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Humidity effects on gravitational settling and Brownian diffusion of atmospheric aerosol particles

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Abstract

The dependency on relative humidity of the settling velocity of aerosol particles in stagnant air and of the diffusion coefficient due to Brownian motion of aerosol particles was computed for six aerosol types and different particles sizes in dry state. The computations are based (1) on mean bulk densities of dry aerosol particles obtained from measurements or from the knowledge of the chemical composition of the particles, (2) on micro-balance measurements of the water uptake per unit mass of dry aerosol substance versus water activity at thermodynamic equilibrium, and (3) on measurements of the equilibrium water activity of aqueous sea salt solutions. The results show a significant dependence of the settling velocity and Brownian diffusion of aerosol particles on relative humidity and on the particle's chemical composition.

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Abbreviations

A :

surface parameter of a particle

B :

surface parameter of a particle

c L :

velocity of sound in moist air

C :

1+Kn[A+Qexp(−B/Kn]=slip correction

D :

diffusion coefficient of a particle

D 1 :

D(κ=1)=diffusion coefficient of a spherical particle

f :

P w /P we (T,P)=relative humidity (f=0 dry air,f=1 saturated air)

g:

acceleration due to gravity

g :

|g|

k :

1.3804×10−16 erg/°K=Boltzmann constant

Kn :

λ L /r=Knudsen number of a particle

Kn 0 :

λ 0L /r 0=Knudsen number of a dry particle

m :

4πr 3ϱ/3=mass of a particle

m L :

4πr 3ϱ L /3=mass of the moist air displaced by a particle

M :

mobility of a particle

M 0 :

molar mass of dry air

M w :

molar mass of water

Ma :

|u−u L |/c L =Mach number of the particles motion relative to the ambient air

n :

particle number per unit volume of air

P :

P 0+P w =pressure of the moist air

P 0 :

partial pressure of the dry air

P w :

partial pressure of the water vapour

P we :

P we (T,P)=equilibrium partial water vapour pressure over a plane surface of water saturated with air

Q :

surface parameter of a particle

r :

equivalent radius of a particle (radius of a sphere with the particles volume)

r 0 :

equivalent radius of a particle in dry state

R :

1+0.13Re 0.85=inertia correction

R 0 :

specific gas constant of dry air

R w :

specific gas constant of water

Re :

2rρ L ❘u−u L ❘/η L =Reynolds number of the particles motion relative to the ambient air

t :

time

T :

absolute temperature

u:

velocity of a particle

u :

(amount of the) settling velocity of a particle in stagnant air

u 1 :

u(κ=1)=(amount of the) settling velocity of a spherical particle in stagnant air

u L :

velocity of the ambient moist air (far enough from the particle where the flow pattern remains undistorted)

W :

drag coefficient of a particles equivalent sphere

δ:

empirical parameter in equation (3.1)

η:

dynamic viscosity of a particles liquid cover

η L :

dynamic viscosity of moist air

η0L :

dynamic viscosity of dry air (at the same pressure and temperature like the moist air)

ϑ:

celsius temperature

κ:

dynamic shape factor of a particle (κ=1 for a sphere)

κ0 :

dynamic shape factor of a dry particle

λ L :

mean free path of the molecules in moist air

λ0L :

mean free path of the molecules in dry air (at the same pressure and temperature like the moist air)

λ Po :

mean free path of the molecules in dry air at the pressureP 0 of the dry air and the temperature given

ξ:

factor of solid to liquid change-over (ξ=1 for a solid particle)

ρ:

mean bulk density of a particle

ρ L :

density of the moist air

ρ0L :

density of the dry air at the same pressure and temperature like the moist air

ρ0 :

mean bulk density of a dry particle

σ0 :

mean diameter of the molecules of dry air

σ w :

diameter of water molecules

τ:

relaxation time of a particle

▿:

gradient operation

π:

3.141593

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Authors and Affiliations

  1. Institut für Meteorologie, Johannes Gutenberg-Universität, Mainz, BRD

    Gottfried Hänel

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  1. Gottfried Hänel
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Hänel, G. Humidity effects on gravitational settling and Brownian diffusion of atmospheric aerosol particles. PAGEOPH 115, 775–797 (1977). https://doi.org/10.1007/BF00881210

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