Abstract:Recently developed methods of predicting water activities of multicomponent aqueous solutions use binary data. At high concentrations these methods are limited inasmuch as they require binary data beyond the solubility limit of individual solutes. A method is proposed whereby ternary water activity data may be used to calculate water activities of supersaturated binary solutions. The new method is compared with two extrapolation procedures on a known system and gives the best agreement. Values of the water act… Show more
“…The so-called ZSR (Zdandovskii-Stokes-Robinson) method [Sangster et al, 1973;Stokes and Robinson, 1966] has been used in treating multicomponent aerosol solutions. However, the curvature effect of droplets was not taken into consideration in this approach, which limits its application only to large aerosol droplets.…”
Section: Ambient Aerosol Sizementioning
confidence: 99%
“…[13] There exist several methods to estimate the water uptake by mixed soluble aerosols [Cohen et al, 1987a[Cohen et al, , 1987bSaxena and Peterson, 1981]. The so-called ZSR (Zdandovskii-Stokes-Robinson) method [Sangster et al, 1973;Stokes and Robinson, 1966] has been used in treating multicomponent aerosol solutions. However, the curvature effect of droplets was not taken into consideration in this approach, which limits its application only to large aerosol droplets.…”
[1] A size-segregated multicomponent aerosol algorithm, the Canadian Aerosol Module (CAM), was developed for use with climate and air quality models. It includes major aerosol processes in the atmosphere: generation, hygroscopic growth, coagulation, nucleation, condensation, dry deposition/sedimentation, below-cloud scavenging, aerosol activation, a cloud module with explicit microphysical processes to treat aerosol-cloud interactions and chemical transformation of sulphur species in clear air and in clouds. The numerical solution was optimized to efficiently solve the complicated size-segregated multicomponent aerosol system and make it feasible to be included in global and regional models. An internal mixture is assumed for all types of aerosols except for soil dust and black carbon which are assumed to be externally mixed close to sources. To test the algorithm, emissions to the atmosphere of anthropogenic and natural aerosols are simulated for two aerosol types: sea salt and sulphate. A comparison was made of two numerical solutions of the aerosol algorithm: process splitting and ordinary differential equation (ODE) solver. It was found that the process-splitting method used for this model is within 15% of the more accurate ODE solution for the total sulphate mass concentration and <1% accurate for sea-salt concentration. Furthermore, it is computationally more than 100 times faster. The sensitivity of the simulated size distributions to the number of size bins was also investigated. The diffusional behavior of each individual process was quantitatively characterized by the difference in the mode radius and standard deviation of a lognormal curve fit of distributions between the approximate solution and the 96-bin reference solution. Both the number and mass size distributions were adequately predicted by a sectional model of 12 bins in many situations in the atmosphere where the sink for condensable matter on existing aerosol surface area is high enough that nucleation of new particles is negligible. Total mass concentration was adequately simulated using lower size resolution of 8 bins. However, to properly resolve nucleation mode size distributions and minimize the numerical diffusion, a sectional model of 18 size bins or greater is needed. The number of size bins is more important in resolving the nucleation mode peaks than in reducing the diffusional behavior of aerosol processes. Application of CAM in a study of the global cycling of sea-salt mass accompanies this paper [Gong et al., 2002].
“…The so-called ZSR (Zdandovskii-Stokes-Robinson) method [Sangster et al, 1973;Stokes and Robinson, 1966] has been used in treating multicomponent aerosol solutions. However, the curvature effect of droplets was not taken into consideration in this approach, which limits its application only to large aerosol droplets.…”
Section: Ambient Aerosol Sizementioning
confidence: 99%
“…[13] There exist several methods to estimate the water uptake by mixed soluble aerosols [Cohen et al, 1987a[Cohen et al, , 1987bSaxena and Peterson, 1981]. The so-called ZSR (Zdandovskii-Stokes-Robinson) method [Sangster et al, 1973;Stokes and Robinson, 1966] has been used in treating multicomponent aerosol solutions. However, the curvature effect of droplets was not taken into consideration in this approach, which limits its application only to large aerosol droplets.…”
[1] A size-segregated multicomponent aerosol algorithm, the Canadian Aerosol Module (CAM), was developed for use with climate and air quality models. It includes major aerosol processes in the atmosphere: generation, hygroscopic growth, coagulation, nucleation, condensation, dry deposition/sedimentation, below-cloud scavenging, aerosol activation, a cloud module with explicit microphysical processes to treat aerosol-cloud interactions and chemical transformation of sulphur species in clear air and in clouds. The numerical solution was optimized to efficiently solve the complicated size-segregated multicomponent aerosol system and make it feasible to be included in global and regional models. An internal mixture is assumed for all types of aerosols except for soil dust and black carbon which are assumed to be externally mixed close to sources. To test the algorithm, emissions to the atmosphere of anthropogenic and natural aerosols are simulated for two aerosol types: sea salt and sulphate. A comparison was made of two numerical solutions of the aerosol algorithm: process splitting and ordinary differential equation (ODE) solver. It was found that the process-splitting method used for this model is within 15% of the more accurate ODE solution for the total sulphate mass concentration and <1% accurate for sea-salt concentration. Furthermore, it is computationally more than 100 times faster. The sensitivity of the simulated size distributions to the number of size bins was also investigated. The diffusional behavior of each individual process was quantitatively characterized by the difference in the mode radius and standard deviation of a lognormal curve fit of distributions between the approximate solution and the 96-bin reference solution. Both the number and mass size distributions were adequately predicted by a sectional model of 12 bins in many situations in the atmosphere where the sink for condensable matter on existing aerosol surface area is high enough that nucleation of new particles is negligible. Total mass concentration was adequately simulated using lower size resolution of 8 bins. However, to properly resolve nucleation mode size distributions and minimize the numerical diffusion, a sectional model of 18 size bins or greater is needed. The number of size bins is more important in resolving the nucleation mode peaks than in reducing the diffusional behavior of aerosol processes. Application of CAM in a study of the global cycling of sea-salt mass accompanies this paper [Gong et al., 2002].
“…This method can be assumed as a reliable way of obtaining supersaturated binary data in the absence of actual supersaturated values which are often difficult to obtain experimentally. 3,22 The estimated osmotic coefficients of K 2 SO 4 (aq) in the supersaturated region obtained by the simple extrapolation of ternary system data (ZR) were generally consistent except for the estimation results from the system K 2 SO 4 + Li 2 SO 4 + H 2 O (Figure 2). When the modified Zdanovskii relation (MZR), with inclusion of parameter b, was used in the estimation of the osmotic coefficients of K 2 SO 4 (aq), the results were consistent in the lower concentration region and showed a good mutual agreement with the results obtained by Sangster et al 3 (Figure 3).…”
Section: Resultsmentioning
confidence: 58%
“…The osmotic coefficients obtained from the ZR against the K 2 SO 4 (aq) molality are given in Figure . The osmotic coefficients originating from the MZR prediction are illustrated in Figure together with the results of Sangster et al obtained from the ternary systems K 2 SO 4 + Na 2 SO 4 + H 2 O, K 2 SO 4 + NaCl + H 2 O, and K 2 SO 4 + KCl + H 2 O by the modified Zdanovskii rule. 2 Osmotic coefficients of K 2 SO 4 (aq) at T = 298.15 K against the molality, obtained from different systems by the Zdanovskii rule (ZR): * , K 2 SO 4 + Cs 2 SO 4 + H 2 O; □, K 2 SO 4 + Li 2 SO 4 + H 2 O; ☆, K 2 SO 4 + Na 2 SO 4 + H 2 O; ▴, K 2 SO 4 + Rb 2 SO 4 + H 2 O; ▵, K 2 SO 4 + (NH 4 ) 2 SO 4 + H 2 O; ○, experimental data of Palmer et al in the unsaturated region. 3 Osmotic coefficients of K 2 SO 4 (aq) at T = 298.15 K against the molality, obtained from different systems by the modified Zdanovskii rule (MZR): * , K 2 SO 4 + Cs 2 SO 4 + H 2 O; □, K 2 SO 4 + Li 2 SO 4 + H 2 O; ☆, K 2 SO 4 + Na 2 SO 4 + H 2 O; ▴, K 2 SO 4 + Rb 2 SO 4 + H 2 O; ▵, K 2 SO 4 + (NH 4 ) 2 SO 4 + H 2 O; ·, estimated values by Sangster et al 3 ; ○, experimental data of Palmer et al in the unsaturated region.…”
Section: Introductionmentioning
confidence: 78%
“…There have been attempts to estimate the thermodynamic properties in the supersaturated concentration region of electrolyte solution. The prediction of the osmotic coefficients of K 2 SO 4 (aq) above the solubility limit m ) 0.7 mol‚kg -1 at T ) 298.15 K, up to molalities of m ) 1.2 mol‚kg -1 , m ) 4.0 mol‚kg -1 , and m ) 2.3 mol‚kg -1 , was made by Robinson et al 1 , Kuschel and Seidel, 2 and Sangster et al 3 , respectively. Palmer et al 4 evaluated the osmotic coefficients of supersaturated Rb 2 SO 4 (aq) and Cs 2 SO 4 (aq) by the A °kerlo ¨f-Thomas rule.…”
The Zdanovskii rule, in simple and modified form, was used for the estimation of supersaturated K 2 SO 4 -(aq) osmotic coefficients at T ) 298.15 K by treatment of the isopiestic data of the mixed electrolyte solutions. The results were compared with the predictions of the A °kerlo ¨f-Thomas rule and of weighted averages. Estimated values by the Zdanovskii rule together with the K 2 SO 4 (aq) osmotic coefficient experimental data in unsaturated solution were used in fitting the data to the extended Pitzer equation. The reliability of the Zdanovskii rule estimation was tested on the prediction of the osmotic coefficients in several mixed electrolyte solutions containing K 2 SO 4 and having an ionic strength much greater than the ionic strength of saturated K 2 SO 4 (aq) and on the osmotic coefficient estimation for supersaturated Na 2 SO 4 (aq) at T ) 298.15 K.
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