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Rain scavenging of soluble gases by non-evaporating and evaporating droplets from inhomogeneous atmosphere

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Abstract

We suggest a one-dimensional model of precipitation scavenging of soluble gaseous pollutants by non-evaporating and evaporating droplets that is valid for arbitrary initial vertical distribution of soluble trace gases in the atmosphere. It is shown that for low gradients of soluble trace gases in the atmosphere, scavenging of gaseous pollutants is governed by a linear wave equation that describes propagation of a wave in one direction. The derived equation is solved by the method of characteristics. Scavenging coefficient and the rates of precipitation scavenging are calculated for wet removal of sulfur dioxide (SO2) and ammonia (NH3) using measured initial distributions of trace gases. It is shown that scavenging coefficient for arbitrary initial vertical distribution of soluble trace gases in the atmosphere is non-stationary and height-dependent. In case of exponential initial distribution of soluble trace gases in the atmosphere, scavenging coefficient for non-evaporating droplets in the region between the ground and the position of a scavenging front is a product of rainfall rate, solubility parameter, and the growth constant in the formula for the initial profile of a soluble trace gas in the atmosphere. This expression yields the same estimate of scavenging coefficient for sulfur dioxide scavenging by rain as field estimates presented in McMahon and Denison (1979). It is demonstrated that the smaller the slope of the concentration profile the higher the value of a scavenging coefficient.

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Abbreviations

a :

Raindrop radius, cm

c :

Total concentration of soluble trace gas in gaseous and liquid phases, mole l−1

c (G) :

Concentration of soluble trace gas in gaseous phase, mole l−1

c (G)c :

Concentration of soluble gas at cloud bottom, mole l−1

c (G)gr :

Concentration of soluble gas at the ground, mole l−1

c (L) :

Concentration of dissolved gas in droplet, mole l−1

d :

Raindrop diameter, m

D G :

Coefficient of diffusion in a gaseous phase, cm2 s−1

H A :

Henry’s law constant, mole l−1 atm−1

k 1 :

Growth constant, cm−1

k a :

Thermal conductivity of air, kcal s−1 cm−1 K−1

K v :

Evaporation coefficient, cm2 s−1

L :

Distance between ground and cloud bottom, cm

L v :

Latent heat of evaporation, kcal g−1

m = H A R g T :

Dimensionless Henry’s law coefficient

R :

Rainfall rate, cm s−1

R g :

Universal gas constant, atm l mole−1 K−1

q c :

Mass flux density of dissolved gas transferred by rain droplets, mole cm−2 s−1

Sh = β d/D G :

Sherwood number

t :

Time, s

u :

Terminal velocity of droplet, cm s−1

U :

“wash-down” front velocity, cm s−1

U 0 :

“wash-down” front velocity for non-evaporating droplets, cm s−1

x (G) :

Mole fraction of a soluble trace gas in gaseous phase

z :

Vertical coordinate, cm

β :

Coefficient of mass transfer, cm s−1

ϕ L :

Volume fraction of droplets in air

τ ch :

Characteristic time of concentration change in gaseous phase, s

τ D :

Characteristic time of diffusion, s

Λ:

Scavenging coefficient, s−1

0:

Initial value

c :

Value at cloud bottom

gr:

Value at ground

G :

Gaseous phase

L :

Liquid phase

v :

Vapor

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Acknowledgments

This study was performed in the framework of COST ES1004 “European Framework for Online Integrated Air Quality and Meteorology Modeling”.

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Authors and Affiliations

  1. Department of Mechanical Engineering, The Pearlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, P. O. B. 653, 84105, Beer-Sheva, Israel

    Tov Elperin, Andrew Fominykh & Boris Krasovitov

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  1. Tov Elperin
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  2. Andrew Fominykh
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  3. Boris Krasovitov
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Correspondence to Tov Elperin.

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Responsible editor: S. Trini Castelli.

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Elperin, T., Fominykh, A. & Krasovitov, B. Rain scavenging of soluble gases by non-evaporating and evaporating droplets from inhomogeneous atmosphere. Meteorol Atmos Phys 122, 215–226 (2013). https://doi.org/10.1007/s00703-013-0283-3

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