The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime

Lai, F. S.; Friedlander, Sheldon K.; Pich, J.; Hidy, George M.

doi:10.1016/0021-9797(72)90034-3

Cited by 273 publications

(139 citation statements)

References 7 publications

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“…40,53 For this case, the particles have a narrow size distribution with a geometric standard deviation of 1.37 for the diameter, and the coefficient α has a value of 6.55, not very different from the value of 5.66 for a monodisperse aerosol. Solution of eq 6 for a fixed volume fraction of aerosols f v then yields the following relations for particle number and particle size:…”

Section: Particle (Soot) Inception By Chemical Reactionmentioning

confidence: 93%

Combustion Aerosols: Factors Governing Their Size and Composition and Implications to Human Health

Lighty

Veranth

Sarofim

2000

Journal of the Air & Waste Management Association

991

594

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Particulate matter (PM) emissions from stationary combustion sources burning coal, fuel oil, biomass, and waste, and PM from internal combustion (IC) engines burning gasoline and diesel, are a significant source of primary particles smaller than 2.5 µm (PM 2.5 ) in urban areas. Combustion-generated particles are generally smaller than geologically produced dust and have unique chemical composition and morphology. The fundamental processes affecting formation of combustion PM and the emission characteristics of important applications are reviewed. Particles containing transition metals, ultrafine particles, and soot are emphasized because these types of particles have been studied extensively, and their emissions are controlled by the fuel composition and the oxidant-temperature-mixing history from the flame to the stack. There is a need for better integration of the combustion, air pollution control, atmospheric chemistry, and inhalation health research communities. Epidemiology has demonstrated that susceptible individuals are being harmed by ambient PM. Particle surface area, number of ultrafine particles, bioavailable transition metals, polycyclic aromatic hydrocarbons (PAH), and other particle-bound organic compounds are suspected to be more important than particle mass in determining the effects of air pollution. Time-and size-resolved PM measurements are needed for testing mechanistic toxicological hypotheses, for characterizing the relationship between combustion operating conditions and transient emissions, and for source apportionment studies to develop air quality plans. Citations are provided to more specialized reviews, and the concluding comments make suggestions for further research.

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Section: Particle (Soot) Inception By Chemical Reactionmentioning

confidence: 93%

Combustion Aerosols: Factors Governing Their Size and Composition and Implications to Human Health

Lighty

Veranth

Sarofim

2000

Journal of the Air & Waste Management Association

991

594

View full text Add to dashboard Cite

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“…For the concrete calculations later in this section, we employ the flow equation (13). To observe the specific properties of the potential u τ , however, it is favorable to revert to the full Wetterich equation (6).…”

Section: A the One-loop Expansion And Restrictions On The Flow Equationmentioning

confidence: 99%

Long-range and many-body effects in coagulation processes

Winkler

Frey

2013

Phys. Rev. E

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We study the problem of diffusing particles which coalesce upon contact. With the aid of a nonperturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violating this classical law. It originates in long-range and many-particle fluctuations and is a simple, universal function of the macroscopic decay rate.

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“…For completely coalescing particles, Df equals 3 and Eq. 1 reduces to the classical theory for spherical particles (Lai et al, 1972).…”

Section: Applications Of Nanoparticlesmentioning

confidence: 99%

Production of Nanometer-Sized Metal Oxide Particles by Gas Phase Reaction in a Free Jet. I: Experimental System and Results

Windeler¹,

Friedlander²,

Lehtinen

1997

Aerosol Science and Technology

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ABSTRACT. In a study of the effect of process conditions and material properties on aerosol characteristics, nanosized metal oxide particles were produced by injecting precursors as a free jet into a methaneair flame. Primary particle size increased with volume loading, solid state diffusion coefficient, and maximum temperature. Larger particles were also obtained by decreasing the jet velocity. The number of particles per agglomerate increased with volume loading and decreased with solid state diffusion coefficient and maximum temperature. Metal oxides with diffusion coefficients ranging over several orders of magnitude produced different sized particles under the same process conditions (temperature profile and aerosol volume loading). Niobium oxide (largest diffusion coefficient) formed the largest particles with geometric volume mean diameters between 5.7 and 33.7 nm. Titania (mid-range diffusion coefficient) and alumina (lowest diffusion coefficient) formed particles with geometric volume mean diameters ranging from 3.8 to 21.3 nm and 2.8 to 10.7 nm, respectively. The geometric standard deviation for the metal oxide particles was about 1.2. The properties of the primary particles and agglomerates depend on the characteristic collision and coalescence times. The collision time was controlled by varying the aerosol volume loading from 10 ' to 10 -'. The coalescence time depends strongly on the solid state diffusion coefficient which ranged over several orders of magnitude as the jet temperature changed. Maximum jet temperatures from 1050 to 1920 K were obtained by adjusting the precursor jet and flame gas exit velocities from 4.8 to 53.2 m/s and 0.14 to 0.51 m/s, respectively. The mass production rate ranged from 0.05 to 1.0 g/h for a jet orifice of 1.2 mm.

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The self-preserving particle size distribution for Brownian coagulation in the free-molecule regime

Cited by 273 publications

References 7 publications

Combustion Aerosols: Factors Governing Their Size and Composition and Implications to Human Health

Combustion Aerosols: Factors Governing Their Size and Composition and Implications to Human Health

Long-range and many-body effects in coagulation processes

Production of Nanometer-Sized Metal Oxide Particles by Gas Phase Reaction in a Free Jet. I: Experimental System and Results

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