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:	r : float droplet radius, m r_dry : float dry particle radius, m T : float ambient air temperature, K kappa: float particle hygroscopicity parameter
Returns:	float \(S_\text{eq}\) for the given aerosol/droplet system