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Water uptake and equilibrium sizes of aerosol particles at high relative humidities: Their dependence on the composition of the water-soluble material

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Equilibrium water uptake and the sizes of atmospheric aerosol particles have for the first time been determined for high relative humidities, i.e., for humidities above 95 percent, as a function of the particles chemical composition. For that purpose a new treatment of the osmotic coefficient has been developed and experimentally confirmed. It is shown that the equilibrium water uptake and the equilibrium sizes of atmospheric aerosol particles at large relative humidities are significantly dependent on their chemical composition.

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A :

proportionality factor

a w :

activity of water in a solution

c p v :

specific heat of water vapour at constant pressure

c w :

specific heat of liquid water

f :

relative humidity

l w :

specific heat of evaporation of water

M i :

molar mass of solute speciesi

M s :

mean molar mass of all the solute species in a solution

M w :

molar mass of water

m 0 :

mass of an aerosol particle in dry state

m i :

mass of solute speciesi

m s :

mass of solute

m w :

mass of water taken up by an aerosol particle in equilibrium state

m :

total molality=number of mols of solute species in 1000 g of water

m i :

molality of solute speciesi

m k :

total molality of a pure electrolytek

O(m 2):

remaining terms being of the second and of higher powers ofm

p + :

standard pressure

p′ :

total pressure of the gas phase

p″ :

pressure within a droplet

p 1,p 2,p 3 :

coefficients in the expansion of φM

p 1i, p2i, p3i :

specific parameters of ioni

p s :

saturation vapour pressure

p′ w :

water vapour pressure

R w :

individual gas constant of water

r :

radius of a droplet

r 0 :

equivalent volume radius of an aerosol particle in dry state

T :


T 0 :

standard temperature

T 1 :

temperature of the pure water drop in the osmometer

v w :

specific volume of pure water

z i :

valence of ioni

αi :

relativenumber concentration of ioni in a solution


correction term due to the adsorption of ions at liquid-solid interfaces


activity coefficient of solute speciesi in a solution, related to molalities

ΔI :

bridge current

ΔT :

temperature difference between solution and pure water drop in the osmometer


exponential mass increase coefficient

μ w :

specific chemical potential of water vapour

μ w :

specific chemical potential of water

μ′ 0 w :

specific chemical potential of pure water vapour

μ″ 0 w :

specific chemical potential of pure water

ρ0 :

density of an aerosol particle in dry state

ρw :

density of pure water


surface tension of a droplet

σ0 :

surface tension of pure water, i.e., at infinite dilution of the solute


osmotic coefficient

ϕk :

osmotic coefficient of a solution of a pure electrolytek

ϕk :

osmotic coefficient of a solution of a mixed solute

ϕM :

fugacity coefficient of water vapour


s i=1 αi z 2 i


  1. Bjerrum, N. (1918),Die Dissoziation der starken Elektrolyte, Z. Elektrochemie24, 321–328.

  2. Chen, C. S. (1974),Evaluation of the vapor pressure over an aerosol particle, J. Atm. Sci.31, 847–849.

  3. Debye, P. andHückel, E. (1923),Zur Theorie der Elektrolyte, Physik. Z.24, 185–206.

  4. Dufour, L. andDefay, R.,Thermodynamics of Clouds (Academic Press, New York 1963).

  5. Ferron, G. A.,On the Deposition of Aerosols in the Human Airways (Delft University Press, Delft 1976).

  6. Fitzgerald, J. W. (1974),Effect of aerosol composition on cloud droplet size distribution: A numerical study, J. Atm. Sci.31, 1358–1367.

  7. Grassl, H. (1973),Aerosol influence on radiative cooling, Tellus25, 386–395.

  8. Hänel, G. (1968),The real part of the mean complex refractive index and the mean density of samples of atmospheric aerosol particles, Tellus20, 371–379.

  9. Hänel, G. (1976),The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air, Advances in Geophysics19, 73–187.

  10. Hänel, G. andHeyder, J. (1976),A simple model for the deposition of particles in man considering the actual relative humidity in the lung, Proc. of the Annual Congress of the ‘Gesellschaft für Aerosolforschung’, Bad Soden.

  11. Harned, H. S. andOwen, B. B.,The Physical Chemistry of Electrolytic Solutions (Reinhold Book Corporation, New York 1958).

  12. Jacobi, W. (1967),Abscheidung und Verteilung von Aerosolen im Atemtrakt, Experientia Supplementum 13, 60–74 (Birkhäuser Verlag, Basel and Stuttgart).

  13. Low, R. D. H. (1969),A generalized equation for the solution effect in droplet growth, J. Atm. Sci.26, 608–611.

  14. Mason, B. J.,The Physics of Clouds (Clarendon Press, Oxford 1971).

  15. Reiter, R., Sladkovič, R. andPötzl, K. (1974),Eine vierjährige Reihe aerosolchemischer Reinluftuntersuchungen in 1780 m Meereshöhe; Messergebnisse und ihre atmosphärisch-physikalische Interpretation, Wissenschaftliche Mitteilung No. 9 of the Institute for Atmospheric Environmental Research at Garmisch-Partenkirchen.

  16. Robinson, R. A. andStokes, R. H. (1949),Tables of osmotic and activity coefficients of electrolytes in aqueous solution at 25°C, Trans. Farad. Soc.45, 612–624.

  17. Robinson, R. A. andStokes, R. H.,Electrolyte Solutions (Butterworths, London 1959).

  18. Rush, R. M. andJohnson, J. S. (1966),Osmotic coefficients of synthetic sea-water solutions at 25°C, J. Chemical and Engineering Data11, 590–592.

  19. Stokes, R. H. (1948),A thermodynamic study of bivalent metal halides in aqueous solution. Part XVII —Revision of data for all 2∶1 and 1∶2 electrolytes at 25°, and discussion of results, Trans. Farad. Soc.44, 295–307.

  20. Thudium, J. (1976),A gas pycnometer (microliter) for determining the mean density of atmospheric aerosol particles, J. Aerosol Sci.7, 167–173.

  21. Thudium, J. (1977),Über den Flüssigwassergehalt und die Grösse atmosphärischer Aerosolteilchen im Bereich hoher relativer Luftfeuchtigkeiten, Ph.D. thesis, Johannes Gutenberg-Universität, Mainz.

  22. Winkler, P. andJunge, C. (1972),The growth of atmospheric aerosol particles as a function of relative humidity. Part I: Method and measurements at different locations, J. Rech. Atmos. (Mémorial Henri Dessens), 617–638.

  23. Zdunkowski, W. G. andMcQuage, N. D. (1972),Short-term effects of aerosol on the layer near the ground in a cloudless atmosphere, Tellus24, 237–254.

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This work is part of a Ph.D. thesis carried out at the Meteorological Institute of the Johannes Gutenberg-Universität, Mainz.

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Thudium, J. Water uptake and equilibrium sizes of aerosol particles at high relative humidities: Their dependence on the composition of the water-soluble material. PAGEOPH 116, 130–148 (1978). https://doi.org/10.1007/BF00878988

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Key words

  • Condensation nuclei
  • Aerosol particles
  • -water uptake of
  • -growth of