Atmospheric ion depletion as a measure of aerosol particle diameter concentration

Pergamon

J. Aerosol Sci. Vol. 28, Suppl. 1, pp. $377-$378, 1997 ©1997 Elsevier Science Ltd. All fights reserved Printed in Great Britain 0021-8502/97 $17.00+0.00

PII:S0021-8502(97)00235-8

ATMOSPHERIC ION DEPLETION AS A MEASURE OF AEROSOL PARTICLE DIAMETER CONCENTRATION

H. Tammet Department of Environmental Physics, University of Tartu, 18 lJlikooli Str., Tartu EE2400, Estonia

KEYWORDS air ions, polydisperse particles, charge balance, ion-aerosol attachment, aerosol concentration

ATMOSPHERIC ION BALANCE The balance of monomobile small ions in tropospheric air is described by equation oo

d n i = q _ c~ltn-i _ ni f ~ _ , f S i , j ( r ) p j ( r ) f ( r ) d r dt 0 J=-°°

(1)

where i is the number charge of ions (+ 1 or -1), n, is the number concentration of corresponding ions, j =q~e is the number charge of particles, f i r ) & is the number concentration of particles in the radius interval of dr, q is the ionization rate, ct is the ion-ion recombination coefficient, 13,,jis the ion-particle combination or attachment coefficient, and pj(r) is the probability to carry the chargej. The probabilities pj are calculated according to the combination coefficients as shown by Hoppel (1985). The particles of the radius of over 0.2 ~tm are described by the continuum regime model je 2 x = i 4nreok---------f '

4rtrkTZix [ScJ - e(exp(x) - 1)'

(2)

where Z, is the small ion mobility. The values ofnanometer particle combination coefficients presented by different authors vary in a range of about 50%, probably due to the uncontrolled mobility and mass distribution of small ions. In the present study an approximate function 13(i,j. T, Z,) has been designed and implemented as a computer procedure. The function converges to the continuum regime model when increasing the particle size, and fits the theoretical and experimental results by Pui et al. (1988), Hoppel (1990), Mayya and Sapra (1996), and Reischl et al. (1996), in the ultrafine and nanometer size range. AEROSOL ELECTRICAL DENSITY The ion depletion term in Equation (1) is a product of ion concentration and an integral that depends essentially only on the aerosol concentration and size distribution. Thus it can be interpreted as an integral aerosol effect g~0 defined according to Jaenicke (1976) through its specific weight function Wg(') Qt~

g°'= fw(s"(r)f(r)dr

w(s°(r) = Z [ 3 , , j ( r ) p j ( r ) ,

,

0

j=-o~

$377

(3)

$378

Abstracts of the 1997 European Aerosol Conference

and called the aerosol electrical density (Tarnmet, 1991). Aerosol electrical density differs for positive and negative ions. The average electrical density g = (g~q) + g~-l)) / 2 is recommended as an aerosol characteristic. It is a measure of the ion depletion capacity o f a polydispersed aerosol. CORRELATION BETWEEN AEROSOL ELECTRICAL DENSITY AND PARTICLE DIAMETER CONCENTRATION The particle diameter concentration Ca = j'2rflr)dr is interpreted as the length of a chain composed of all particles in a volume unit. In the continuum limit, all combination coefficients are proportional to the particle size. Assuming average small ion mobility 1.45 cm2V-ls-1 the continuum regime conversion equation is Ca - (4.5 s/cm2)g Fine and ultrafine particles increase the conversion coefficient and make it dependent on the particle size distribution. The effect of particle size distribution is studied using computer simulation. The particles are assumed to be distributed according to the KL-model (Tammet, 1988) const r f ( r ) = (r/r×) x + (r×/r) L ' (4) and the parameters are chosen as independent triangle-distributed random numbers from the intervals r --- 50+30 nm, K = 3+1, L = 1+1. The result is a regression equation Cd -- (5.1 sdcm2)g

(5)

fitting the computed integrals with the relative standard deviation of 2.7%. The error caused by the variation of the atmospheric aerosol size spectra has proved to be considerably less than typical errors of different origin in atmospheric aerosol measurements. Thus an instrument measuring the air ion depletion can be calibrated as a meter of the particle diameter concentration. The average value g ~ 0.02 s-~ known from atmospheric electrical research corresponds to the particle diameter concentration of 1 km / m 3. ACKNOWLEDGEMENTS This research has been supported in part by the Estonian Science Foundation grant no. 3050. REFERENCES Hoppel, W.A. (1985) Ion-aerosol attachment coefficients, ion depletion, and the charge distribution on aerosols. J. Geophys. Res. D, 90, 5917-5923. Hoppel, W . A and G M Frick (1990) The nonequilibrium character of aerosol charge distributions produced by neutralizers. Aerosol Sci. Technol., 12, 471--496. Jaenicke, R. (1976) Methods for determination of aerosol properties. In Free Particles, pp. 468-483. Acad. Press, N e w York. Mayya, Y.S. and B . K Sapra (1996) Variation of the aerosol charge neutralization coefficient in the entire particle size range. ~ Aerosol Sci., 27, 1169-1178. Pui, D Y H . , Fruin, S and McMurry, P.H. (1988) Unipolar diffusion charging of ultrafine aerosols. Aerosol Sci. Technol., 8, 173-187. Reischl, G.P, Makel~, J.M., Karch, R. and Necid, J. (1996) Bipolar charging ofultrafine particles in the size range below 10 nm. J. Aerosol Sci., 27, 931-949. Tammet, H. (1988) Models of size spectrum of tropospheric aerosol. Lecture Notes in Physics, 309, 75-79. Tammet, H. (1991) Aerosol electrcal density: interpretation and principles of measurement. Rep. Ser. Aerosol Sci. (Helsmki), 19, 128-133. Yair, Y. and Z. Levin (1989) Charging of polydispersed aerosol particles by attachment of atmospheric ions. J. Geophys. Res. D, 94, 13,085-13,091.