Coagulation from Gravitational Settling

FIGURE 12.7 Comparison between coagulation mechanisms for a particle of 1 ivc radius as a function of the particle radius of the second interacting particle. 

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Figure 4. Residence time of particles in seconds (left axis) and days (right axis) as a function of particle radius. The shaded areas represent estimates of the lifetimes made as follows 1, molecular or ionic clusters C, coagulation of particles P, removal by precipitation F, gravitational settling A, derived from spatial distribution of Aitken particles R, derived from the distribution of small radioactive particles. From Kreidenweis et al. (1999) in Atmospheric Chemistry and Global Change by Brassem et al. 1999 by Oxford University Press, Inc. Used by permission.

The parameters for differential-sedimentation coagulation and settling have the same grouping of constants but different units because differential sedimentation is second order in the particle size distribution from Equation 2, while gravitational settling is first order in the size distribution as seen in Equation 1. All parameters were chosen to be independent of particle size, assuming further that particle density is also independent of particle size. 

Sedimentation velocities of aerosol particles depend on particle shape. The models of aerosol behaviour that are now available are derived for perfect spheres that have no porosity. The deviations of real particles from this ideal are handled by correction factors called shape factors. In the case of gravitational settling, the dynamic shape factor is used to account for deviations from sphericity and for porosity. These shape factors are not known well and frequently are estimated by back calculation from experimental data for simulant aerosols. This, of course, is not a reliable procedure. There have been some attempts to predict shape factors based on the fractal nature of particles that have grown by coagulation [A-7b]. 

The molecules of both HSl and HS2 have a high colloid stability due to their very low collision efficiency and small size which prevent them from settling under normal gravitational acceleration. Their separation in a centrifuge with a g value of some thousands is still practically inefficient. This fact is used for sedimentation analysis to investigate the destabilization and aggregation rate of the coagulation process of humic substances. 

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