Outputs for Köhler Calculations

The results of the calculations consist of saturation values and particle water contents and other properties as a function of particle radius. They are either output sequentially to the screen (column output), or can be plotted as graphs (not yet implemented). If graphical output is selected, a new page will open containing lists of x and y variables for plotting. The results can also be downloaded as a "comma separated value" (csv) file which can be read by Excel and other programs. The link to this file is displayed near the top of the page containing the column output.

Notes describing the meanings of each of the column headers are printed at the bottom of each output page, as is the size and composition of the dry particle used to determine hygroscopic growth factors and κ (kappa) values (E-AIM calculations only).

The assumed geometry of the particle is "core-shell": a spherical core containing any solid salts that have formed, surrounded by a shell of aqueous solution.

Column Output

This includes the following information:

First, the peak supersaturation (critical supersaturation Sc) is identified and its value determined by interpolation of the tabulated results. The following characteristics of the particle at Sc are listed: the value of Sc; the particle radius, liquid water content, density, and surface tension; and the the partial molar volume of water in the particle. All units are SI, so that these numbers can be used together with R (8.3144 J K⁻¹ mol⁻¹) and T to calculate the influence of surface curvatiure on the saturation vapour pressure of the aqueous particle (the Kelvin effect).

The peak value will still be listed if the particle is large enough that the peak equilibrium RH above the particle, i.e. the highest value of S in the column of results in this page, is less than unity (or 100%).

In calculations where E-AIM is used to determine the properties of particles (all types of input except "Particle radius, and volume fractions of solids (κ - Köhler)") all of the particle properties, and its equilibrium state, are calculated using E-AIM. The value of the saturation S is calculated using the Kelvin equation, as described on the methods page. The model outputs are as follows:

• Peak – the star marks the nearest of the tabulated results to the calculated peak saturation (which is interpolated from values listed on this page).
• S – this is the saturation relative humidity (RH, as a fraction) above the aqueous particle. (The calculation includes the Kelvin correction for particle size).
• aW – this is the equilibrium water activity of the aqueous particle, and is the same as that of a bulk solution of the same chemical composition.
• Radius – the radius of the aqueous particle in meters (m).
• HGrFac – the hygroscopic growth factor, relative to the radius of the dry particle. The size and composition of the particle are listed after the column results on the output page.
• Kappa – the κ parameter of "κ - Köhler" theory, calculated for each particle composition using eq (6) of Petters and Kreidenweis (1). Note that the κ values are obtained using the partial molar volume (or M_w/ρ_w) and surface tension of pure water (following Petters and Kreidenweis), and not those of the aqueous particle.
• SurfTens – the calculated surface tension of the aqueous particle (N m⁻¹) at the specified temperature.
• Density – the calculated density of the aqueous particle (kg m⁻³) at the specified temperature.
• V(H2O) – the partial molar volume of water in the particle (m³ mol⁻¹) at the specified temperature. This is calculated by partial differentiation of the total volume of the particle with respect to the amount of water present. In dilute solutions the value of V(H2O) is close to, but not identical to, the molar volume of water.
• molesH2O – the amount of water (moles) in the aqueous particle.
• prefix m_ – the molality of each of the indicated species (in mol kg⁻¹ of water).
• solids – these are listed after the molalities of aqueous species, whcih three columns for each solid: the number of moles (header "moles_s01" for solid number 1), the volume (in m³), a numerical id, and then the solid name.

In calculations where the κ - Kölher equation is used to determine the properties of particles, the outputs are similar to those from E-AIM. The main differences are listed below:

• SurfTens – this is the value for pure water (in N m⁻¹) at the specified temperature.
• Density – this is obtained by adding the total volumes of water and solid in the particle, as in eq (4) of Petters and Kreidenweis (1), and dividing the total mass by this number. The units are kg m⁻³.
• V(H2O) – this is the partial molar volume of pure water in (m³ mol⁻¹) at the specified temperature.
• prefix m_ – the ion molalities listed are total values, thus no association of H⁺ and SO₄²⁻ (to form HSO₄⁻) is calculated.
• solids – the κ - Köhler calculations do not include the formation of solids.

Graphical Output

This has not been implemented yet.

References

(1)  M. D. Petters and S. M. Kreidenweis (2007) A single parameter representation of hygroscopic growth and cloud condensation nucleus activity. Atmos. Chem. Phys. 7, 1961-1971.