The effect of a black sphere on the flux distribution in an infinite moderator

Sahni, D.C.

doi:10.1016/0368-3230(66)90129-7

Cited by 26 publications

(15 citation statements)

References 5 publications

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“…which is comprised of the continuum regime condensation rate multiplied by the semi-empirical Fuchs-Sutugin interpolation function (Fuchs and Sutugin, 1971) (the last term in the equation). It has been obtained by fitting Sahni's (1966) numerical results for the solution of Boltzmann's equation, and extends the validity of Eq.…”

Section: Free-molecular Condensationsupporting

confidence: 65%

A model for particle formation and growth in the atmosphere with molecular resolution in size

Lehtinen¹,

Kulmala²

2002

Preprint

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The formation and growth of atmospheric aerosol particles is considered using an exact discrete method with molecular resolution in size space. The method is immune to numerical diffusion problems that are a nuisance for typical simulation methods using a sectional representation for the particle size distribution. For condensational growth, a slight modification is proposed for the Fuchs-Sutugin expression, which improves the prediction of the growth rate of nanosized particles by as much as a factor of two. The presented method is applied to particle formation in a Finnish Boreal forest and is shown to capture the essential features of the dynamics quite nicely. Furthermore, it is shown that the growth of the particles is roughly linear, which means that the amount of condensable vapour is constant (of the order 10 13 1/m 3 ).

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Section: Free-molecular Condensationsupporting

confidence: 65%

A model for particle formation and growth in the atmosphere with molecular resolution in size

Lehtinen¹,

Kulmala²

2002

Preprint

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“…Equations (2a) and (2b) follow from the work of Fuchs & Sutugin 27 , who used Sahni's solution 59 to the Boltzmann equation for non-continuum mass transfer of a point mass to a sphere to infer vapor molecule condensation and evaporation rates to particles. More recently, this equation has been found to agree well with alternative calculation approaches 28 , as well as experimental data 60 .…”

Section: Models Of Neutral and Ion Evaporationmentioning

confidence: 99%

Simultaneous ion and neutral evaporation in aqueous nanodrops: experiment, theory, and molecular dynamics simulations

Higashi

Tokumi

Hogan

et al. 2015

Phys. Chem. Chem. Phys.

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We use a combination of tandem ion mobility spectrometry (IMS-IMS, with differential mobility analyzers), molecular dynamics (MD) simulations, and analytical models to examine both neutral solvent (H2O) and ion (solvated Na + ) evaporation from aqueous sodium chloride nanodrops. For experiments, nanodrops were produced via electrospray ionization (ESI) of an aqueous sodium chloride solution. Two nanodrops were examined in MD simulations: a 2,500 water molecule nanodrop with 68 Na + and 60 Cl -ions (an initial net charge of z = +8), and (2) a 1,000 water molecule nanodrop with 65 Na + and 60 Cl -ions (an initial net charge of z = +5). Specifically, we used MD simulations to examine the validity of a model for the neutral evaporation rate incorporating both the Kelvin (surface curvature) and Thomson (electrostatic) influences, while both MD simulations and experimental measurements were compared to predictions of the ion evaporation rate equation of Labowsky et al [Anal Chim Acta, 2000, 406, 105-118]. To within a single fit parameter, we find excellent agreement between simulated and modeled neutral evaporation rates for nanodrops with solute volume fractions below 0.30. Similarly, MD simulation inferred ion evaporation rates are in excellent agreement with predictions based on the Labowsky et al equation. Measurements of the sizes and charge states of ESI generated NaCl clusters suggest that the charge states of these clusters are governed by ion evaporation, however, ion evaporation appears to have occurred with lower activation energies in experiments than was anticipated based on analytical calculations as well as MD simulations. Several possible reasons for this discrepancy are discussed.

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“…Although this approach results in an analytical expression for β, F remains as a free parameter, which precludes β calculation without additional information. As an alternative, Fuchs and Sutugin (1970) later interpolated Sahni's (1966) solution to the Boltzmann equation for neutron absorption by a black body, giving an expression for β for all ratios of the colliding entities' persistence distance to particle radius. Collision kernel expressions for particle collisions with small entities have also been proposed by Loyalka (1973Loyalka ( , 1982, Seaver (1984), and Sitarski and Nowakowski (1979).…”

Section: Introductionmentioning

confidence: 99%

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

Gopalakrishnan

Hogan

2011

Aerosol Science and Technology

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Particle-vapor molecule (condensation) and particle-particle (coagulation) collision kernels are critically important parameters for the description of particle size distribution evolution in aerosols. We use mean first passage time calculations to find a dimensionless form of the collision kernel that applies in the limit where the ratio of the masses of colliding entities (aerosol particles or vapor molecules) to gas molecule mass, Z, approaches infinity, and the colliding entities are dilute in concentration. In these calculations, the motion of colliding entities is monitored with Langevin dynamics, and the collision kernel is inferred from the time required for collision. The presented analysis reveals that the dimensionless collisional kernel (H) is a function solely of the diffusive Knudsen number (Kn D , the square root of the product of kT and the reduced mass divided by the product of the reduced friction factor and collision radius), and a number of commonly used expressions for the collision kernel also collapse to the functional form H(Kn D ), irrespective of whether they were derived for Z → ∞ or Z → 0 conditions. The examined collision kernel expressions are further found to agree within 10% of our calculations as well as with each other across the entire Kn D range. This result suggests that a single collision kernel can be used to describe all transition regime collision rates, i.e., both condensation and coagulation rates, with reasonable accuracy, and establishes that Langevin-equationbased mean first passage time calculations can serve as a simple approach to examine transition regime collision phenomena.

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The effect of a black sphere on the flux distribution in an infinite moderator

Cited by 26 publications

References 5 publications

A model for particle formation and growth in the atmosphere with molecular resolution in size

A model for particle formation and growth in the atmosphere with molecular resolution in size

Simultaneous ion and neutral evaporation in aqueous nanodrops: experiment, theory, and molecular dynamics simulations

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

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