Non equilibrium kinetics: mass-transfer of H O between gas and liquid phases

Ž . On a large scale thousands of kilometers , clouds are organized in broad and complex systems that are responsible for the transport of species from the boundary Ž . layer to the free troposphere Renard et al., 1994; Edy et al., 1996 . Tracer redistribution can be greatly changed in case of precipitating clouds systems due to their efficient scavenging. Photochemical processes can be modified through cloudrradiation interac- Ž . tions Thompson, 1984 . Within these systems, each individual cloud is the host of complex microphysical processes that influence the partitioning of species among the Ž . air, the cloud and the precipitation Gregoire et al., 1994 . Finally, on microscale level, ´ gas absorption and chemical reactions greatly depend on the microstructure of the cloud such as the droplet spectrum. Therefore, one has to consider complex interfacial transfer Ž . between gaseous and liquid phases Wurzler et al., 1995; Ricci et al., 1997 . Moreover, these small scale features cannot be ignored at larger scales because removal processes and radiative properties of clouds that perturb photochemistry depend Ž . on the microphysical characteristics of the clouds Madronich, 1987 . In order to simulate such complex interactions on the whole range of scales at which they are important, it is necessary to use several types of models from box chemical model, to mesoscale models. In this paper, scavenging processes that occur in clouds and their dependency on the fine microphysical features, such as droplet size, liquid water content will be discussed for one particular chemical species, hydrogen peroxide, which is both a soluble and a reactive compound in clouds. The way clouds interact with this particular species will be described in details. In particular, deviations from Henry’s law can occur in clouds for this species at the sudden apparition of the aqueous phase or in a cloud, presenting Ž . different types of granulometry cloud droplets vs. raindrops .

2. Non equilibrium kinetics: mass-transfer of H O between gas and liquid phases

2 2 The rate equation in gaseous phase for a particular species may be written as: dC g s P y L C 1 Ž . g g g d t where P and L are respectively the production and destruction terms and C the g g g gaseous concentration of the species. With the introduction of cloud water, this equation becomes: dC k C g t aq s P y L C y Lk C q 2 Ž . g g g t g d t H RT eff where k describes the mass transfer between the gas and aqueous phases, L the liquid t Ž . water content, H the Henry’s law effective constant of the species Schwartz, 1986 eff and C the aqueous concentration. The transfer coefficient k is function of gaseous aq t diffusion and interfacial transport: y1 2 a 4 a k s q 3 Ž . t ž 3d 3Õa g Ž where a is the droplet radius, d is the coefficient of diffusion in gaseous phase egal to g 2 y1 . 0.1 cm s , v is the mean molecular speed and a is the accommodation coefficient. As soon as cloud water is present, additional rate equation for the aqueous concentra- tion C has to be accounted for: aq dC k C aq t aq s P y L C q Lk C y 4 Ž . aq aq aq t g d t H RT eff Ž . In pure gas phase chemistry, the characteristic time scales lifetimes are expressed by the inverse of the term , and in gas-aqueous chemistry two different terms are involved: y1 k t y1 D q Lk and D q . 5 Ž . Ž . g t aq ž H RT eff The equilibration time is often taken as the characteristic lifetime of the species. In fact, the equilibration time t is just proportional to this lifetime for pure gaseous eq chemistry, and it is given by: C y C g g eq s D C 6 Ž . g g t eq Ž . where D is the inverse of the lifetime of the species chemical destruction rate and g C the equilibrium concentration. g eq With transfer to aqueous phase, this equation becomes: C y C g g eq s D C q Lk C 1 y q 7 Ž . Ž . g g t g t eq Ž where q s C rLH RTC expresses the deviation from Henry’s law equilibrium q aq eff g . equals 1 in Henry’s law equilibrium . This ratio q is linked to the partitioning of material between gas and liquid phases. If Ž . Ž . q 1 or q - 1 , this means that the species is preferably in the aqueous or gaseous phase. This ratio has been discussed by other authors but rather in experimental studies Ž . Laj et al., 1997; Ricci et al., 1997; Winiwarter et al., 1988, 1994 . Most of the time, it has been studied for very soluble species such as NH , HNO and HCOOH and its 3 3 Ž . evolution has been drawn versus either drop radius or pH. Laj et al. 1997 are the ones that complete the quantification of this partitioning process for H O , but the results 2 2 have also been discussed only as a function of pH. Here, we want to look at this ratio as a function of the variation of the liquid water content and consider various scenarios that include the limitation by mass transfer and Ž . the reactivity of the hydrogen peroxide with SO in particular . 2

3. Deviations from Henry’s law for hydrogen peroxide during a cloud lifetime