Mass Transport and Aqueous-Phase Chemistry

5 Characteristic Time for Aqueous-Phase Chemical Reactions 

To develop an expression for the characteristic time for aqueous-phase chemical reaction, let us consider as an example the oxidation of S(IV). The characteristic time can be calculated by dividing the S(1V) aqueous-phase concentration by its oxidation rate, 

It is also possible to define a characteristic time for chemical reaction relative to the gas-phase SO2 concentration. 

If the aqueous-phase concentration is uniform and satisfies Henry s law equilibrium, then [S(IV)] = 7[802(g)] and the two timescales are related by 

The reactants for aqueous-phase atmospheric reactions are transferred to the interior of cloud droplets from the gas phase by a series of mass transport processes. We would like to compare the rates of mass transport in the gas phase, at the gas-water interface, and in the aqueous phase in an effort to quantify the mass transport effects on the rates of aqueous-phase reactions. If there are no mass transport limitations, the gas and aqueous phases will remain at Henry s law equilibrium at all times. Our objective will be to identify cases where mass transport limits the aqueous-phase reaction rates and then to develop approaches to quantify these effects. 

Note that the timescale is proportional to the square of the droplet radius. A typical value of Daq is 10 5 cm2 s 1, so we can evaluate Tcja as function of Rp. For a typical cloud droplet of 10 pm radius, iA, = 0.01 s. For a rather large cloud droplet of 100 pm radius the timescale is 1 s. For raindrops of size 1 mm the timescale becomes appreciable as it is equal to 100 s. 

---

Gas-Phase limitation The problem of coupled gas-phase mass transport and aqueous-phase chemistry was solved in Section 12.3.1 resulting in (12.82). Solving for the aqueous-phase reaction term / aq and noting that in this case Henry s law will be satisfied at the interface (pA(Rp) = Caq/// ) ... 

MASS TRANSPORT AND AQUEOUS-PHASE CHEMISTRY 621 itations on the aqueous-phase kinetics. This criterion can be written as... 

The choice of an appropriate model is heavily dependent on the intended application. In particular, the science of the model must match the pollutant(s) of concern. If the pollutant of concern is fine PM, the model chemistry must be able to handle reactions of nitrogen oxides (NOx), sulphur dioxide (SO2), volatile organic compounds (VOC), ammonia, etc. Reactions in both the gas and aqueous phases must be included, and preferably also heterogeneous reactions taking place on the surfaces of particles. Apart from correct treatment of transport and diffusion, the formation and growth of particles must be included, and the model must be able to track the evolution of particle mass as a function of size. The ability to treat deposition of pollutants to the surface of the earth by both wet and dry processes is also required. 

The equations above have been the basis of most atmospheric aqueous-phase chemistry models that include mass transport limitations [e.g., Pandis and Seinfeld (1989)]. These equations simply state that the partial pressure of a species in the cloud interstitial air changes due to mass transport to and from the cloud droplets (incorporating both gas and interfacial mass transport limitations). The aqueous-phase concentrations are changing also due to aqueous-phase reactions that may be limited by aqueous-phase diffusion included in the factor Q. 

MASS TRANSPORT LIMITATIONS IN AQUEOUS-PHASE CHEMISTRY 611 a point close to the particle surface (r — Rp) < and... 

Schwartz, S. E., Mass-Transport Considerations Pertinent to Aqueous Phase Reactions of Gases in Liquid-Water Clouds, NATO AS1 Series, G6, 416-471 (1986), and in Chemistry of Multiphase Atmospheric Systems (W. Jaeschke, Ed.), pp. 415-471, Springer-Verlag, New York, 1986. 

The large S02 mass accommodation coefficient (7 - 0.11) indicates that interfacial mass transport will not limit the rate of S02 uptake into clean aqueous cloud and fog droplets. Either gas phase diffusion, Henry s law solubility, or aqueous reactivity will control the overall rate of aqueous S(IV) chemistry. This conclusion is demonstrated by modeling studies of S02 oxidation in clouds by Chamedies (3) showing that the conversion time of S(FV) to S(IV) is independent of the mass accommodation coefficient for 1 7 > 10 2 Schwartz (1 ) has also shown that, with 7 as large as our measured value, the interfacial mass transport is unlikely to inhibit the oxidation of SC by or Ho02 in cloud droplets for gas concentrations typical of non-urban industrialized regions. 

Table 4.17 Expressions for gas-particle mass transfer n , g, Mq and Haq molecule density of the same substance far from the particle, close to the particle, at particle surface and within the particle (droplet) p — gas partial pressure far from the droplet, c g - aqueous-phase concentration, k - mass transfer coefficient (recalculable into spjecific rate constant) g - gas-phase, aq - aqueous-phase, het - interfadal layer (chemistry), in - interfacial layer (transport), coll - collision, ads — adsorption (surface striking), sol - dissolution, diff -diffusion in gas-phase, des - desorption.

---