1. Modeling of heat and mass transfer during gas adsorption by aerosol particles in air pollution plumes
T. Elperin1, A. Fominykh1, I. Katra2, and B. Krasovitov1
1Department of Mechanical Engineering, The Pearlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, P.O.B. 653, , Israel
2Department of Geography and Environmental Development, Ben-Gurion University of the Negev, P.O.B. 653, , Israel

2. Motivation and goals Power plant (Ashquelon, Israel)
Scavenging of air pollutions by cloud and rain droplets
Ne'ot Hovav chemical factory (Northern Negev, Israel)
Power plant (Ashquelon, Israel)
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 2

3. Gaussian plume model Gaussian Plume model
Scavenging of air pollutions by cloud and rain droplets
Gaussian Plume model
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 3

4. Pasquill-Gifford dispersion parameters
Pasquill-Gifford stability categories
Gradient Richardson number reads
where q is potential temperature that can be calculated as follows
Γ is the adiabatic lapse rate ( K/m over the distance to the mixing depth)
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 4

5. Pasquill-Gifford dispersion parameters
Pasquill-Gifford horizontal dispersion parameters
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 5

6. Pasquill-Gifford dispersion parameters
Pasquill-Gifford vertical dispersion parameters
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 6

7. Turbulent diffusion of active gas in ABL
Scavenging of air pollutions by cloud and rain droplets
Mass transfer of gaseous adsorbent in atmospheric boundary layer (ABL) can be described using advection diffusion equation that reads
(1)
where is the mean concentration of gaseous adsorbent, are the components of mean wind velocity, are components of turbulent fluxes, is the rate of gas adsorption. Hereafter we adopted the turbulence closure based on the hypothesis of the gradient transport (K-theory)
(2)
where are the diagonal components of eddy diffusivity.
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 7

8. Turbulent diffusion of active gas in ABL
Governing equation
Boundary conditions
Scavenging of air pollutions by cloud and rain droplets at
(4)
(3) at
- rate of loss of active gas due to adsorption by aerosol particles
- height of ABL
For stable boundary layer (SBL) coefficient reads (Blackadar, 1979):
(5)
where l is the turbulent mixing length, zm = 200 m, k = 0.4, RiC = 0.25
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 8

9. Turbulent diffusion of active gas in ABL
Gas adsorption by PM
Scavenging of air pollutions by cloud and rain droplets
Time derivative of the radius-average concentration of the adsorbed gas in a porous particle reads:
(6)
Henry’s constant of adsorption
specific surface area of a particle
For an ensemble-average concentration field
(7)
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 9

10. Turbulent diffusion of active gas in ABL
Gas adsorption by PM
Scavenging of air pollutions by cloud and rain droplets
from Eqs. (17) and (16) we obtain:
(8)
solution of Eq. (8) reads:
(9)
Consequently
(10)
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 10

11. Gas adsorption by aerosol particles
expression for scavenging coefficient is the following:
Scavenging of air pollutions by cloud and rain droplets
(11) m
- Henry’s adsorption constant DG
- coefficient of molecular diffusion
- volume fraction of particles
- scavenging coefficient
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 11

12. Gas adsorption by aerosol particles
Table 1. Henry’s law constant of adsorption of active gases NO2, HNO3 and I-131 by carbon-based aerosols at temperature T = 298 K
Scavenging of air pollutions by cloud and rain droplets
aKalberer et al. (1999); bSeinfeld & Pandis (2016); cMunoz et al. (2002)
dNoguchi et al. (1988) or
- linear form of isotherm of adsorption
U - adsorbed amount of active gas
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 12
- volume fraction of particles

13. Gas adsorption by aerosol particles
Scavenging of air pollutions by cloud and rain droplets
Fig. 4. Dependence of adsorbed amount of iodine vs. time ( ,
, )
Fig. 3. Dependence of adsorbed amount of iodine vs. time ( ,
, )
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 13

14. Mean wind velocity profile
In ABL the wind profile can be described by the logarithmic law
Scavenging of air pollutions by cloud and rain droplets
(6)
- friction velocity
- shear stress at the surface level
- air density
- aerodynamic surface roughness length that is 1/30
of the field roughness elements σ
- standard deviation of velocity fluctuations
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 14

15. Measurements of mean wind velocity profile
Scavenging of air pollutions by cloud and rain droplets
Fig. 6. A cup anemometer
Measuring range
0 – 50 m/s
Accuracy
 0.49 m/s
Fig. 5. A 10-m wind mast
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 15

16. Measurements of mean wind velocity profile
Scavenging of air pollutions by cloud and rain droplets
For each height the average wind velocity was calculated as follows
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 16

17. Governing equation and boundary conditions
Scavenging of air pollutions by cloud and rain droplets at
(4)
(3) at
- rate of loss of active gas due to adsorption by aerosol particles
- height of ABL
For stable boundary layer (SBL) coefficient reads (Blackadar, 1979):
(5)
where l is the turbulent mixing length, zm = 200 m, k = 0.4, RiC = 0.25
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 17

18. Numerical solution
- Parabolic partial differential Eq. (3) was solved using the method of lines developed by Sincovec and Madsen [1975].
Scavenging of air pollutions by cloud and rain droplets
- Spatial discretization on a three-point stencil with uniformly distributed mesh points was used in order to reduce partial differential equation (3) to the approximating system of coupled ordinary differential equations.
- The resulting system of ordinary differential equations was solved using a backward differentiation method.
Sincovec, R.F., Madsen, N.K. [1975] Software for nonlinear partial differential equations. ACM T. Math. Software, Vol. 1, pp. 232–260.
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 18

19. Results and discussion
NO2
HNO3
Scavenging of air pollutions by cloud and rain droplets
Fig. 7.
Concentration distributions in the XZ-plane, evaluated at Y=0.
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017 19

20. Conclusions
The model is based on an application of theory of turbulent diffusion in the atmospheric boundary layer (ABL) in conjunction with plume dispersion model and model of gas adsorption by porous solid particles.
The wind velocity profiles used in the simulations were fitted from data obtained in field measurements conducted in the Northern Negev (Israel) using the experimental wind mast.
The adsorbate concentration distributions are calculated for the particulate matter PM2.5-10, which is typical for industrial emissions.
It is shown that the concentration of the gases adsorbed by aerosol plume strongly depends on the level of atmospheric turbulence.
The results of present study can be useful in the analysis of different atmospheric pollution models including gas adsorption by aerosol plumes emitted from industrial sources.
Ben-Gurion University of the Negev
CHT-17, Napoli, Italy, 28 May - 02 June 2017