Crossover from Ballistic to Epstein Diffusion in the Free-Molecular Regime

Heinson, William R.; Pierce, Flint; Sorensen, Christopher M.

doi:10.1080/02786826.2014.922677

Cited by 11 publications

(12 citation statements)

References 24 publications

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“…For all reported results, n tot D 10,000 (though results are found insensitive to n tot through simulations with both larger and smaller numbers of primary particles) and we vary a from 0.001 to 0.20 to examine the influence of the solid volume fraction. Although such a values are extremely high for aerosols, we show that the evolution of Kn ave and Kn D,ave is minimally influenced by a over the simulation times examined (i.e., the nearest neighbor Knudsen number remains roughly constant and close to 0; Heinson et al 2014). Finally, based on prior simulations (Gopalakrishnan and Hogan 2011), the function Dt D 0.005/ Kn D,ave 2 is used, hence the time step increases as aggregation proceeds.…”

Section: Simulation Parametersmentioning

confidence: 76%

“…However, in their simulations, assumptions of either Kn D 0 or Kn D 1 were still invoked, without considering Kn evolution. More recently, Heinson et al (2014) simulated aggregation monitoring approximately the influence of the Kn D distribution on aggregation, along with non-dilute system influences (quantified by a nearest neighbor Knudsen number, Kn N , the ratio of the persistence distance to the nearest neighbor distance) but with a friction factor expression based upon measurements specifically in the Kn ! 1 limit (Sorensen 2011).…”

Section: Introductionmentioning

confidence: 99%

“…1 limit (Sorensen 2011). Finally, the converse to the work of Heinson et al (2014), Melas et al (2014a) have performed aggregation simulations with variable and evolving Kn, but Kn D D 0 assumed.…”

Section: Introductionmentioning

confidence: 99%

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Langevin Simulation of Aggregate Formation in the Transition Regime

Thajudeen

Deshmukh

Hogan

2015

Aerosol Science and Technology

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We study the aggregation of monomers in an aerosol via nondimensional Langevin simulations, in which particles remain in point contact upon collision, and report the hydrodynamic radii and projected areas of the formed aggregates with less than 300 primary particles. Unique from prior studies, in examining aggregation we monitor the evolution of the distributions of two Knudsen numbers: the traditional Knudsen number (Kn) and the diffusive Knudsen number (Kn D ), which both shift to smaller mean values as aggregation proceeds. As Kn transitions from large to small values, momentum transfer changes from a free molecular to a continuum process; analogously, as Kn D decreases, aggregation is altered from occurring ballistically to diffusively in a dilute system. During simulations, the change in drag coefficient with both changing Kn and changing aggregate structure is accounted for. We find that as compared to completely coalescing particles (spheres), non-coalescing aggregates with the same initial Kn and Kn D have Kn D values, which decrease more rapidly due to aggregation; hence, aggregates are more likely to collide with one another diffusively when compared with their spherical counterparts of the same Kn distribution. Further, we find that aggregation with evolving Knudsen numbers does not lead to strong scaling between the number of monomers in a formed aggregate and the aggregate radius of gyration for aggregates composed of 300 or fewer primary particles. In spite of this, aggregate hydrodynamic radii and orientationally averaged projected areas are found to scale well with the number of monomers per aggregate.

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Section: Simulation Parametersmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

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Langevin Simulation of Aggregate Formation in the Transition Regime

Thajudeen

Deshmukh

Hogan

2015

Aerosol Science and Technology

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“…Computer simulations confirmed these experimental findings. Additionally, it has also been verified through simulations that, when the density of the gas increases, a transition happens from ballistic to diffusion-limited aggregation (where particle motion becomes diffusive following Epstein diffusion) [39].…”

Section: Interaction Potentialmentioning

confidence: 99%

Fractal-like structures in colloid science

Lazzari

Nicoud

Jaquet

et al. 2016

Advances in Colloid and Interface Science

175

126

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a b s t r a c tThe present work aims at reviewing our current understanding of fractal structures in the frame of colloid aggregation as well as the possibility they offer to produce novel structured materials. In particular, the existing techniques to measure and compute the fractal dimension d f are critically discussed based on the cases of organic/inorganic particles and proteins. Then the aggregation conditions affecting d f are thoroughly analyzed, pointing out the most recent literature findings and the limitations of our current understanding. Finally, the importance of the fractal dimension in applications is discussed along with possible directions for the production of new structured materials.

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“…One consideration in many aerosol studies is the relative importance of rotational effects on aerosol transport properties. Studies often ignore rotational effects .e.g., on coagulation rates and the resulting shapes of aggregates [Mountain et al 1986;Heinson et al 2014]). This approach is valid if rotational diffusion is negligible relative to translational diffusion, i.e., if particle orientation changes very little in the time it takes for the particle to diffuse an appreciable distance.…”

Section: Relative Importance Of Translational and Rotational Diffusionmentioning

confidence: 99%

Analytical expression for the rotational friction coefficient of DLCA aggregates over the entire Knudsen regime

Corson

Mulholland

Zachariah

2017

Aerosol Science and Technology

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We apply a self-consistent field method (Corson et al. 2017c) to calculate the rotational friction coefficient for fractal aerosol particles in the transition flow regime. Our method considers hydrodynamic interactions between spheres in a rotating aggregate due to the linear velocities of the spheres. Results are consistent with electro-optical measurements of soot alignment. Calculated rotational friction coefficients are also in good agreement with continuum and free molecule results in the limits of small (Kn D 0.01) and large (Kn D 100) primary sphere Knudsen numbers. As we previously demonstrated (Corson et al. 2017b) for the translational friction coefficient, the rotational friction coefficient approaches the continuum limit as either the primary sphere size and the number of primary spheres increases. We apply our results to develop an analytical expression Equation (26) for the rotational friction coefficient as a function of the primary sphere size and number of primary spheres. One important finding is that the ratio of the translation to rotational diffusion times is nearly independent of cluster size. We include an extension of previous scaling analysis for aerosol aggregates to include rotational motion. EDITORYannis Drossinos tion coefficient, as a function of primary sphere size and the number of spheres in the aggregate. $ t , J $ O;r , and J $O;c are the translational, rotational, and translation-rotation coupling friction tensors. The translational, rotational, and coupling friction tensors relate the particle translational velocity to the force on the particle, the particle angular velocity to the torque on the particle, and the particle translational or angular velocity to the torque or force on the particle, respectively. Note that the subscript O indicates that the property is described relative to the particle's center of mass, while the dagger symbol represents the transpose of a tensor. These equations apply for creeping flow in the continuum, free molecule, and transition regimes, characterized by very small, very large, and intermediate Knudsen numbers, respectively. For spheres, the Knudsen number is defined as Kn D λ=a, where λ is the gas mean free path and a is the sphere radius.Brenner (1967) demonstrated that a particle's friction and diffusion tensors are connected by a generalized Stokes-Einstein relationship, D $ O D kTM $ O ¡ 1 [4] where the grand mobility and diffusion tensors M $ O and D $ O are defined as M $ O D J $ t J $y O;c J $ O;c J $ O;r 2 4 3 5 [5] D $ O D D $ O;t

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Crossover from Ballistic to Epstein Diffusion in the Free-Molecular Regime

Cited by 11 publications

References 24 publications

Langevin Simulation of Aggregate Formation in the Transition Regime

Langevin Simulation of Aggregate Formation in the Transition Regime

Fractal-like structures in colloid science

Analytical expression for the rotational friction coefficient of DLCA aggregates over the entire Knudsen regime

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