pyrcel.thermo.Seq_approx¶

pyrcel.thermo.Seq_approx(r, r_dry, T, kappa)¶

Approximate 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, using a simplified expression derived by Taylor-expanding the original equation,

\[S_\text{eq} = \frac{2\sigma_{w} M_w}{RT\rho_w r} - \kappa\frac{r_d^3}{r^3}\]

which is valid when the equilibrium supersaturation is small, i.e. in most terrestrial atmosphere applications.

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