Solution of general dynamic equation for nanoparticles in turbulent flow considering fluctuating coagulation

A new averaged general dynamic equation （GDE） for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The experiments are performed. The numerical results of particle size distribu- tion correlate well with the experimental data. The results show that, for a turbulent nanoparticulate flow, a fluctuating coagulation term should be included in the averaged particle GDE. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet, the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds num- ber is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with a smaller Schmidt number and the flow with a higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher considering fluctuating coagulation than that without considering fluctuating coagulation.

The collision efficiency of spherical dioctyl phthalate aerosol particles in the Brownian coagulation

The collision efficiency in the Brownian coagulation is investigated. A new mechanical model of collision between two identical spherical particles is proposed, and a set of corresponding collision equations is established. The equations are solved numerically, thereby obtaining the collision efficiency for the monodisperse dioctyl phthalate spherical aerosols with diameters ranging from 100 to 760 nm in the presence of van der Waals force and the elastic deformation force. The calculated collision efficiency, in agreement with the experimental data qualitatively, decreases with the increase of particle diameter except a small peak appearing in the particles with a diameter of 510 nm. The results show that the interparticle elastic deformation force cannot be neglected in the computation of particle Brownian coagulation. Finally, a set of new expressions relating collision efficiency to particle diameter is established.

Nanoparticle nucleation and coagulation in a mixing layer

Numerical simulation of nanoparticle nucleation and coagulation in a mixing layer with sulfuric acid vapor binary system is performed using the large eddy simulation and the direct quadrature method of moment. The distributions of number concentration, volume concentration, and average diameter of nanoparticles are obtained. The results show that the coherent structures have an important effect on the distributions of number concentration, volume concentration and average diameter of nanoparticles via continuously transporting and diffusing the nanoparticles to the area of low particle concentration. In the streamwise direction, the number concentration of nanoparticles decreases, while the volume concentration and the average diameter increase. The distributions of number concentration, volume concentration and average diameter of nanoparticles are spatially inhomogeneous. The characteristic time of nucleation is shorter than that of coagulation. The nucleation takes place more easily in the area of low temperature because where the number concentration of nanoparticles is high, while the intensity of coagulation is mainly affected by the number concentration. Both nucleation and coagulation result in the variation of average diameter of nanoparticles.

MULTI-MONTE-CARLO METHOD FOR GENERAL DYNAMIC EQUATION CONSIDERING PARTICLE COAGULATION

Monte-Carlo （MC） method is widely adopted to take into account general dynamic equation （GDE） for particle coagulation, however popular MC method has high computation cost and statistical fatigue. A new Multi-Monte-Carlo （MMC） method, which has characteristics of time-driven MC method, constant number method and constant volume method, was promoted to solve GDE for coagulation. Firstly MMC method was described in details, including the introduction of weighted fictitious particle, the scheme of MMC method, the setting of time step, the judgment of the occurrence of coagulation event, the choice of coagulation partner and the consequential treatment of coagulation event. Secondly MMC method was validated by five special coagulation cases in which analytical solutions exist. The good agreement between the simulation results of MMC method and analytical solutions shows MMC method conserves high computation precision and has low computation cost. Lastly the different influence of different kinds of coagulation kernel on the process of coagulation was analyzed： constant coagulation kernel and Brownian coagulation kernel in continuum regime affect small particles much more than linear and quadratic coagulation kernel,whereas affect big particles much less than linear and quadratic coagulation kernel.

Simulation of the Brownian coagulation of nanoparticles with initial bimodal size distribution via moment method

The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diameter and geometric standard deviation are given in the free molecular regime, the continuum regime, the free molecular regime and transition regime, the free molecular regime and continuum regime, respectively. The results show that, both in the free molecular regime and the continuum regime, the num- ber concentration of mode i and j decreases with increasing time. The evolutions of particle geometric average diameter with different initial size distribution are quite different. Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimoda/and shifts to a larger particle size range. In the free molecular regime and transition regime, the inter- modal coagulation becomes dominant when the number concentrations of mode i and j are of the same order. The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible, while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct. In the free molecular regime and continuum regime, the higher the initial number concentration of mode j, the more obvious the variation of the number concentration of mode i.

New expression for collision efficiency of spherical nanoparticles in Brownian coagulation

The collision efficiency of dioctyl phthalate nanoparticles in Brownian coag- ulation has been studied. A set of collision equations is solved numerically to find the relationship between the collision efficiency and the particle radius varying in the range of 50 nm to 500 nm in the presence of Stokes resistance, lubrication force, van der Waals force, and elastic deformation force. The calculated results are in agreement with the experimental data qualitatively. The results show that the collision efficiency decreases with the increase of the particle radii from 50 nm to 500 nm. Based on the numerical data, a new expression for collision efficiency is presented.

Simulation of nanoparticle coagulation in radio-frequency C_2H_2/Ar microdischarges

The nanoparticle coagulation is investigated by using a couple of fluid models and aerosol dynamics model in argon with a 5% molecular acetylene admixture rf microdischarges,with the total input gas flow rate of 400 sccm.It co-exists with a homogeneous,secondary electron-dominated low temperature γ-mode glow discharges.The heat transfer equation and flow equation for neutral gas are taken into account.We mainly focused on investigations of the nanoparticle properties in atmospheric pressure microdischarges,and discussed the influences of pressure,electrode spacing,and applied voltage on the plasma density and nanoparticle density profiles.The results show that the characteristics of microdischarges are quite different from those of low pressure radio-frequency discharges.First,the nanoparticle density in the bulk plasma in microdischarges is much larger than that of low pressure discharges.Second,the nanoparticle density of 10 nm experiences an exponential increase as soon as the applied voltage increases,especially in the presheath.Finally,as the electrode spacing increases,the nanoparticle density decreased instead of increasing.

PARTICLE ELECTROSTATIC COAGULATION AND ITS APPLICATIONS IN DUST CONTROL

Fine particulates instead of others create particulate pollution and they are easier to escape from almost all conventional collectors of low- or medium-efficiency. It is of practical significance to take full advantages of particle coagulation by electrostatic forces to upgrade the collertors' performance. This paper investigates the main mechanisms of coagulation, all possible electrostatic forces existing in the collectors and their effects on the particle coagulation. To make particle kinetic coagulation electrostatically enhanced be a step of the conventional collectors. operations,certain conditions should be created through some medifications of the collectors. Based on that ,the authors suggest that a precharger electro-cyclone technique be applied to improve the performance of common cyclones still widely used in many places. And a preliminary semi-industrial test has been carried out at Jiawang Power Station, Xuzhou, Jiangsu Province, and the results show that the modified cyclone increases its efficiency from about 80% to 92~94%.

Collision efficiency of two nanoparticles with different diameters in Brownian coagulation

The collision efficiency of two nanoparticles with different diameters in the Brownian coagulation is investigated. The collision equations are solved to obtain the collision efficiency for the dioctyl phthalate nanoparticle with the diameter changing from 100 nm to 750 nm in the presence of the van der Waals force and the elastic deformation force. It is found that the collision efficiency decreases as a whole with the increase of both the particle diameter and the radius ratio of two particles. There exists an abrupt increase in the collision efficiency when the particle diameter is equal to 550 nm. Finally, a new expression is presented for the collision efficiency of two nanoparticles with different diameters.

Modeling of the nanoparticle coagulation in pulsed radio-frequency capacitively coupled C_2H_2 discharges

The role of pulse parameters on nanoparticle property is investigated self-consistently based on a couple of fluid model and aerosol dynamics model in a capacitively coupled parallel-plate acetylene（C2H2） discharge. In this model, the mass continuity equation, momentum balance equation, and energy balance equation for neutral gas are taken into account.Thus, the thermophoretic force arises when a gas temperature gradient exists. The typical results of this model are positive and negative ion densities, electron impact collisions rates, nanoparticle density, and charge distributions. The simulation is performed for duty ratio 0.4/0.7/1.0, as well as pulse modulation frequency from 40 kHz to 2.7 MHz for pure C2H2 discharges at a pressure of 500 mTorr. We find that the pulse parameters, especially the duty ratio, have a great affect on the dissociative attachment coefficient and the negative density. More importantly, by decreasing the duty ratio, nanoparticles start to diffuse to the wall. Under the action of gas flow, nanoparticle density peak is created in front of the pulse electrode,where the gas temperature is smaller.

Large eddy simulation of a planar jet flow with nanoparticle coagulation

Coagulation and growth of nanoparticles subject to large coherent structures in a planar jet has been explored by using large eddy simulation. The particle field is obtained by employing a moment method to approximate the nanoparticle general dynamic equa- tion. An incompressible fluid containing particles of 1 nm in diameter is projected into a particle-free ambient. The results show that the coherent structures dominate the evolution of the nanoparticle number intensity, diameter and polydispersity distributions as the jet develops. In addition, the coherent structures act to increase the diffusion of particles, and the vortex rolling-up makes the particles distributing more irregularly while the vortex pairing causes particle distributions to become uniform. As the jet travels downstream, the time-averaged particle number concentration becomes lower in the jet core and higher in the outskirts, whereas the time- averaged particle mass over the entire flow field maintains unaltered, and the time-averaged particle diameter and geometric standard deviations grow and reach their maximum on the interface of the jet region and the ambient.

Nanoparticle coagulation in a planar jet via moment method

Large eddy simulations of nanoparticle coagulation in an incompressible planar jet were performed. The particle is described using a moment method to approximate the particle general dynarnics equations. The time-averaged results based on 3000 time steps for every case were obtained to explore the influence of the Schmidt number and the Damkohler number on the nanoparticle dynamics. The results show that the changes of Schmidt number have the influence on the number concentration of nanoparticles only when the particle diameter is less than 1 nm for the fixed gas parameters. The number concentration of particles for small particles decreases more rapidly along the flow direction, and the nanoparticles with larger Schmidt number have a narrower distribution along the transverse direction. The smaller nanoparticles Coagulate and disperse easily, grow rapidly hence show a stronger polydispersity. The smaller coagulation time scale can enhance the particle collision and coagulation. Frequented collision and coagulation bring a great increase in particle size. The larger the Damkohler number is, the higher the particle polydispersity is.

Quadrature Method of Moments for Nanoparticle Coagulation and Diffusion in the Planar Impinging Jet Flow

A computational model combining large .eddy simulation with quadrature moment method was em-ployed to study nanoparticle evolution in a confined impinging jet. The investigated particle size is limited in the transient regime, and the particle collision kernel was obtained by using the theory of flux matching. The simulation was validated by comparing it with the experimental results. The numerical results show coherent structure acts to dominate particle number intensity, size and polydispersity distributions, and it also induce particle-laden iet to be diluted by .the ambient.The evolution of particle dynarnics in.the impinging jet flow are strongly related to the Rey-nolds number and nozzle-to-plate distance, and their relationships were analyzed.

Nanoparticle Transport and Coagulation in Bends of Circular Cross Section via a New Moment Method

Transport of nanoparticles and coagulation is simulated with the combination of CFD in a circular bend. The Taylor-expansion moment method(TEMOM)is employed to study dynamics of nanoparticles with Brownian motion,based on the flow field from numerical simulation.A fully developed flow pattern in the present simulation is compared with previous numerical results for validating the model and computational code.It is found that for the simulated particulate flow system,the particle mass concentration,number concentration,particle polydispersity, mean particle diameter and geometric standard deviation over cross-section increase with time.The distribution of particle mass concentration at different time is independent of the initial particle size.More particles are concen-trated at outer edge of the bend.Coagulation plays more important role at initial stage than that in the subsequent period.The increase of Reynolds number and initial particle size leads to the increase of particle number concentration.The particle polydispersity,mean particle diameter and geometric standard deviation increase with decreasing Reynolds number and initial particle size.

Research on nucleation and coagulation of nanoparticles in parallel twin jets

The large eddy simulation method has been used to simulate the diffusion of H2SO4 vapor in the parallel twin jets. The distributions of number concentration and size of nanoparticles produced by nucleation and coagulation in sulfuric acid/water system are given. The functions of the sulfur content, relative humidity and jet Reynolds number are evaluated according to the distributions of number concentration and size of nanoparticles. The results show that the nucleation in sulfuric acid/water system produces large number of nanoparticles , and gas-to-nanoparticle conversion mostly takes place in the middle and interface of the twin jets. The coagulation process of particles reduces the number concentration, while increases the mean particle size. For the case with higher sulfur content, more number and smaller size nanoparticles are produced by nucleation and coagulation. There is also a larger number of nanoparticles for the cases with higher relative humidity and jet Reynolds number.

Effect of Coagulation and Diffusion on Nanoparticle Distribution in a Fully Developed Turbulent Boundary Layer

Nanoparticle distributions in a fully developed turbulent boundary layer are simulated numerically using the moment method.The effects of Schmidt number and Damk(o)hler number on the nanoparticle distribution are studied.It is found that the particle number concentration and total particle mass increase from the wall to the outside.The difference of particle number concentration and total particle mass near the wall and near the outside becomes smaller with the increasing Schmidt number Sc.The particle diameter and geometric standard deviation increase from the wall to the outside at a fixed Damk(o)hler number Da,and grow with the increase of Da at the same lateral position.

Nanoparticle Migration in a Fully Developed Turbulent Pipe Flow Considering the Particle Coagulation

Numerical simulations of nanoparticle migration in a fully developed turbulent pipe flow are performed.The evolution of particle number concentration,total particle mass,polydispersity,particle diameter and geometric standard deviation is obtained by using a moment method to approximate the particle general dynamic equation.The effects of Schmidt number and Damkhler number on the evolution of the particle parameters are analyzed.The results show that nanoparticles move to the pipe center.The particle number concentration and total particle mass are distributed non-uniformly along the radial direction.In an initially monodisperse particle field,the particle clusters with various sizes will be produced because of coagulation.As time progresses,the particle cluster diameter grows from an initial value at different rates depending on the radial position.The largest particle clusters are found in the pipe center.The particle cluster number concentration and total particle mass decrease with the increase of Schmidt number in the region near the pipe center,and the particles with lower Schmidt number are of many dif-ferent sizes,i.e.more polydispersity.The particle cluster diameter and geometric standard deviation increase with the increase of Damkhler number at the same radial position.The migration properties for nano-sized particles are different from that for micro-sized particles.

Direct Monte Carlo Method Simulation of the Synthesis of Carbon Particle Through Coagulation in the Detonation of Explosives

A model is constructed and used in computing the coagulation probability of free carbon during the detonation of explosives. A direct simulation Monte Carlo (DSMC) program is constructed to simulate the coagulation of free carbon particles. The evaluation of the distribution spectrum of particles in the system is obtained. The simulation result is consistent with the experimental curve.

Hyper-Miniaturisation of Monodisperse Janus Hydrogel Beads with Magnetic Anisotropy Based on Coagulation of Fe₃O₄Nanoparticles

We describe a simple and robust technique for fabricating monodisperse Janus hydrogel beads with magnetic anisotropy smaller than the microchannel used to produce them.

Large Eddy Simulation of the Particle Coagulation in High Concentration Particle-Laden Planar Jet Flow

Particle coagulation by Brownian motion is an important but difficult research topic.When particle volume concentration is larger than 0.1%,the classic SMOLUCHOWSKI equation is not applicative anymore.The high concentration coagulation,with HEINE＇s correction,source terms for the Taylor-series expansion method of moments（TEMOM） are firstly driven in this paper.Ultra-fine particle（d0？100 mm） with initial volume fraction f？1% coagulation in a planar jet turbulence flow is simulated via the large eddy simulation（LES）.The instantaneous and time-averaged particle distributions and the high concentration enhancement are given out.The particle number concentration distribution results show that the coagulation is more intense comparing to dilute case in previous research,especially near the nozzle exit.After jet flow is fully developed,the effect is much more obvious at the region between vortexes.The time-averaged γ（the high concentration enhance factor） distributes sharply and symmetrically about the jet centerline at the upstream,but becomes broad and flat at downstream where the cross-stream averaged γ fluctuates drastically.As a new attempt,this paper shows Brownian coagulation with high concentration also can be calculated via TEMOM appropriately,and the coagulation at the region between vortexes is about 1.38 times intensive of the dilute result calculated by the classic Smoluchowski theory.