1. Effect of Diffusion Interactions between Droplets on Gas Absorption of Highly Soluble Gases in Sprays and Clusters
T. Elperin, A. Fominykh and B. Krasovitov
Department of Mechanical Engineering
The Pearlstone Center for Aeronautical Engineering Studies
Ben-Gurion University of the Negev P.O.B. 653, Beer Sheva 84105
ISRAEL

2. Cell model: motivation and goals
Scavenging of air pollutions by cloud and rain droplets
Spray tower
absorbers
Cell model
Clouds
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 2

3. Description of the model
Cell model
Scavenging of air pollutions by cloud and rain droplets
Cell model:
Happel, 1958;
Elperin & Fominykh, 1996, 1999;
Chen et al., 2012
is the species in
dissolved state
Henry’s Law:
Droplet
cell a R
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 3

4. Description of the model
Governing equations
Scavenging of air pollutions by cloud and rain droplets
In the liquid phase, 0 < r < a :
(1)
In the gaseous phase, 0 < r < R :
(2)
Radius of the gaseous shell, R :
where is volumetric liquid water content.
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 4

5. Description of the model
The initial conditions for the system of equations (1) and (2) read:
Scavenging of air pollutions by cloud and rain droplets
(3)
The conditions of the continuity of mass flux at the gas-liquid interface
yields:
(4)
Concentration of absorbate in the droplet at gas-liquid interface:
(5)
The boundary conditions in the center of the droplet and at the cell
boundary read:
(6)
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 5

6. Aqueous-phase chemical equilibria
Nitric acid – water equilibrium:
Scavenging of air pollutions by cloud and rain droplets
(7)
(8)
Total concentration of the dissolved nitric acid:
(9)
Equation (9) and dissociation equilibrium equations (7) – (8) yield:
(10)
where
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 6

7. Aqueous-phase chemical equilibria
Nitric acid – water equilibrium:
Scavenging of air pollutions by cloud and rain droplets
Since
(11)
(12)
(13)
(14)
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 7

8. Aqueous-phase chemical equilibria
Taking into account dissociation reactions and Eq. (13) we obtain:
Scavenging of air pollutions by cloud and rain droplets
(15)
(16)
where
Taking into consideration that
allows determining pH
in a saturated droplet as:
(17)
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 8

9. Aqueous-phase chemical equilibria
Hydrogen peroxide – water equilibrium:
Scavenging of air pollutions by cloud and rain droplets
(18)
(19)
In contrast to the HNO3 solution, H2O2 solution in water is a weak electrolyte
with the dissociation constant at T = 298 K.
for pH < 7.5
Thus for H2O2 the “equilibrium concentrations” read:
(20)
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 9

10. Description of the model
Governing equations
Scavenging of air pollutions by cloud and rain droplets
In the liquid phase, 0 < r < a :
(1)
In the gaseous phase, 0 < r < R :
(2)
Radius of the gaseous shell, R :
where is volumetric liquid water content.
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 10

11. Results and discussion
Scavenging of air pollutions by cloud and rain droplets
Fig. 1. Dependence of the total concentration, [N(V)], of the nitric acids and pH in a liquid phase vs. time and radial coordinate (CG,0 = 5.16 mg/m3).
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 11

12. Results and discussion
Scavenging of air pollutions by cloud and rain droplets
Fig. 2. Dependence of the total concentration, [N(V)], of the nitric acids and pH in a liquid phase vs. time and radial coordinate (CG,0 = mg/m3).
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 12

13. Results and discussion
Fig. 3. Dependence of the concentration of the soluble gas (HNO3) in the gaseous phase vs. time and radial coordinate (CG,0 = 5.16 mg/m3). .
Fig. 4. Dependence of the concentration of the soluble gas (HNO3) in the gaseous phase vs. time and radial coordinate (CG,0 = mg/m3).
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK

14. Results and discussion
Fig. 5. Dependence of pH in the saturated droplet vs. initial concentration of HNO3 in the gaseous phase for different values of liquid water content in a cloud.
Fig. 6. Dependence of the average concentration of HNO3 in the gaseous phase, the rate of concentration change - dc/dt and scavenging coefficient vs. time (j L = 10-6 ).
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK

15. Results and discussion
Fig. 7. Dependence of the scavenging coefficient of HNO3 vs. time.
Fig. 8. Equilibrium fraction of the total H2O2 and HNO3 in the gaseous phase as a function of liquid water content at 298 K.
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 15

16. Results and discussion
Fig. 10. Dependence of the scavenging coefficient for the hydrogen peroxide H2O2 on time taking into account gamma droplet size distribution.
Fig. 9. Dependence of the scavenging coefficient for the nitric acid HNO3 on time taking into account gamma droplet size distribution.
Gamma size distribution of droplets (PDF) (Wyser, 1998):
Scale parameter:
Shape parameter: a = 6
is the average radius
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 16

17. Results and discussion
Fig. 12. Dependence of the average concentration of nitric acid HNO3 in a gaseous phase on time taking into account log-normal droplet size distribution (CG,0 = mg/m3).
Fig. 11. Dependence of the average concentration of nitric acid HNO3 in a gaseous phase on time taking into account log-normal droplet size distribution (CG,0 = 5.16 mg/m3).
PDF for log-normal size distribution of droplets (Yoon, et al., 2007) :
is dimensionless standard deviation of
the logarithm of the diameter:
s = 0.2, 0.4, 0.6
is the mean diameter
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK 17

18. Conclusions
It is shown that absorption of highly soluble gases by clouds and droplet clusters causes a significant decrease of the soluble gas concentration in the interstitial air.
Calculations conducted for the hydrogen peroxide (H2O2) and the nitric acid (HNO3) showed that in spite of the comparable values of the Henry’s law constants for the hydrogen peroxide and the nitric acid, the nitric acid is absorbed more effectively than the hydrogen peroxide.
Using the suggested model we calculated temporal evolution of pH in cloud droplets. It was shown that pH strongly depends on the liquid content in the cloud and on the initial concentration of the soluble trace gas in the gaseous phase.
The results of the present study can be useful in an analysis of different meteorology-chemistry models and adequately describes gas absorption by mist formed in gas streams inside gas absorbers.
Ben-Gurion University of the Negev
ILASS 2016
September 4 – 7, 2016
Brighton, UK