Friction factor for aerosol fractal aggregates over the entire Knudsen range

2017

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We use a self-consistent field method, which we have previously validated, to calculate the translational friction coefficient of fractal aerosol particles formed by diffusion-limited cluster aggregation (DLCA). Our method involves solving the Bhatnagar-Gross-Krook model for the velocity around a sphere in the transition flow regime. The velocity and drag results are then used in an extension of Kirkwood-Riseman theory to obtain the drag on the aggregate. Our results span a range of primary sphere Knudsen numbers from 0.01 to 100 for clusters with up to N D 2000 primary spheres. Calculated friction coefficients are in good agreement with experimental data and approach the correct continuum and free molecule limits for small and large Knudsen numbers, respectively. Results show that particles exhibit more continuumlike behavior as the number of primary spheres increase, even when the primary particle is in the free molecule regime; as an illustrative example, the friction coefficient for aggregates with primary sphere Kn D 1 is approximately equal to the continuum friction coefficient for N > 500. We estimate that our calculations are within 10% of the true values of the friction coefficients for the range of Kn and N presented here. Finally, we use our results to develop an analytical expression (Equation (38)) for the friction coefficient over a wide range of aggregate and primary particle sizes. . Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uast. 1 In this article, we define the viscosity by the relation m D 0:499rcλ, where r is the gas density and c is the mean thermal speed. This expression describes a hard sphere gas. Furthermore, we use Davies' coefficients (A D 1.257, B D 0.4, and C D 1.1) in the slip correction factor.

Section: Uncertainty In the Calculated Friction Coefficientssupporting

confidence: 75%

Section: Uncertainty In the Calculated Friction Coefficientssupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

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Analytical expression for the friction coefficient of DLCA aggregates based on extended Kirkwood–Riseman theory

2017

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“…To apply our method for calculating the rotational friction coefficient, one simply needs the coordinates of the primary spheres in the particle (either from a clustercluster aggregation algorithm, as we use for this study, from a detailed Brownian simulation, or from a TEM image) and the velocity field around a sphere. .See Corson et al [2017a] for velocity results at select Knudsen numbers./ Given this information, one forms a 3N-by-3N matrix where each 3-by-3 block is Q…”

Section: Theoretical Methodsmentioning

confidence: 99%

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

2017

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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

“…The present study applies the theory of Li et al (2014a) for the average particle mobility as a function of field strength to calculate the mobility of aggregates with a fractal dimension of 1.78, which is characteristic of soot and other particles formed by diffusion-limited cluster aggregation (DLCA). In the present study, we apply our extended Kirkwood-Riseman (EKR) method (Corson et al 2017a) to obtain the translational friction tensor that appears in the theory of Li et al (Li et al 2012, 2014a. We compare our results to experimental data (Li et al 2016) and show how the particle mobility changes with electric field strength for a wide range of primary sphere diameters and aggregate sizes.…”

Section: Introductionmentioning

confidence: 99%

The effect of electric-field-induced alignment on the electrical mobility of fractal aggregates

2018

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We study the effects of electric field strength on the mobility of soot-like fractal aggregates (fractal dimension of 1.78). The probability distribution for the particle orientation is governed by the ratio of the interaction energy between the electric field and the induced dipole in the particle to the energy associated with Brownian forces in the surrounding medium. We use our extended Kirkwood-Riseman method to calculate the friction tensor for aggregates of up to 2000 spheres, with primary sphere sizes in the transition and near-free molecule regimes. Our results for electrical mobility versus field strength are in good agreement with published experimental data for soot, which show an increase in mobility on the order of 8% from random to aligned orientations. Our calculations show that particles become aligned at decreasing field strength as particle size increases because particle polarizability increases with volume. Large aggregates are at least partially aligned at field strengths below 1000 V/cm, though a small change in mobility means that alignment is not an issue in many practical applications. However, improved differential mobility analyzers would be required to take advantage of small changes in mobility to provide shape characterization.