Polydispersed aerosols, theory

Figures 3 and 4 show the variation of the average attachment coefficient with CMD. It can be seen that for particles of CMD less than 0.06 ym and Og = 2 the kinetic theory predicts an attachment coefficient similar to the hybrid theory, whereas for CMD greater than about 1 ym the diffusion theory and the hybrid theory give approximately the same results. For a more polydisperse aerosol (Og = 3) the kinetic theory deviates from the hybrid theory even at a CMD = 0.01 ym. The diffusion theory is accurate for a CMD greater than about 0.6 ym. These results are easily explained since as the aerosol becomes more polydisperse, there are more large diameter particles (CMD >0.3 ym) which attach according to the diffusion theory. In contrast, the kinetic theory becomes more inaccurate as the aerosol becomes more polydisperse.

Unattached fractions of RaA (at t = °°) for two mine aerosols and for a typical room aerosol are shown in Table III. It is usually assumed that the attachment of radon progeny to aerosols of CMD < 0.1 ym follows the kinetic theory. In Table III it is apparent that the hybrid and kinetic theories predict similar unattached fractions for monodisperse aerosols. However, for more polydisperse aerosols, the kinetic theory predicts lower unattached fractions than the diffusion theory and thus the diffusion theory is the more appropriate theory to use. It is also evident that the kinetic-diffusion approximation predicts unattached fractions similar to those predicted by the hybrid theory in all cases. 

Figure 5 shows the variation of the hybrid theory with CMD for various Og. It is obvious that assuming an aerosol to be mono-disperse when it is in fact polydisperse leads to an underestimation of the attachment coefficient, leading in turn to large errors in calculation of theoretical unattached fraction. 

The kinetic theory and the diffusion theory may be used for certain aerosol distributions. However, these two theories begin to deviate from the hybrid theory as the aerosol polydispersity increases. Use of either the kinetic theory or the diffusion theory may therefore result in large errors. 

To study charging mechanisms theoretically for either diffusion charging or field charging, it is necessary to make several assumptions regarding the aerosol. First, the particles are assumed to be spherical. This assumption is reasonable for isometric particles. Second, it is also assumed that the particles are monodisperse. The effect of polydispersity complicates but does not invalidate theory. Third, there are no interactions between individual particles. Finally, the ion concentration and electric field near each particle are assumed to be uniform. These last two assumptions are essentially true for all natural and industrial aerosols. Thus except in the most extreme cases, theoiy should be adequate without other modification. 

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