pyrcel.thermo.Seq

pyrcel.thermo.Seq(r, r_dry, T, kappa)

κ-Kohler theory equilibrium saturation over aerosol.

Calculates the equilibrium supersaturation (relative to 100% RH) over an aerosol particle of given dry/wet radius and of specified hygroscopicity bathed in gas at a particular temperature

Following the technique of [PK2007], classical Kohler theory can be modified to account for the hygroscopicity of an aerosol particle using a single parameter, \(\kappa\). The modified theory predicts that the supersaturation with respect to a given aerosol particle is,

\[\begin{split}S_\text{eq} &= a_w \exp \left( \frac{2\sigma_{w} M_w}{RT\rho_w r} \right)\\ a_w &= \left(1 + \kappa\left(\frac{r_d}{r}^3\right) \right)^{-1}\end{split}\]

with the relevant thermodynamic properties of water defined elsewhere in this module, \(r_d\) is the particle dry radius (r_dry), \(r\) is the radius of the droplet containing the particle (r), \(T\) is the temperature of the environment (T), and \(\kappa\) is the hygroscopicity parameter of the particle (kappa).

Parameters:

rfloat

droplet radius, m

r_dryfloat

dry particle radius, m

Tfloat

ambient air temperature, K

kappa: float

particle hygroscopicity parameter

Returns:

float

\(S_\text{eq}\) for the given aerosol/droplet system

See also

Seq_approx

compute equilibrium supersaturation using an approximation

kohler_crit

compute critical radius and equilibrium supersaturation

References

[PK2007]

Petters, M. D., and S. M. Kreidenweis. “A Single Parameter Representation of Hygroscopic Growth and Cloud Condensation Nucleus Activity.” Atmospheric Chemistry and Physics 7.8 (2007): 1961-1971