Direct measurement of mass transfer to agglomerates in the transition regime

Abstract

Mass transfer to aerosol particles is an important process in many natural and industrial systems. For example, the enrichment of atmospheric aerosols with heavy metals has been attributed to condensation of metal vapors on particle surfaces in combustion systems. The transport of organics to a particle is an important mechanism in soot formation. In addition to these examples involving the transport of molecules, mass transfer of ultrafine particles plays an important role in powder synthesis and in the measurement of atmospheric aerosols with the recently developed epiphaniometer (Bahensperger et al., 1990). This instrument measures the attachment rate of hydrated radioactive lead atoms to an aerosol sample. For each of these systems, it is critical to understand the relationship between the mass transfer to a particle and its physical characteristics. Theoretical descriptions of mass transfer to particles have traditionally been based on the assumption that the particles are dense spheres. However, many combustion systems emit fumes consisting of agglomerates of tiny spherules. The structure of these agglomerates has been described as "fractal" or "self-similar" (Forrest and Witten, 1979; Meakin, 1986). Although the accuracy of the fractal model is still an active area of research, such models are useful in characterizing the structure. An important property of an agglomerate is the hydrodynamic radius R_H , the radius of the sphere that experiences the same drag as an agglomerate when both particles are moving at the same speed in the same gas. In the continuum regime, when the gas mean free path λ is smaller than R_H, R_H typically scales with R_g. In the free molecular regime, where the particle diameter is small compared to the mean free path λ, the drag is determined by the impingement rate of gas molecules on the surface so R_H is proportional to the projected area equivalent radius, which is generally not equal to the radius of gyration. The mass transfer equivalent radius RD of an agglomerate is analogous to the hydrodynamic radius. The free molecule (i.e. kinetic) regime mass transfer should be well correlated with drag because both processes are controlled by the molecular impingement rate (Meakin et al., 1989; Schmidt-Ott et al., 1990). In the continuum regime, the mass transfer and hydrodynamic radii are expected to be similar, based on the results for such shapes as slender rods. In the transition regime, one expects that R_H and R_D will be different unless the mean free path of the diffusing species λ_D is similar to the gas mean free path λ. In this paper we compare measurements of the drag and mass transfer for nearly spherical particles of ammonium sulfate, spherical polystyrene latex and titanium dioxide agglomerates. For each aerosol, a narrow mobility range was selected with the differential mobility analyzer (DMA). This nearly monodisperse aerosol was mixed with a controlled concentration of radioactive lead atoms using the epiphaniometer (Gäggeler et al., 1989). The amount of lead attached to the particles was measured, giving an indication of the relative transfer rates of the lead to the spheres and agglomerates.

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