Determination of Kelvin Radii and Bulk Hygroscopicity of Volume Based Hygroscopicity for Atmospheric Aerosols

In this study, a volume based hygroscopicity (kv) model was applied to the data obtained from Optical Properties of Aerosol and Clouds (OPAC), the properties obtained were the radii of arctic, continental clean, continental polluted, maritime clean, maritime polluted, Sahara and urban at eight relative humidity of 0%, 50%, 70%, 80%, 90%, 95%, 98%, and 99%. The Kelvin radii (A) and bulk hygroscopicity (B) were determined using regression analysis, the result shows that B is more dominant than A for maritime clean and maritime polluted, also discovered that maritime clean and maritime polluted has higher value of kv while Saharan has lowest. We also discovered that R 2 is greater than 90%, p-value and significance are less than 0.05, therefore the parameter kv is good for atmospheric modeling. Citation: Saadu B, Tijjani BI, Galadanci GSM (2017) Determination of Kelvin Radii and Bulk Hygroscopicity of Volume Based Hygroscopicity for Atmospheric Aerosols. Fluid Mech Open Acc 4: 153. doi: 10.4172/2476-2296.1000153


Introduction
Atmospheric aerosols interact with water vapour which is one of the central issues of current research in atmospheric and climate. The atmospheric RH in equilibrium with the aqueous solutions of atmospheric aerosols at a given temperature depends on the hygroscopic nature of the solutes, their compositions, concentrations and the effective sizes of these aerosols [1]. The effect of aerosols on the atmosphere climate and public health also among the central topics in current environmental research.
Aerosols particle scatter and absorb solar and terrestrial radiation and also involved in the formation of clouds and precipitation as cloud condensation nuclei (CCN). The efficiency of particles as CCN also affects both aerosol particle and cloud droplet lifetimes [2]. It is well recognized that these effects represent one of the largest uncertainties in assessing the changes in radiative forcing from pre-industrial times to the present [3]. As such, understanding the hygroscopic properties of aerosols and the processes that govern cloud droplet activation are important. Kohler theory has been used to predict the CCN-activity of inorganic compounds for many years [1]. This paper focus on volume based hygroscopicity (k v ) model were it is applied to the data extracted from optical properties of aerosols and clouds (OPAC) to determine the Kelvin radii and bulk hygroscopcity of the aerosols.
The kohler theory that will describe the equilibrium water vapor saturation ratio S is given by Where a w represent the water activity and k e is the Kelvin effect. The relationship between Droplet radius and RH at equilibrium can also be given as: Where R is the universal gas constant and T is the temperature. According to ref. [13], eqn (2) can be written as: The aerosol's hygroscopicity growth factor g(S), [13,14] is defined as: Where S can be set for eight values, substituting eqn (5) in to eqn (4) we get are assumed to be constants.
The first term on the RHS of eqn (6) is the Kelvin effect given as The Second term on the RHS of eqn (3.6) is the water activity given as:

Result and Discussion
From Table 2, we can observe that, based on the values of R 2 , the data fitted the equation very well and by looking at the table, we can observe that B is more dominant than A for maritime clean and maritime polluted due to their p-values and from the values of Kelvin radii, it observed that, only Saharan aerosols is negative which means that the Kelvin radii apart from positive ( Figure 1 and Table 2) [26].
From Figure 1, It can be seen that volume based Kelvin effect on the Saharan, is linear and is while Urban, Continental polluted, continental clean are independent of RH and are greater than one. The Maritime polluted and Arctic have the same type of pattern, that is why they increase with the increase in RH and is more sensitive at higher RHs (90-99%). Lastly the Maritime clean is more sensitive to RH and is nonlinear (Table 3). Table 3 show that, the data fitted the equation very excellent by considering the values of R 2 . By observing the result it can be seen that maritime clean and maritime polluted has high values of k v due to dominant of sea salt while it is moderate for arctic aerosols and is less for Saharan due to sufficient mineral at the region.
But atmospheric aerosols usually comprised mixtures of soluble components, therefore an effective hygroscopic growth factor of the mixture, g eff (S) representative for the entire aerosols particle population is giving from the previous study as: The effective or volume equivalent radius of the mixture was determined using the relation ( ) Where x k denote the volume fractions, using the Zdanovskii-Stokes-Robisnson relation (ZSR relation) [15][16][17][18].
For many components eqn (6) can be written to represent the property of the bulk components using eqns (9) and (10) as: By using regression analysis with SPSS 16, the constants A and B were determined. Therefore eqn (7) can be written as The hygroscopicity parameter κ v relates the volume of the dry aerosol particle (V d ) to the volume of water (V w ) and the activity of water (a w ) in the aqueous droplet: From Figure 4, it can be seen that only Sahara aerosol has a good agreement between volumes based hygroscopicity and bulk hygroscopicity.

Conclusion
From the results obtained, we observed that bulk hygroscopicity (A) dominates the Kelvin radii (B) for maritime clean and maritime polluted and also as RH increase, the Kelvin effect increases. This implies that, they are more sensitive at deliquescence point (90-99%). By observing the volume based hygroscopicity parameter k v , it can be seen that, it has higher value for maritime clean and maritime polluted and less for Saharan and Figure 2 shows a good agreement between Kelvin radii and bulk hygroscopicity except for Saharan due to its compositions.     The results of volume based hygroscopicity using eqn (12).