Formation of agglomerate particles by coagulation and sintering—Part I. A two-dimensional solution of the population balance equation

Xiong, Yi; Pratsinis, Sotiris E.

doi:10.1016/0021-8502(93)90003-r

Cited by 247 publications

(171 citation statements)

References 26 publications

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“…where the inter-and intrasectional coagulation coef cients,¯s, and the sintering coef cients,H s, are the same as in Xiong and Pratsinis (1993) and D k;l is the sectional diffusion coef cient as written below:…”

Section: Sectional Methods and Sensitivity Testsmentioning

confidence: 99%

“…where d p in cm is the primary particle size and is equal to 6v=a (Xiong and Pratsinis 1993) in the present study. However, for very small primary particles (<»10 nm), the above equation for coalescence rate is known to signi cantly underestimate the particle growth of silica (Ehrman et al 1998).…”

Section: Various Sintering Models For Silica Nanoparticlesmentioning

confidence: 98%

“…For particles undergoing generation, diffusion, coagulation, and coalescence, two-dimensional aerosol dynamics has been analyzed by solving the following equation (Xiong and Pratsinis 1993):…”

Section: Two-dimensional Aerosol Dynamics For Nonspherical Particle Gmentioning

confidence: 99%

“…Xiong and Pratsinis (1993) extended the sectional method (Gelbard et al 1980) to a two-dimensional aerosol dynamics model using volume and surface area of particles as independent variables and including the effect of coalescence of particles. A simple model accounting for collision and coalescence of particles has been proposed by Kruis et al (1993) with monodisperse particles assumed.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of Growth of Nonspherical Silica Nanoparticles in a Premixed Flat Flame

Lee¹,

Oh²,

Choi³

2001

Aerosol Science and Technology

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The growth of nonspherical silica nanoparticles in a premixed at ame has been simulated, including the effects of convection, diffusion, thermophoresis, chemical reactions, coagulation, and coalescence. Considering both radiation effect and multistep chemical reactions of methane/air including both oxidation and hydrolysis of SiCl 4 , combustion analysis in a premixed at ame was done rst to obtain temperature, concentration of gas species, and ow elds. The predicted ame temperatures were in good agreement with the previous experimental data. Two-dimensional aerosol dynamics in which both particle volume and surface area are independent variables was then analyzed to investigate the growth of nonspherical silica particles. Several different models of coalescence of silica particles were studied: viscous ow sintering, atomistic diffusion sintering, fast sintering, and hybrid sintering models. Since the residence time was short and temperatures were not high enough for perfect coalescence of silica particles in the present study, the resulting particles were partially sintered or open-structured aggregates. The variations of total volume/number concentration and diameter of average volume along the ame height were obtained and compared with experimental data. Bi-modal size distributions were obtained at some ame heights.

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Section: Sectional Methods and Sensitivity Testsmentioning

confidence: 99%

Section: Various Sintering Models For Silica Nanoparticlesmentioning

confidence: 98%

Section: Two-dimensional Aerosol Dynamics For Nonspherical Particle Gmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulation of Growth of Nonspherical Silica Nanoparticles in a Premixed Flat Flame

Lee¹,

Oh²,

Choi³

2001

Aerosol Science and Technology

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show abstract

“…For example, to understand the formation of aggregates, Xiong and Pratsinis (1993) employed a "two-dimensional" sectional method where both surface area and volume distribution were determined and the surface fractal dimension was estimated from first principles. With the standard sectional method, fractal dimension is lost and modifying the scheme to retrieve it is not an easy task.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulation of Multicomponent Aerosols Undergoing Simultaneous Coagulation and Condensation

Sun

Axelbaum

Huertas

2004

Aerosol Science and Technology

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A Monte Carlo method was developed to simulate multicomponent aerosol dynamics, specifically with simultaneous coagulation and fast condensation where the sectional method suffers from numerical diffusion. This method captures both composition and size distributions of the aerosols. In other words, the composition distribution can be obtained as a function of particle size. In this method, particles are grouped into bins according to their size, and coagulation is simulated by statistical sampling. Condensation is incorporated into the Monte Carlo method in a deterministic way. If bins with fixed boundaries are used to simulate the condensation process numerical dispersion occurs, and thus a moving bins approach was developed to eliminate numerical dispersion. The method was validated against analytical solutions, showing excellent agreement. An example of the usefulness of this model in understanding aerosol evolution is presented. The effects of the number of particles and number of bins on the accuracy of the numerical results are also discussed. It was found that with 20 bins per decade and 10 5 particles in the control volume results with less than 5% error can be obtained. The results are further improved to within 2% error by filtering the statistical noise with a cubic spline algorithm.

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Process Intensification

Linke¹,

and²,

Alva-Argáez³

2006

Computer Aided Process and Product Engineering

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a b s t r a c tFlame spray pyrolysis (FSP) offers a proven and inexpensive route for nanoparticle production. To date, the research on FSP made nanoparticles was focused mostly on the lab scale and medium scale production. Scale-up requirements for FSP process control need to be developed to define the operation window at industrial scale production rate. In this work, FSP synthesis of ZrO 2 particles has been addressed from a process intensification perspective, since FSP characteristics perfectly fit into several fundamental process intensification aspects. The possible solutions for the precursor delivery system and the atomization quality at high precursor concentrations were investigated to intensify the production rate and reduce the cost of an additional solvent. The simulation results showed that the particle size could be controlled at near a constant (∼20 nm) while the production rate was intensified by a factor of 5. Finally, the potential of gas to liquid flow ratio (GLFR) and replacing oxygen dispersion gas by air for further reducing the particle size and the production cost were investigated. The simulation results can be used as a framework of PI in FSP process design at industrial scale production.

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Formation of agglomerate particles by coagulation and sintering—Part I. A two-dimensional solution of the population balance equation

Cited by 247 publications

References 26 publications

Simulation of Growth of Nonspherical Silica Nanoparticles in a Premixed Flat Flame

Simulation of Growth of Nonspherical Silica Nanoparticles in a Premixed Flat Flame

Monte Carlo Simulation of Multicomponent Aerosols Undergoing Simultaneous Coagulation and Condensation

Process Intensification

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