Preferential settling of elongated mineral dust particles in the atmosphere

Authors


Abstract

[1] Positions of particles' centers of gravity and folding centers were analyzed for individual dust particles in snow on a high mountain in Japan. Bias of dust particles' centers of gravity was observed: L1 (the longest distance from the center of gravity to the boundary of particles) is 5% (of L1, on average) longer than L2 (1/2 of the longest axis of particles), suggesting that a preferential orientation exists for particles settling heavy side down. Applying that preferential orientation of settling particles to Ginoux's model, the settling velocity for ellipsoids with Reynolds numbers lower than 2 was estimated. The results show that, for long-range transport particles, settling velocity of spherical particles is lower than that of ellipsoids with equal surface area. Our results also indicate that, away from the source regions, dust particles are essentially spherical, which considerably simplify the calculation of settling velocity in transport and of radiative transfer models.

1. Introduction

[2] Atmospheric mineral dust particles play an important role in atmospheric radiation transfer [Sokolik and Toon, 1996; Tegen et al., 2002; Intergovernmental Panel on Climate Change, 2001] and the geochemical cycle of atmospheric constituents [Duce et al., 1980; Uematsu et al., 1983; Arimoto et al., 1985]. For precedent global atmospheric transport models of mineral dust particles, dust particles have usually been assumed as sphere [Genthon, 1992; Ginoux et al., 2001; Tegen et al., 2002; Zender et al., 2003]. However, many studies have shown that nonsphericity of dust particles strongly affects mineral dusts' optical and aerodynamic properties [Sokolik et al., 2001; Kahnert and Kylling, 2004; Kahnert et al., 2005; Kahnert and Nousiainen, 2006; Volken and Schumann, 1993]. Therefore, nonsphericity of mineral dusts must be well characterized for application to various optical and transport models.

[3] Fuchs [1964] examined dynamics of nonspherical particles in the air. Kagermann and Koehler [1982] studied the motion of nonspherical particles in a turbulent flow. Ginoux [2003] also studied the effects of nonsphericity on mineral dust transport modeling at Reynolds numbers of less than 2. The calculations of settling velocity were based on the assumption that dust particles randomly orientated in the air during gravitational settling. Ginoux [2003] showed that changing the particle shape from spherical to ellipsoidal with an aspect ratio (ratio of the longest dimension a to the orthogonal width b of particles) of 2 engendered little difference in settling velocities. However, when particles were simulated as more oblong (aspect ratio = 5), the settling velocity of non-spherical particles was apparently less than that of spherical particles.

[4] On the other hand, based on analyses of individual dust particles in precipitation samples, in our former paper we found that the proportion of nearly spherical (higher circularity) and less elongated (aspect ratio close to 1) dust particles was higher in a sample deposited after long-distance transport from dust source areas [Li and Osada, 2007]. These results suggest selective settling of dust particles during transport in the atmosphere: quicker settling for irregular shaped and elongated nonspherical dust particles and slower settling for nearly spherical particles. For that reason, our observations do not support the model results of Ginoux [2003].

[5] The objectives of this paper are to show a bias of the center of gravity to either side of the longest axis and to explain the observational results in our former paper using Ginoux's model with different assumption based on the bias of the center of gravity.

2. Samples and Measurements

[6] Shape factors of mineral dust particles in six spring snow samples obtained at Mt. Tateyama, central Japan, were analyzed using scanning electron microscopy and optical microscopy equipped with image analysis software. The analytical methods and atmospheric conditions of dust deposition have been reported in detail by Li and Osada [2007]. Taking dust particles from snow samples of the high mountain areas provide two advantages to study free tropospheric aerosols: (1) the samples of several dust deposition events are obtained simultaneously, (2) the samples are less contaminated by local soil dust because of snow cover near the mountain. The parameters of shape factors are measured on projection area of particles and include particles' centers of gravity (G), particles' folding centers (F), the longest distance from the center of gravity to the particle boundary (L1), and the longest distance from the folding center to the particle boundary (1/2 the longest axis of particle) (L2), as illustrated in Figure 1. A particle's center of gravity was estimated by centering the cumulative frequency distribution of pixels projected on rectangular axes. The folding center of a particle was identified as the point of 1/2a along the line of a particle's longest axis a. Thereby, L1 will be equal to L2 if the location of the center of gravity is the same as the folding center, as a sphere or spheroid. L1 is larger than L2 if a particle has an asymmetric shape with respect to the longest axis, like a cone or other irregular shape. For each snow sample, at least 1400 particles were measured in this study.

Figure 1.

Parameters of shape factor for projection area of a dust particle. G is the center of gravity, F is the folding center, L1 is the longest distance from the center of gravity to the boundary of a particle, L2 is the 1/2a (the longest axis of particles) for F.

3. Bias of the Center of Gravity

[7] Figure 2 shows the relationship of the center of gravity to the folding center for mineral dust particles in six snow samples. It can be seen that most points are located below the 1:1 line, the length of the center of gravity to the particle's boundary is always greater than that of the folding center, the differences between L1 and L2 [(L1 − L2)/L2 × 100%] were 5% on average, 0% minimum, and 24% maximum, suggesting that the dust particles' centers of gravity are very likely biased to either side of the longest axis. The bias of the center of gravity might lead to a preferential orientation for settling particles as heavy side down.

Figure 2.

Relationship of the center of gravity to the folding center of dust particles obtained at Mt. Tateyama, Japan.

[8] For preferential orientation of settling particles, Fuchs [1964] examined the orientation of elongated particles in a shear flow and suggested that particles are oriented with their broad sides parallel to the flow direction. Kagermann and Koehler [1982] studied the motion of non-spherical particles in a turbulent flow and suggested that the orientation of settling particles at the terminal velocity maintains a preferential orientation. Therefore, settling particles might retain a preferential orientation. In the next section, we will apply this hypothesis to Ginoux's model.

4. Settling Velocity as a Function of the Aspect Ratio

[9] Ginoux [2003] extended a mathematical model of settling velocity for spherical particles to ellipsoids with Reynolds number lower than 2. The momentum equation can be expressed in the vertical as

equation image

where u, g, and Fdrag respectively indicate the vertical components of the velocity, the acceleration of gravity, and the drag force. At a steady state, the settling particle reaches a terminal settling velocity u and (1) can be simplified to Fdrag = −mpg. The drag force is a function of an empirical drag coefficient, the projection area of the body normal to the flow, and terminal settling velocity. Derivation of formulae to calculate the terminal settling velocity for an ellipsoid as a function of aspect ratio has been reported in details by Ginoux [2003], on the assumption that the particles were oriented randomly.

[10] Different from Ginoux [2003], we assume here that ellipsoidal particles will settle heavier side down along their longer axis. By replacing the projection area Ap of an ellipsoid as πb2, we reformulated the work of Ginoux [2003] and obtained the following terminal setting velocity u:

equation image

where λ is the aspect ratio, Φp(λ) is the sphericity factor, and ΨD(λ) is a function of λ related to the equivalent diameter Dp(λ), which is defied as the diameter of spherical particles with the same surface area, Re is the Reynolds number, ρ is the density of air, ρp is the density of particles, and μ is the dynamic viscosity of air.

[11] Using λ, Φp(λ) and ΨD(λ) is given as

equation image
equation image

[12] For a given equivalent diameter Dp and aspect ratio λ, terminal setting velocity u is solvable numerically from Equation (2). Figure 3 shows results of the settling velocity calculated for ellipsoidal particles with Dp varying from 2 to 100 μm, and λ from 1 to 10 with a step of 1. First, the settling velocities increase greatly with increasing particle size; the settling velocity of a 100-μm particle is 1000 times higher than that of a particle with 2-μm diameter. Second, considering the effect of the aspect ratio, settling velocity curves show different characteristics with a particle size range divided at about 11 μm. For particles smaller than 11 μm, the settling velocity of spherical particles is lower than that of ellipsoidal particles, and the settling velocity of ellipsoidal particles increases with increasing the aspect ratio from 2 to 10. At about 20 μm, the settling velocity of ellipsoidal particles is comparable to that of spherical particles. However, for particles larger than 30 μm, the settling velocity decreases concomitant with the increasing aspect ratio. To summarize, the settling velocity is more sensitive to the aspect ratio for particles smaller than 11 μm and more sensitive to the particle size for particles larger than 30 μm.

Figure 3.

Settling speed of ellipsoidal particles as a function of size and aspect ratio for sizes of 2–100 μm and aspect ratios of 1–10, changing with a step of 1.

[13] Maring et al. [2003] modeled mineral dust aerosol size distribution change during atmospheric transport and showed that the shape of dust size distribution does not change over thousands of kilometre for particles smaller than 10 μm. Other studies also showed that dust size distribution is essentially similar in everywhere (except near the source areas) with median diameter at around 1–4 μm [Duce et al., 1980; Arao and Ishizaka, 1986; Rea and Hovan, 1995; Li and Osada, 2007]. The size of those dust particles in the atmosphere was primarily in the range of <10 μm where an increased settling for elongated ellipsoids can be found and preferential settling of elongated ellipsoids is active.

[14] Figure 4 shows the relative difference of calculated settling velocity between ellipsoidal and spherical particles {Δu = 100% × [u (λ) − u (λ = 1)]/u (λ = 1)}. For example, the settling velocity of particles of 2 μm diameter increases respectively around 50%, 100%, and 165% for aspect ratios of 2, 4, and 10. The relative difference decreases with increasing particle size. For particles of 10 μm, the settling velocity increase for ellipsoids is around 30–40%, with little difference shown for aspect ratios of 1–10. On the other hand, a 40% decrease of settling velocity for ellipsoids is apparent at around 40–50 μm for the aspect ratio of 10.

Figure 4.

Relative difference of calculated settling velocity between spherical and ellipsoidal particles, calculated as Δu = 100% × [u (λ) − u (λ = 1)]/u (λ = 1).

[15] Our results differ from those of Ginoux [2003] because we use a preferential orientation as an initial condition of ellipsoidal particles rather than assuming that particles are oriented randomly. Our results correspond with those of Fuchs [1964] who also noticed an increased settling velocity for particles settling along their polar axis for aspect ratios of less than 4. As shown in Figures 3 and 4, elongated particles smaller than 11 μm will deposit faster than spherical particles with equal surface area.

[16] After mineral dust particles are injected into the atmosphere by strong surface winds, larger (>20 μm) particles would be dry deposited immediately near the source area because of their higher terminal velocity. The remaining smaller (<15 μm) particles might be further transported into the free troposphere, where dust particles can be transported long distances. The dust particles in the free troposphere were primarily of sizes less than 10 μm [Maring et al., 2003]. During long-range transport in the atmosphere, ellipsoidal elongated particles would settle faster than spherical particles with equal surface area. At receptor downwind areas such as Japan, the proportion of nearly spherical dust particles would be higher than that in source areas such as the Chinese desert areas, as observed by Li and Osada [2007]. The essentially nearly spherical dust particles observed at downwind area after long-range transport could also suggest that, except over dust sources, it is valid to assume spherical particles for transport model and radiative calculation.

5. Summary and Conclusions

[17] The positions of particles' centers of gravity and the folding centers were analyzed for dust particles in snow from a high mountain in Japan. Measurement results showed that the centers of gravity of dust particles are very likely biased to one side of the longest axis. The difference between L1 (the longest distance from the center of gravity to the boundary of particles) and L2 (1/2 of the longest axis of particles) was 5% on average, 0% minimum, and 24% maximum. The bias of the center of gravity might lead to a preferential orientation for settling particles as heavy side down. Applying the preferential orientation of settling particles to the Ginoux's model, settling velocity for ellipsoidal particles at Reynolds number lower than 2 was estimated as a function of the aspect ratio.

[18] The calculation results for particles smaller than 11 μm showed that (1) the settling velocity of spherical particles is lower than that of ellipsoids, and (2) the settling velocity increases with increasing aspect ratio. The relative differences of settling velocity of ellipsoidal to spherical particles were positive and high for 2 μm particles, but decreased to negative values for particles larger than 20 μm. Therefore, elongated particles smaller than 11 μm will be deposited faster than spherical particles with equal surface area. The preferential settling of elongated particles leads to an increased proportion of nearly spherical particles after long range transport in the atmosphere, as observed in Li and Osada [2007]. Our results also indicate that, away from dust sources, it is valid to assume spherical particles for gravitational settling in transport model and for radiative calculation in transfer radiative model.

Acknowledgments

[19] We are grateful to two anonymous reviewers for their valuable comments which improve our paper considerably. We also wish to thank Jonas Wiklund (Graduate School of Mathematics, Nagoya University) for his help with equations. This study was partially supported by Ministry of Education, Culture, Sports, Science and Technology, Grants-in-Aid for Scientific Research (C) 13680601 and (B) 15310012, and Grants-in-Aid for Scientific Research on Priority Areas 18067005.

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