particles than the naphthalene molecules. So increasing the content of steam in the flue gas are helpful to the filtration of dust particles.
Acknowledgements The present work is supported by the National Key R&D Program of China (2016YFB0601100).
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Tab. 1 Description of all MD models Model
N1 (SiO2)
N2 (H2O)
N3 (naphthalene)
W(Å)
H(Å)
T(Å)
L(Å)
D(Å)
A B C E F G
50 50 50 50 50 50
500 500 500 0 500 0
200 200 200 0 0 200
187.19 242.23 350.27 242.23 242.23 242.23
60.51 60.51 60.51 60.51 60.51 60.51
21.65 21.65 21.65 21.65 21.65 21.65
60.51 60.51 60.51 60.51 60.51 60.51
10 10 10 10 10 10
Flue gas flow
...... . . .. ....... ... ...... ..... . . . .. ..... ....... ... .... . . . . . ...... . . ...
O D=10Å SiO2 (Dust particles)
H2 O (Steam)
Naphthalene(PAHs)
C
(b)
H W
Si y
Clean gas flow
(a)
T
H
T
(c)
x
z
(d)
Fig. 1 Simulation system:(a) A schematic diagram of the filtration process in a GBF, (b) Three kinds of components containing in flue gas, (c) Simulation model, (d) Atomic species
Fig. 2 Time-lapse images of the agglomeration of dust particles and growth behaviors of dust clusters
(a) naphthalene (b) H2O Fig. 3 Variation of mean square displacement
Fig. 4 Variation of self-diffusion coefficient
(a) naphthalene-naphthalene
(b) H2O-H2O
Fig. 5 Typical radial distribution functions
Model A Model B Model C Fig. 6 Time-lapse images of the agglomeration and growth behaviors of dust particles. (a), (e), (i) initial state; (b), (f), (j) c1=3.5 K/ps, final state; (c), (g), (k) c2=1.75 K/ps, final state; (d), (h), (l) c3=0.875 K/ps, final state
Fig. 7 Density distribution of SiO2 particles, H2O molecules and naphthalene molecules along Z-axis
Fig. 8 Density distribution of SiO2 particles along Z-axis
Fig. 9. The average number of hydrogen bonds in the system
z a
b
c
x
y
(a) Model E (b) Model F (c) Model G Fig. 10 Time-lapse images of the agglomeration and growth behaviors of dust particles with different gas composition
(a) t=0 ps (b) t=100 ps Fig. 11 Density distribution of dust particles along Z-axis direction
1 The microscopic mechanism of dust particles agglomeration and growth was revealed. 2 The growth of dust clusters are driven by agglomeration of dust particles. 3 The factors affecting the dust growth behavior were determined.
S0032-5910(19)30863-0
DOI:
https://doi.org/10.1016/j.powtec.2019.10.029
Reference:
PTEC 14777
To appear in:
Powder Technology
Received Date: 24 September 2018 Revised Date:
22 April 2019
Accepted Date: 9 October 2019
Please cite this article as: Y. Yu, Y. Tao, J. Sun, Y.-L. He, Molecular dynamics simulation on agglomeration and growth behavior of dust particles during flue gas filtration, Powder Technology (2019), doi: https://doi.org/10.1016/j.powtec.2019.10.029. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Time-lapse images of the agglomeration of dust particles and growth behaviors of dust clusters
Molecular dynamics simulation on agglomeration and growth behavior of dust particles during flue gas filtration Yinsheng Yua, Yubing Taoa,* , Jie Sunb, Ya-Ling Hea 1
(a. Key Laboratory of Thermo-fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China; b. School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China)
Abstract: High efficiency purification of dust particles contained in industrial flue gas is urgently needed to mitigate environmental pollution and improve waste heat recovery efficiency. The agglomeration and growth behavior of dust particles has significant effects on filtration efficiency of industrial flue gas. In this paper, in order to reveal the microscopic mechanism of dust particles agglomeration and growth, three kinds of typical components in industrial flue gas, such as steam (H2O), PAHs (naphthalene) and dust particles (SiO2) were selected to establish a molecular dynamics (MD) simulation system. The agglomeration behavior of dust particles and the formation and growth process of dust clusters were characterized by MD simulation. The effects of temperature, channel width, cooling rate and gas composition on the agglomeration behavior of dust particles and the growth of dust clusters were investigated. It is found that the formation and growth of dust clusters are driven by agglomeration of dust particles. The decrease of gas temperature, cooling rate and channel width can accelerate the agglomeration of dust particles and the growth of dust clusters, which is beneficial to dust particles filtration. In addition, the hydrogen bonds formed between the H2O molecules and SiO2 particles can promote the adsorption of SiO2 particles to the H2O molecules, which is also beneficial to the formation and growth of dust clusters. So increasing the content of
*
Corresponding author. Tel.: +86 29 82664349; fax: +86 29 82665445. E-mail address: [email protected] (Y.B. Tao)
steam in industrial flue gas is helpful to the growth of dust clusters and the filtration of dust particles. Keywords: Flue gas; Dust particles; Agglomeration; Molecular dynamics simulation
1 Introduction Coal has been playing a major role in the world energy consumption structure for a long time, because of its low cost, abundance and broad distribution etc. It has been widely used in many industrial fields including electricity generation, steel production, winter heating and conversion to gaseous fuels [1-4]. However, the industrial flue gas discharged from the coal-fired power plants and steel plants has been considered to be the main source of a large number of pollutants, such as particulate matter (PM), NOx, SOx, heavy metals, organic pollutants, and polycyclic aromatic hydrocarbons (PAHs) [5-7]. In addition, the industrial flue gas usually has high temperature, so a lot of energy will be wasted if the industrial flue gas emissions into the atmosphere directly. In order to recover the waste heat from the industrial flue gas, heat exchangers have been widely used. However, the deposition of dust particles accompanied by condensation, solidification and adhesion of condensable gases on the surface of the heat exchangers has made serious performance deterioration of the heat exchangers [8-11]. Therefore, the filtration of dust particles contained in industrial flue gas has received widespread concern. Granular bed filter (GBF) is considered as an excellent candidate for dust particles filtration because of its low cost and high efficiency. In recent years, GBF has been widely used in the purification of industrial flue gas with complex composition and high temperature [12-14]. When the industrial flue gas flows through a GBF, the suspended dust particles will be captured and deposited on the surface of filter granules under the influence of various forces. Furthermore, the filter granules can be
cleaned and regenerated for continuous operation. Over the past few years, a variety of studies have been carried out to evaluate and improve the performance of GBF based on experimental and numerical simulation methods. The parameters that determine the filtration efficiency are concluded: superficial velocity, bed depth, granular size, dust particles size and thickness of the dust cake etc. [15]. Guan et al. [14] found that increasing the superficial velocity of the industrial flue gas could improve the filtration efficiency for dust particles greater than 7 µm while it is useless for the particles smaller than 5 µm. The filtration efficiency is also approximately linearly correlates with the granule diameter. Chen et al. [16] experimentally investigated the filtration and resistance characteristics of the moving GBF used for filtration of dust particles. The flow patterns of the filter granules, filtration efficiency and pressure drop under different filtration operating conditions at room temperature were studied. It was found that the decrease of the GBF porosity leads to the increase of both the filtration efficiency and the filtration resistance when the amount of smaller filter granules increased. Chen et al. [17] developed an experimental method to understand the formation and growth of dust cakes and found that the thickness of the dust cake could be controlled. Although researchers have done a lot of experiments and simulation studies on the improvement of the filtration performance of GBF, the filtration mechanism of dust particles is still unclear. Because there are diverse compositions (e.g. solid particles, condensable gases etc.) and complicated interactions (e.g. the collision and agglomeration of solid particles, the condensation of condensable gases and the adsorption between the solid particles and condensable gases) in industrial flue gas. To achieve better filtration performance, the microscopic filtration mechanism, such as the interactions between the solid particles and condensable gases, and their effects
on dust particles agglomeration, dust clusters formation and growth are required. Unfortunately, the microscopic behaviors are difficult to be observed in detail by macroscopic experimental methods. Thus, the investigations from the microscopic point of view is urgently needed to develop filtration theory for dust particles and guide the design of GBF. Molecular dynamics (MD) simulation has been proved to be powerful tools to gain insight into behaviors of systems and provides ultimate detail for addressing specific questions concerning inherent mechanism at nanoscale. To understand the failure mechanisms of the asphalt concrete resulted from the moisture damage, Dong et al. [18] carried out MD simulations to characterize the nanostructure of the asphaltaggregate interface. The simulation results indicate that at the asphalt-aggregate interface, the nanostructure is constructed by periodical molecular bulgy boundaries and central cavities. Besides, it was found that the intermolecular gaps can be filled by naphthene aromatics, and molecular micelles can be lubricated by saturates. Lu et al. [19] studied the mechanical properties and failure behavior of asphalt-aggregate interface using the MD method. Ding et al. [20] carried out MD simulations to investigate the diffusion between virgin and aged asphalt binders. The model of aged binder was constructed by increasing the asphaltenes ratio on the basis of virgin binder. The simulation results show that the diffusion of large molecules in asphalt was a critical factor for the binder’s diffusion, where it was more susceptible to the changes of temperature. The formation of nanoparticles is an important issue for environment assessments. However, the exact mechanism of the diffusion process between virgin and aged asphalt binders is still unclear. Sergio et al. [21] carried out a set of MD simulations to study the nanoparticle-formation from bioethanol-gasoline blend emissions and found that phenanthrene and acetaldehyde quickly generate
nanoparticles with dimensions of 2-5 nm in vacuum. Furthermore, acetaldehyde appears to localize on the surface of the formed nanoparticles, and seemingly acts with the planar geometry of phenanthrene as a facilitator for CO2 absorption. Zhao et al. [22] performed MD simulations to obtain the transport diffusion coefficient from self-diffusion coefficient via thermodynamic factor based on the Wiser bituminous coal model, the properties of CO2 and CH4 diffusion in coal micropores were obtained. Zhou et al. [23] proposed a novel MD workflow to generate organic pores on residuetype kerogen molecules and to simulate the gas adsorption in the pores. Zhang et al. [24] carried out MD simulations to investigate the adsorption behavior of different surfactants-water-oil mixture on quartz surfaces. Wu et al. [25] studied and revealed the mechanisms about adsorption and displacement of methane in carbon nanochannels using MD simulations. They found that as the width of slit pore increases, the structure of adsorbed methane transforms from single adsorption layer to four adsorption layers. From the above literature review, it can be found that MD simulation is well suited to describe the behaviors of diffusion, agglomeration and growth from microscopic point of view. Consequently, in this paper, MD simulations were performed on a flue gas system to reveal the agglomeration behavior of dust particles and the formation and growth process of dust clusters in nanochannel, and analyze the effects of temperature, channel width, cooling rate and gas composition on them. The results are expected to be useful to understand the filtration mechanism and improve the filtration efficiency of dust particles contained in industrial flue gas.
2 Simulation models and methods MD simulations provide the methodology for detailed microscopic modeling on molecular scale. In MD simulations, the motion of atoms is dominated by the second
law of Newton. Firstly, the classical Newton’s equation is applied and solved, then the molecular positions, velocities and trajectories are obtained, finally thermodynamic properties are estimated from the molecular trajectories. Hence, MD is a kind of method which describes the movement, structure and geometry of molecules to reveal the micro/nano-mechanisms at molecular scale. 2.1 Simulation model The schematic for a GBF is shown in Fig. 1 (a). The industrial flue gas flows through the GBF, where the dust particles contained in industrial flue gas are captured by the filter granules. To simulate the agglomeration process of dust particles at molecular scale, MD models are developed. Based on the in-depth analysis of the industrial flue gas components and the filtering process of GBF, three kinds of typical components: steam (H2O), PAHs (naphthalene) and dust particles (SiO2) which are shown in Fig. 1(b) were selected to establish a MD system, as shown in Fig. 1(c). The configurations of atoms are visualized by the Material Studio platform [26]. The surface of silica (-1 0 0) was selected to build layers with different channel widths. The scales in the direction of X and Y are expressed in L and H respectively. While T, W and D represent the thickness of the surface, the width of the channel and diameter of SiO2 particles respectively. N1, N2 and N3 represent the number of SiO2 particles, H2O molecules and naphthalene molecules in each system respectively. The values of the above parameters are shown in Tab. 1. Three models with different channel widths are established to evaluate the effect of channel width on the agglomeration of dust particles and formation and growth of dust clusters, which are named model A, model B and model C respectively. Similarly, the model E, model F and model G with different components are used to study the effect of gas composition on the agglomeration process. In all simulation models, the values of the lattice
parameters α, β and γ which determine the relative orientation of the lattice vectors are all 90°. 2.2 Force field All MD calculations were carried out using the Materials Studio software package including Discover and Amorphous modules that have already been successfully used to explore diffusion, agglomeration and adsorption processes in different fields [20, 27, 28]. The total potential energy is based on the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field, which is a general all-atom force field and first ab initio force field. The COMPASS force field has been parameterized, tested and validated, which is applicable for simulation of biological, organic and main-group inorganic molecules to determination of structures and dynamics. The COMPASS potential energy function is shown as follows [29]:
Etotal =
∑ E ( b ) + ∑ Eθ (θ ) + ∑ b
bond
angle
Eϕ (ϕ ) +
dihedral
+ ∑ E ( b,θ , ϕ ) + Ecoulomb + Evdw
∑ out -of -plane
Eχ ( χ ) (1)
cross
Where the terms of Eb ( b ) , Eθ (θ ) , Eϕ (ϕ ) , Eχ ( χ ) and E ( b, θ , ϕ ) represent the contributions of bond stretching, angle bending, torsion angle, out-of-plane angle coordinates and cross-coupling interactions respectively. The items Ecoulomb and Evdw represent non-bond interactions, which can be expressed as:
Ecoulomb = ∑ i> j
Evdw
qi q j rij
6 r 0 9 rij0 ij = ∑ ε ij 2 + 3 r rij ij
(2)
(3)
Where qi and qj are the charges of atoms i and j with a distance rij, ε is the potential well depth for the interaction between the two atoms.
2.3 Simulation details In the present study, MD simulations are performed by Materials Studio. Some of the properties are analyzed by our homemade PERL scripts. Periodic boundary conditions are applied in X, Y and Z directions. Nose Hoover thermostat and barostat were applied to control the temperature and pressure of systems. All the simulations were performed with a time step of 1 fs. The cutoff distance of each system was set as 12.5 Å. The van der Waals and Coulomb interactions were calculated by Atom based [30] and Eward [31] method. Besides, the equations of motion were integrated by the Velocity Verlet algorithm. Initially, the Forcite module was used to geometrically optimize the simulation systems, so that the total energy of the system was minimized. In the process of geometric optimization, smart minimizer algorithm with an iterative step of 1000 was used to refine the conformation, which starts with the steepest descent method, followed by the conjugate gradient method and ends with a Newton method. Then, the systems were equilibrated at 998 K for 100 ps in constant-volume, constant-temperature NVT ensemble. Next, the system is cooled with a temperature interval of 100 K until the temperature of the system reaches 298 K. The system runs 100 ps at each temperature to achieve the equilibrium state, and runs another 50 ps to calculate the physical quantities. Finally, in order to study the effects of the width and cooling rate on the agglomeration process, different cooling rates (e.g. 3.5 K/ps, 1.75 K/ps and 0.875 K/ps) were used to cool the system down to 298 K respectively. After the system reaches the equilibrium state, the system runs 100 ps again. In this way, the physical quantity of the system was calculated.
3 Results and discussion
3.1 Evolutions of dust particles agglomeration and dust clusters growth process Typical coordinate snapshots of the cooling process from 998 K to 298 K with a cooling rate of 3.5 K/ps in the system of model A are shown in Fig. 2. At the initial state, the system has experienced sufficient relaxation, therefore it can be seen from Fig. 2 that steam (H2O), PAHs (naphthalene) and dust particles (SiO2) are all distributed evenly in the nanoscale channel at 0 ps. During the cooling process, the H2O molecules and naphthalene molecules are observed to be adsorbed on the surface of nanoscale SiO2 particles at 20 ps and then agglomerate with other SiO2 particles, so that the dust clusters are formed and then they grow further. This phenomenon indicates that the formation and growth of dust clusters are driven by agglomeration of SiO2 particles. As the cooling process continues, more H2O molecules and naphthalene molecules are adsorbed, which subsequently leads to agglomeration of the SiO2 particles. According to the time-lapse images, the phase transition of H2O molecules and naphthalene molecules has occurred successively with the decrease of temperature, which thus strengthen the adsorption of H2O molecules and naphthalene molecules on the surface of nanoscale SiO2 particles and promote the formation of dust clusters. The dust cluster structure is more stable, and the growth process is clearly observed at 80 ps and 100 ps, which is roughly in line with few results of similar simulations and experiments [32-35].
3.2 Effect of temperature on agglomeration of dust particles According to the viewpoint of classical statistical mechanics, the dynamic behavior of the atom is closely related to temperature. The agglomeration of SiO2 particles in this study is also closely related to the dynamic behavior of the atoms, which means temperature has important effect on the agglomeration and growth of the
dust clusters. Therefore, the mean square displacement (MSD) and self-diffusion coefficient of the system were calculated to investigate the effects of temperature, and the radial distribution function (RDF) was also calculated to reflect the microstructures of the system.
3.2.1 Diffusion characteristics Indeed, for a given material, the self-diffusion coefficient is generally a singlevalued function of temperature when the material is in a single phase. Besides when the state of the substance changes from gaseous state to liquid state and then to solid state, the diffusion ability of the system is gradually weakened. Therefore, during the cooling process, the self-diffusion coefficient can reflect the physical state of the H2O molecules and naphthalene molecules and affect the agglomeration of SiO2 particles. Thus the self-diffusion coefficient was calculated to describe the movement ability of the molecules in the channel. According to the Einstein equation, the self-diffusion coefficient (D), related to the MSD function, can be expressed as follows [36]: 1 d N (4) lim ∑ MSD 6 t → ∞ dt i =1 Where MSD is the mean square displacement of the system, which means a D=
measure of the average distance of a given particle in a system travels, t is the simulation time. MSD is a typical dynamic parameter, which can be defined as:
r r 2 MSD = R ( t ) − R ( 0 )
(5)
r Where R ( t ) is the position of atom at time t. The value of self-diffusion
coefficient can be calculated by the slope of the MSD curve. The MSD of H2O molecules and naphthalene molecules for different temperatures from 998 K to 298 K are plotted in Fig. 3. The MSD increases with the simulation time and the relationships between the MSD and simulation time are almost linear after sufficient simulation time, e.g. 20 ps in our simulations. Thus, the
diffusion coefficient is defined as the slope of the MSD-simulation time curves for the simulation time larger than 20 ps. Besides, the MSD increases as temperature increases, which is because the atoms have higher degree of mobility for higher temperature. Moreover, the variation trend of MSD of H2O molecules with temperature is consistent with few available results [34, 35], which further implies the reliability of our calculation method. As mentioned before, the agglomeration and growth behavior of SiO2 particles surrounded by H2O molecules and naphthalene molecules are different during the cooling process at different time and temperature, which are closely related to the diffusion coefficient of molecules. Therefore, to give a comprehensive understanding of diffusion of the H2O molecules and naphthalene molecules in the system, the self-diffusion coefficients as a function of temperature were calculated and presented in Fig. 4. It is found that the self-diffusion coefficients of naphthalene molecules are much lower than that of H2O molecules when the temperature is higher than 640 K. For example, when the temperature is 998 K, the self-diffusion coefficient of H2O molecules and naphthalene molecules are 39.052×10-8 m2/s and 11.698×10-8 m2/s respectively, the self-diffusion coefficient of naphthalene molecules was 70.045% lower than that of H2O molecules. However, as the temperature continues to decrease, the self-diffusion coefficient of naphthalene molecules begins to be higher than that of H2O molecules. When the temperature is 598K, the corresponding self-diffusion coefficient are 0.046×10-8 m2/s and 0.410×10-8 m2/s respectively, which means the self-diffusion coefficient of H2O molecules was 88.915% lower than that of naphthalene molecules. The results are attributed to the difference between H2O molecules and naphthalene molecules microstructure. On the one hand, due to the strong polar oxygen atoms, it is easier to form hydrogen bonds between H2O molecules, which are absent in naphthalene molecules; on the other
hand, when the H2O molecules are in liquid state, the distance between molecules is close, which lead to the increase of hydrogen bond number density, so the effect of hydrogen bond on the ability of diffusion is obvious, which limits the diffusion of H2O molecules. With the increase of temperature, the kinetic energy of molecules increased, which weakened the role of hydrogen bonds, the effect of temperature become the dominant factor, and significantly enhance the ability of molecular diffusion.
3.2.2 Radial distribution function The radial distribution function (RDF) represents the atomic density varies as a function of the distance from one designated atom, which is donated by g(r). Usually, RDF is used to analyze the phase state of particles in a system. The result of g(r) is given by the expression [37]:
1 χα χ β ρ gαβ ( r ) = N
Nα N β
∑∑ δ ( r − r − r ) i =1 i =1
i
j
(6)
Where, χα and χβ are the mole fraction of chemical type α and β, ρ is the overall number density, N is the total number of atoms, Nα and Nβ is the number of atoms of chemical type α and β. Here, the RDFs of H2O molecules and naphthalene molecules in the systems are plotted in Fig. 5. The curves of RDF under different agglomeration states are different. So the agglomeration states of the system roughly determined according to the corresponding RDF curves at different temperatures. For H2O molecules, at the condition of 998 K, the first peak of the RDF is 0.95 Å, and from 898 K to 298 K, the first peak of the RDFs is all at 0.97 Å. Similarly, for naphthalene molecules, at temperatures of 998 K and 898 K, the first peak of the RDF is 1.11 Å, and from 898 K to 298 K, the first peak of the RDFs is all at 1.09 Å. The peaks of radial distribution
functions of the H2O molecules and naphthalene molecules are slightly higher and steeper at lower temperatures. It was indicated that as the temperature decreases, more molecules will be adsorbed on the surface of the SiO2 particles, which makes the agglomeration more significant and contributes to the growth of dust clusters.
3.3 Effect of channel width on agglomeration of dust particles As pointed out by many researchers [38-40], cooling rate is an important factor in many thermo-physical processes, e.g., nucleation, agglomeration and dissolution. The few macroscopic experimental results also show that cooling rate would affect the filtration of dust particles. However, the discussion about the effect of cooling rate on agglomeration mechanism from microscopic point of view is especially rare. Consequently, MD is employed hereby to study the agglomeration of SiO2 particles with different cooling rates of 3.5 K/ps, 1.75 K/ps and 0.875 K/ps. In addition, the channel width affects the distribution of the SiO2 particles, H2O molecules and naphthalene molecules, which means the interaction between atoms was significantly affected by the channel width, thus the agglomeration process was also affected. Therefore, considering the factor of channel width, the models A, B, and C with different channel widths as shown in Tab. 1, have been simulated at different cooling rates, and the simulation results are compared to reveal the effect of cooling rate and channel width on the agglomeration process. The time-lapse images for the agglomeration of dust particles and the growth behavior of dust clusters under different channel widths and cooling rates are presented in Fig. 6. The systems are divided into 50 layers along the Z-axis and the density distributions of SiO2 particles, H2O molecules and naphthalene molecules along the direction of the Z-axis were calculated to accurately reflect the size of the dust clusters, which are shown in Fig. 7. It was found that in the initial state of
simulation, SiO2 particles, H2O molecules and naphthalene molecules distributed evenly in the channel, as shown in Fig.6 (a), (e) and (i). This phenomenon can also be reflected from the density distribution curves, as shown in Fig. 7, where the curves are almost parallel to the X-axis. Then with time ongoing, the agglomeration occurs and a peak of the density distribution curve appears when a dust cluster is formed due to agglomeration. It is worth noting that at the same cooling rate, the size of dust clusters decreases gradually as the channel width increases. For model A, B and C, the peak value of density for SiO2 particles at the end of the simulations are 0.44 g/cm3, 0.27 g/cm3 and 0.15 g/cm3 respectively. As the width of the channel increases, the peak value of the density is reduced by 38.6% and 65.9% respectively. This can be explained that with the increase of the channel width, the distribution of molecules within the channel becomes looser, the average distance between atoms increases, which weakens the interaction between atoms, so the molecules collide with molecules nearby, and the smaller dust clusters are formed because of the agglomeration.
3.4 Effect of cooling rate on agglomeration of dust particles However, in the same channel width, the size of dust clusters increases with the decrease of cooling rate. In order to study the effect of cooling rate on the dust particles agglomeration and dust cluster growth, the density distribution of SiO2 particles along Z-axis was calculated based on the model A and it is shown in Fig. 8. As shown in Fig. 8, the initial configuration is consistent and it can be seen that the SiO2 particles fluctuates up and down near the average density in the channel at the initial time, which indicates that the distribution of SiO2 particles is basically uniform. When the system is cooled at different cooling rates, all density curves have a peak value. This implies the occurrence of agglomeration and the growth of dust clusters.
When the cooling rate is 0.875 K/ps, 1.75 K/ps and 3.5 K/ps, the peak values are 0.47 g/cm3 (z=66.84 Å), 0.43 g/cm3 (z=80.67 Å) and 0.33 g/cm3 (z=71.45 Å) respectively. With the cooling rate increasing from 0.875 K/ps to 3.5 K/ps, the peak values are reduced about 8.51% and 23.26%. In this study, the temperature difference is fixed, so the cooling rate is mainly reflected in the simulation cooling time. With the decrease of cooling rate, the cooling process proceeds slowly, and the longer it takes to reach the equilibrium state at the target temperature. So the growth time of dust cluster during the cooling process increases, it is helpful to the formation of large dust clusters. To further study this phenomena, the average number of hydrogen bonds in the system is calculated and shown in Fig. 9. In the MD simulation, the concept of hydrogen bonds has been proposed by many researchers [41-43]. In this study, the hydrogen bonds calculation tool creates a hydrogen bond between two atoms if the following criteria are met. One atom is a hydrogen atom, the hydrogen atom is single bonded and the attached atom may act as a hydrogen bond donor. The other atom may act as a hydrogen bond acceptor and has at least one lone electron pair. The distance between the hydrogen atom and the acceptor is less than or equal to the maximum hydrogen-acceptor distance which specifies the maximum distance (in Å) between the hydrogen and the acceptor atom with a range of 0 to 4 Å. Similarly, the value of the angle formed by the donor, hydrogen and acceptor atoms is at least the minimum donor-hydrogen-acceptor angle, which specifies the minimum angle between the donor, hydrogen and acceptor atom in degrees with a range of 0 to 180°. If both the hydrogen and acceptor atom are within the same molecule, they are separated by at least four nearest neighbor shells [26]. As shown in Fig. 9, the number of the average hydrogen bonds is greatly reduced because of the formation of dust clusters. For the
model A, B and C, the numbers of hydrogen bonds in the initial state are 2.14, 2.17, 2.12 respectively, as the cooling process proceeds, the number of hydrogen bonds decreases. With the cooling rate decreasing from 3.5 K/ps to 0.875 K/ps, the numbers of hydrogen bonds are reduced about 13.79%, 14.99% and 16.51% for model A. Therefore, the reduction of the number of hydrogen bonds increases with the decrease of cooling rate. For each cooling rate, the existence of hydrogen bonds at the beginning of cooling process accelerated the formation of large dust clusters. As the cooling process goes on, the molecular diffusion capacity slows down and the larger dust clusters begin to form, which reduces the average contact surface area between the molecules, thus the number of hydrogen bonds is reduced. Hence the decrease of cooling rate is beneficial to the formation of larger size dust clusters.
3.5. Effect of gas composition on the agglomeration of dust particles In order to study the influence of gas composition on particle agglomeration, cases based on the model E, F and G (as described in Tab. 1) were investigated. The snapshots of the systems at the initial and the end states are shown in Fig. 10. The systems are divided into 50 layers along the Z-axis, the density distributions of SiO2 particles in each layer are calculated, in particular, the calculation results in the range of 70.77 Å to 223.63 Å along the Z-axis are shown in Fig. 11. It can be seen from the density distribution curves in Fig. 11(a) that in the initial state (0 ps), SiO2 distributes uniformly along the Z-axis in the systems. However, in the final state (100 ps), the density distribution curves of model E, F and G appear a significant peak value which means the formation of dust clusters, as mentioned earlier. It is worth noting that the peak value of the curves of model F and model G are significantly higher than that of model E, which indicates both the adsorption of H2O molecules and naphthalene molecules on the surface of Si2O particles are beneficial to the agglomeration of Si2O
particles and the formation of larger size dust clusters. It can also be seen from Fig. 11(b) that the peak value of density distribution curve for model F is obviously higher than that for model G, the peak values are 0.31g/cm3 for model F at z=121.72 Å and 0.22g/cm3 for model G at z=195.32 Å respectively. It can be concluded that the H2O molecules are more beneficial to the agglomeration of SiO2 particles than the naphthalene molecules. As mentioned above, the phenomenon can be explained that the formation of hydrogen bonds between H2O molecules and SiO2 particles in model F but inexistent in model E and G will promote the interaction between atoms, which is beneficial to the formation and growth of dust clusters.
4. Conclusion In order to reveal the mechanism of dust particles agglomeration and dust clusters formation and growth during flue gas filtration, in this paper, MD simulations were carried out on molecular point of view. Three kinds of typical components, which consist of steam (H2O), PAHs (naphthalene) and dust particles (SiO2), were selected to establish a system. The agglomeration behavior of dust particles and growth of dust clusters were characterized. And the effects of temperature, channel width, cooling rate and gas composition on the agglomeration of dust particles and growth of dust clusters were investigated. The conclusions can be summarized as follows: (1) With the decrease of temperature, the diffusion ability of both H2O molecules and naphthalene molecules are significantly reduced, so it is helpful to the adsorption of molecules on the surface of dust particles. Thus, the decrease of temperature contributes to the formation and growth of dust clusters. (2) With the increase of the channel width, the distribution of molecules within the channel become looser, the average distance between atoms increases, which weakens the interaction between atoms. It is unfavorable to the growth of dust clusters.
(3) The decrease of cooling rate is beneficial to the formation of larger size of dust clusters. (4) H2O molecules are more beneficial to the agglomeration and growth of SiO2 particles than the naphthalene molecules. So increasing the content of steam in the flue gas are helpful to the filtration of dust particles.
Acknowledgements The present work is supported by the National Key R&D Program of China (2016YFB0601100).
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Tab. 1 Description of all MD models Model
N1 (SiO2)
N2 (H2O)
N3 (naphthalene)
W(Å)
H(Å)
T(Å)
L(Å)
D(Å)
A B C E F G
50 50 50 50 50 50
500 500 500 0 500 0
200 200 200 0 0 200
187.19 242.23 350.27 242.23 242.23 242.23
60.51 60.51 60.51 60.51 60.51 60.51
21.65 21.65 21.65 21.65 21.65 21.65
60.51 60.51 60.51 60.51 60.51 60.51
10 10 10 10 10 10
Flue gas flow
...... . . .. ....... ... ...... ..... . . . .. ..... ....... ... .... . . . . . ...... . . ...
O D=10Å SiO2 (Dust particles)
H2 O (Steam)
Naphthalene(PAHs)
C
(b)
H W
Si y
Clean gas flow
(a)
T
H
T
(c)
x
z
(d)
Fig. 1 Simulation system:(a) A schematic diagram of the filtration process in a GBF, (b) Three kinds of components containing in flue gas, (c) Simulation model, (d) Atomic species
Fig. 2 Time-lapse images of the agglomeration of dust particles and growth behaviors of dust clusters
(a) naphthalene (b) H2O Fig. 3 Variation of mean square displacement
Fig. 4 Variation of self-diffusion coefficient
(a) naphthalene-naphthalene
(b) H2O-H2O
Fig. 5 Typical radial distribution functions
Model A Model B Model C Fig. 6 Time-lapse images of the agglomeration and growth behaviors of dust particles. (a), (e), (i) initial state; (b), (f), (j) c1=3.5 K/ps, final state; (c), (g), (k) c2=1.75 K/ps, final state; (d), (h), (l) c3=0.875 K/ps, final state
Fig. 7 Density distribution of SiO2 particles, H2O molecules and naphthalene molecules along Z-axis
Fig. 8 Density distribution of SiO2 particles along Z-axis
Fig. 9. The average number of hydrogen bonds in the system
z a
b
c
x
y
(a) Model E (b) Model F (c) Model G Fig. 10 Time-lapse images of the agglomeration and growth behaviors of dust particles with different gas composition
(a) t=0 ps (b) t=100 ps Fig. 11 Density distribution of dust particles along Z-axis direction
1 The microscopic mechanism of dust particles agglomeration and growth was revealed. 2 The growth of dust clusters are driven by agglomeration of dust particles. 3 The factors affecting the dust growth behavior were determined.