Attachment coefficient

The theory and appHcation of SF BDV and COV have been studied in both uniform and nonuniform electric fields (37). The ionization potentials of SFg and electron attachment coefficients are the basis for one set of correlation equations. A critical field exists at 89 kV/ (cmkPa) above which coronas can appear. Relative field uniformity is characterized in terms of electrode radii of curvature. Peak voltages up to 100 kV can be sustained. A second BDV analysis (38) also uses electrode radii of curvature in rod-plane data at 60 Hz, and can be used to correlate results up to 150 kV. With d-c voltages (39), a similarity rule can be used to treat BDV in fields up to 500 kV/cm at pressures of 101—709 kPa (1—7 atm). It relates field strength, SF pressure, and electrode radii to coaxial electrodes having 2.5-cm gaps. At elevated pressures and large electrode areas, a faH-off from this rule appears. The BDV properties ofHquid SF are described in thehterature (40—41). 

FIG. 25. Simulation results for quasi-Townsend discharges (a) ionization coefficients for SiHa, H2, and Ar (b) attachment coefficients for SiHa and CFa-... 

Theoretical calculations of unattached fractions of radon progeny require prediction of an attachment coefficient. Average attachment coefficients for aerosols of various count median diameters, CMD, and geometric standard deviations, ag, are calculated using four different theories. These theories are ... 

The two fundamental theories for calculating the attachment coefficient, 3, are the diffusion theory for large particles and the kinetic theory for small particles. The diffusion theory predicts an attachment coefficient proportional to the diameter of the aerosol particle whereas the kinetic theory predicts an attachment coefficient proportional to the aerosol surface area. The theory... 

In this study, values of the average attachment coefficient,... 

Solution of this diffusion problem, assuming quasi-steady state coagulation, leads to an attachment coefficient of the form ... 

The kinetic theory of radon progeny attachment to aerosol particles assumes that unattached atoms and aerosol particles undergo random collisions with the gas molecules and with each other. The attachment coefficient, 3(d), is proportional to the mean relative velocities between progeny atoms and particles and to the collision cross section (Raabe, 1968a) ... 

The attachment coefficient is a function of the aerosol particle diameter, d, and mean velocity, v, as well as the unattached progeny diameter, d, and its mean velocity v. Since in most situations d d and v v, equation (2) reduces to... 

The attachment coefficient, 3, corresponding to the hybrid theory can be shown to be (Fuchs, 1964)... 

Fuchs attachment coefficient can be simplified by making various assumptions ... 

This approximation may be considered to be an alternative to the hybrid theory. The value of di can be found by equating the attachment coefficients for the diffusion and kinetic theories (d x = 8D/v). 

From Figure 1 it can be seen that Fuchs theory and equation (5) predict similar attachment coefficients. Equation (5) is therefore used in calculating average attachment coefficients. 

The average attachment coefficient 3 can be calculated for the diffusion and the kinetic theory from the equation ... 

Attachment coefficient is for neutral daughter products. A cylindrical capacitor used as a mobility analyzer. 

Figures 3 and 4 show the variation of the attachment coefficient with count median diameter for the diffusion, kinetic, hybrid and kinetic-diffusion theory for geometric standard deviations of 2 and 3 respectively.

Figure 5 illustrates the effect of the geometric standard deviation on the attachment coefficient using the hybrid theory. 

In Figs. 6 and 7 the attachment coefficient is plotted against the geometric standard deviation using the four theories, for count median diameters of 0.2 ym and 0.3 ym respectively. 

Figure 5. Attachment coefficient vs CMD using the hybrid theory for various particle distributions.

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.

The kinetic-diffusion approximation predicts an attachment coefficient similar to the hybrid theory for all CMDs and for both Og m 2 and 3 (Figs. 3 and 4). The advantage of this theory is that the average attachment coefficient can be calculated from an analytical solution numerical techniques are not required. 

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 variation of attachment coefficient with Og for CMD =0.2 ym and 0.3 ym is shown in Figures 6 and 7. Again it is apparent that the kinetic theory or diffusion theory are correct only at certain CMD and og. Neither is applicable under all circumstances. It is also evident that the kinetic-diffusion theory is a good approximation to the hybrid theory under all circumstances. 

Calculation of the attachment coefficient is required for theoretical prediction of the unattached fraction of radon progeny. The hybrid theory, which is a form of Fuchs theory with certain justifiable assumptions, can be used to describe attachment to aerosols under all conditions of Og and CMD. 

Mean Life, Attachment, Recombination and Plateout. The approximate mean life (T) of Po-218 in ion form can be represented as ( X + an + N + po) where X is the decay constant for Po-218, a is the recombination coefficient for Po-218 and ordinary ions of negative charge in the atmosphere, n is the concentration of small negative ions, 8 is the attachment coefficient, N is the number of condensation... 

The attachment rate to the atmospheric aerosol X=0 Z, is a linear function of the particle concentration Z. Values of 5 10 3 cm3h-l for the average attachment coefficient B measured in laboratory rooms were reported by Mohnen (1969) and Porstendorfer and Mercer (1978). 

The calculated parameters X, qf, cp and ri are presented in Tables lb, lib and III. In addition the attachment equivalent diameter 3 was determined from the attachment coefficient 6 = X/Z by means of the attachment theory (Porstendorfer et al., 1979). 

In poorly ventilated rooms the average value of the attachment coefficient with 7.4 10 3 cm h 1 (Table lb) was significantly higher than the value in rooms with moderate ventilation (2.4 10 3 cm It1 ) (Table lib) corresponding to diameters d = 117 nm and d = 6.5 nm, respectively. This aged aerosols in poorly ventilated rooms did not only show lower particle concentrations but also greater particle diameters. 

Determination of the Attachment Coefficients of Atoms and Ions on Monodisperse Aerosols, J. of Aerosol Science 10 21-28 (1979). 

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