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Ionic charging of aerosol particle in the transition regime
J. Aerosol Sci., Vol. 23, Suppl. 1, pp. $87-$88, 1992 Printed in Great Britain.
0021-8502/92 $5.00 + 0.00 Pergamon Press Ltd
IONIC CHARGING OF AEROSOL PARTICLE IN THE TRANSITION REGIME A.V.Filippov Process- and Aerosol Measurement Technology, University of Duisburg, Postfach 10 15 03, D-4100 Duisburg, F.R.G.
KEYWORDS Aerosol electrification, theory, ion attachment, numerical simulation, Monte Carlo method. Ultrafme particles can be found in substantial quantifies in both industrial and atmospheric aerosols. For instance, particles in the nanometer size range are produced in large amounts in combustion of organic materials. In air, aerosol particles become charged through capture of small ions. In many applications, such as aerosol measurement or calculation of charge distributions in aerosols, knowledge of the rate of capture of ions is essential. In the present work a theory for aerosol charging in the region of moderate Knudsen numbers is proposed. Far from the particle ion concentration n satisfies macroscopic transport equations, which in the case of spherically symmetric electrostatic potential ~b yield the following formula (Fuchs, 1963)
J=
4nn~82Kexp[-bCp(8)l D] 1
(1)
1+exp[-bCp(8)lD] ~foeXp[IMp(S/x)lD]dx
K-- p c
(2)
In equations (1)-(2) J is the charging rate, bi and Di are the mobility and diffusion coefficients o f ions, n t is the background ion concentration, 8 is the radius o f the boundary sphere, E is the electric field intensity, p is the attachment probability and c is the characteristic ion thermal velocity. Inside the boundary sphere r < 8 (r is the distance to the particle center) ion collisions with neutral gas molecules are taken into account and modelled in the framework of
S87
$88
A.V. FILIPPOV
classical Langevin scheme. In the intervals between the ion-neutral molecule collisions ion trajectories are calculated with allowance for electrostatic interaction between the ion and the particle. Probability of ion attachment to the particle p, which is found by calculation of many ion paths, enables to determine the charging current J. The described approach has been realized in a numerical Monte Carlo algorithm and computer code, used for calculation of charging rates in a wide range of particle sizes and ion parameters. Good agreement between the calculated data and experiments on ultrafine particle charging (Adachi et al., 1986; Biischer et al., 1992, Romay and Pui, 1992) is shown. The presented theory can be extended to more complicated cases of nonspherical particles, allowance for external electric field and others.
REFERENCES Adachi, M., Kousaka, Y. and Okuyama, K. (1985). Unipolar and bipolar charging of ultrafine aerosol particles. J.Aerosol Sci., 16, 109-123. Btiseher, P., Sehmidt-Ott, A. and Wiexiensohler, A. (1992) Efficiency of unipolar diffusion charging of ultrafme aerosol as function of the m-product. J.Aerosol Sci. (Submitted). Fuehs, N.A. (1963). On the stationary charge distribution of aerosol particles in a bipolar ionic atmosphere. Oeophys.Pura Appl., 56, 185-193. Romay, F.J. and Pui, D.Y.H. (1992). On the combination coefficient of positive ions with ultrafme neutral particles in the transition and free-molecular re~mes. J.Aerosol SCI.(To be published).
0021-8502/92 $5.00 + 0.00 Pergamon Press Ltd
IONIC CHARGING OF AEROSOL PARTICLE IN THE TRANSITION REGIME A.V.Filippov Process- and Aerosol Measurement Technology, University of Duisburg, Postfach 10 15 03, D-4100 Duisburg, F.R.G.
KEYWORDS Aerosol electrification, theory, ion attachment, numerical simulation, Monte Carlo method. Ultrafme particles can be found in substantial quantifies in both industrial and atmospheric aerosols. For instance, particles in the nanometer size range are produced in large amounts in combustion of organic materials. In air, aerosol particles become charged through capture of small ions. In many applications, such as aerosol measurement or calculation of charge distributions in aerosols, knowledge of the rate of capture of ions is essential. In the present work a theory for aerosol charging in the region of moderate Knudsen numbers is proposed. Far from the particle ion concentration n satisfies macroscopic transport equations, which in the case of spherically symmetric electrostatic potential ~b yield the following formula (Fuchs, 1963)
J=
4nn~82Kexp[-bCp(8)l D] 1
(1)
1+exp[-bCp(8)lD] ~foeXp[IMp(S/x)lD]dx
K-- p c
(2)
In equations (1)-(2) J is the charging rate, bi and Di are the mobility and diffusion coefficients o f ions, n t is the background ion concentration, 8 is the radius o f the boundary sphere, E is the electric field intensity, p is the attachment probability and c is the characteristic ion thermal velocity. Inside the boundary sphere r < 8 (r is the distance to the particle center) ion collisions with neutral gas molecules are taken into account and modelled in the framework of
S87
$88
A.V. FILIPPOV
classical Langevin scheme. In the intervals between the ion-neutral molecule collisions ion trajectories are calculated with allowance for electrostatic interaction between the ion and the particle. Probability of ion attachment to the particle p, which is found by calculation of many ion paths, enables to determine the charging current J. The described approach has been realized in a numerical Monte Carlo algorithm and computer code, used for calculation of charging rates in a wide range of particle sizes and ion parameters. Good agreement between the calculated data and experiments on ultrafine particle charging (Adachi et al., 1986; Biischer et al., 1992, Romay and Pui, 1992) is shown. The presented theory can be extended to more complicated cases of nonspherical particles, allowance for external electric field and others.
REFERENCES Adachi, M., Kousaka, Y. and Okuyama, K. (1985). Unipolar and bipolar charging of ultrafine aerosol particles. J.Aerosol Sci., 16, 109-123. Btiseher, P., Sehmidt-Ott, A. and Wiexiensohler, A. (1992) Efficiency of unipolar diffusion charging of ultrafme aerosol as function of the m-product. J.Aerosol Sci. (Submitted). Fuehs, N.A. (1963). On the stationary charge distribution of aerosol particles in a bipolar ionic atmosphere. Oeophys.Pura Appl., 56, 185-193. Romay, F.J. and Pui, D.Y.H. (1992). On the combination coefficient of positive ions with ultrafme neutral particles in the transition and free-molecular re~mes. J.Aerosol SCI.(To be published).