Scavenging of Gaseous Pollutants by Falling Liquid Droplets in Inhomogeneous Atmosphere

1. Scavenging of gaseous pollutants by falling liquid droplets in inhomogeneous atmosphere with non-uniform temperature and concentration distributions 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. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Outline of the presentation • Motivation and goals • Fundamentals • Description of the model • Results and discussion • Conclusions Ben-Gurion University of the Negev

3. Henry’s Law: Air Soluble gas is the species in dissolved state Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Gas absorption by falling droplets Atmospheric polluted gases (SO2, CO2, CO, NOx, NH3): Scavenging of air pollutions by cloud and rain droplets • In-cloud scavenging of polluted gases • Scavenging of air pollutions by rain droplets Single Droplet Ben-Gurion University of the Negev

4. Vertical concentration gradient of soluble gases Fig. 1a. Aircraft observation of vertical profiles of CO2 concentration (by Perez-Landa et al., 2007) Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Scavenging of air pollutions Gaseous pollutants in atmosphere • SO2 and NH3 – anthropogenic emission • CO2 – competition between photosynthesis, respiration and thermally driven buoyant mixing Ben-Gurion University of the Negev

5. Vertical concentration gradient of soluble gases Fig. 1b. Vertical distribution of SO2. Solid lines - results of calculations with (1) and without (2) wet chemical reaction (Gravenhorst et al. 1978); experimental values (dashed lines) – (a) Georgii & Jost (1964); (b) Jost (1974); (c) Gravenhorst (1975); Georgii (1970); Gravenhorst (1975); (f) Jaeschke et al., (1976) Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Scavenging of air pollutions Gaseous pollutants in atmosphere • SO2 and NH3 – anthropogenic emission • CO2 – competition between photosynthesis, respiration and thermally driven buoyant mixing Ben-Gurion University of the Negev

6. Vertical temperature profile in atmospheric Boundary layer (ABL) Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Scavenging of air pollutions Vertical temperature profile in the lowest few kilometers of the atmosphere • Adiabatic decrease of atmospheric temperature with height • Inversion of vertical temperature gradient as a result of solar radiation heating and ground cooling Fig. 1c. Aircraft observation of potential temperature vs. height (by Perez-Landa et al., 2007) Ben-Gurion University of the Negev

7. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Scientific background • Gas absorption by falling droplets: • Walcek and Pruppacher, 1984 • Alexandrova et al., 2004 • Elperin and Fominykh, 2005 • Measurements of vertical distribution of trace gases in the atmosphere: • SO2 – Gravenhorst et al., 1978 • NH3 – Georgii & Müller, 1974 • CO2 – Denning et al., 1995; Perez-Landa et al., 2007 • Scavenging of gaseous pollutants by falling rain droplets in inhomogeneous atmosphere: • Elperin, Fominykh & Krasovitov 2008 – non-uniform concentration distribution in a gaseous phase • Elperin, Fominykh & Krasovitov 2009 – non-uniform temperature and concentration distribution in the atmosphere Ben-Gurion University of the Negev

8. 0.1 mm R 0.5 mm 10 Re 300 0.7 U 4.5 m/s Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Description of the model In the analysis we used the following assumptions: • dc<<R; dT<<R • Tangential molecular mass transfer rate along the surface is small compared with a molecular mass transfer rate in the normal direction • The bulk of a droplet, beyond the diffusion and temperature boundary layers, is completely mixed by circulations inside a droplet • The droplet has a spherical shape. Fig. 2. Schematic view of a falling droplet and temperature and concentration profiles Ben-Gurion University of the Negev

9. where k = 0.009 0.044 for different Re, and Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Description of the model System of convective diffusion and energy conservation transient equations for the liquid and gaseous phasesread: (1) (i = 1, 2) Fluid velocity components at the gas-liquid interface are (Prippacher & Klett, 1997): (2) Ben-Gurion University of the Negev

10. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Description of the model Initial and boundary conditions Using the transformation z = U t thecoordinate-dependent boundary conditions can be transformed into the time-dependent boundary conditions: (3) (7) at at (4) (8) at at (5) (9) at at (6) (10) at at where Ben-Gurion University of the Negev

11. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Method of the solution Introduction of the self-similar variables: and application of Duhamel's theorem yields a solution of convection diffusion and energy conservation equations (Eqs. 1): (11) where and Ben-Gurion University of the Negev

12. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Method of the solution Integral energy and material balances over the droplet yields: (12) Substituting solutions (11) into Eqs. (12) yields: (13) (14) where - initial value of molar fraction of absorbate in a droplet - value of molar fraction of an absorbate in a gas phase at height H Ben-Gurion University of the Negev

13. (15) Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Method of the solution The system of equations for temperature and absorbate concentration in the bulk of a droplet: is a system of linear convolution Volterra integral equations of the second kind that can be written in the following form: is a system of linear convolution Volterra integral equations of the second kind that can be written in the following form: (15) Ben-Gurion University of the Negev

14. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Method of the solution • The method of solution is based on the approximate calculation of a definite integral using some quadrature formula: • The uniform mesh with an increment h was used: • Using trapezoidal integration rule we obtain a system of linear algebraic equations: • The kernel is a matrix and equation (17) is viewed as a vector equation. (16) where – remainder of the series after the N-th term. (17) Ben-Gurion University of the Negev

15. Fig. 4.Dependence of the potential, atmospheric and droplet surface temperature vs. altitude in the morning. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Results and discussion Fig. 3.Dependence of CO2 concentration in the atmosphere vs. altitude (1) aircraft measurements Valencia 6:23 (by Perez-Landa et al., 2007); (2)-(4) approximation of the measured data; (3) aircraft measurements Valencia 13:03 (by Perez-Landa et al., 2007). . Ben-Gurion University of the Negev

16. Fig. 5.Dependence of the potential, atmospheric and droplet surface temperature vs. altitude in the afternoon Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Results and discussion Fig. 3.Dependence of CO2 concentration in the atmosphere vs. altitude (1) aircraft measurements Valencia 6:23 (by Perez-Landa et al., 2007); (2)-(4) approximation of the measured data; (3) aircraft measurements Valencia 13:03 (by Perez-Landa et al., 2007). . Ben-Gurion University of the Negev

17. Fig. 6.Dependence of the concentration of the dissolved CO2 gas in the bulk of a falling rain droplet vs. time, xb10 = 0. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Results and discussion Fig. 3.Dependence of CO2 concentration in the atmosphere vs. altitude (1) aircraft measurements Valencia 6:23 (by Perez-Landa et al., 2007); (2)-(4) approximation of the measured data; (3) aircraft measurements Valencia 13:03 (by Perez-Landa et al., 2007). . Ben-Gurion University of the Negev

18. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Results and discussion Fig. 8. Dependence of the relative concentration of ammonia (NH3) inside a water droplet vs. time. Fig. 7.Dependence of the interfacial temperature of a falling rain droplet vs. altitude. Ben-Gurion University of the Negev

19. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Results and discussion Fig. 9. Evolution of ammonia (NH3) distribution in the atmosphere due to scavenging by rain Ben-Gurion University of the Negev

20. Summer Heat Transfer Conference San Francisco, CA, July 19-23, 2009 Conclusions The suggested model of gas absorption by a falling liquid droplet in the presence of inert admixtures takes into account a number of effects that were neglected in the previous studies, such as the effect of dissolved gas accumulation inside a droplet and effect of the absorbate and temperature inhomogenity in a gaseous phase on the rate of heat and mass transfer. It is shown than if concentration of a trace gas in the atmosphere is homogeneous and temperature in the atmosphere decreases with height, beginning from some altitude gas absorption is replaced by gas desorption. We found that the neglecting temperature inhomogenity in the atmosphere described by adiabatic lapse rate leads to overestimation of trace gas concentration in a droplet at the ground on tens of percents. If concentration of soluble trace gas is homogeneous and temperature increases with height e.g. during the nocturnal inversion, droplet absorbs gas during all the time of its fall. Ben-Gurion University of the Negev