Mean Free Path¶

The mean free path is the average distance of a molecule between collisions with other molecules present in the medium. We use the kinetic theory of gases to calculate the mean free path in an ideal gas as

$$ \lambda = \frac{2 \mu / p}{(8 \, \mathrm{MW} / (\pi R T))^{1/2}} $$

where $\lambda$ is the mean free path, $\mu$ is the dynamic viscosity, $p$ is the pressure, $\mathrm{MW}$ is the molecular weight, $R$ is the gas constant, $T$ is the temperature. As noted above, the user can provide an explicit value for $\mu$ or it can be calculated using the above formula (that is, the user can provide the inputs to the above formula for $\mu$). At default conditions, $\lambda$ is about 66.5 nm.

In [4]:

from particula.gas.properties import molecule_mean_free_path, get_dynamic_viscosity

air_dynamic_viscosity = get_dynamic_viscosity(temperature=298.15)

mean_free_path = molecule_mean_free_path(
    molar_mass=28.97e-3,
    temperature=298.15,
    pressure=101325,
    dynamic_viscosity=air_dynamic_viscosity,
)

print(f"mean free path is {mean_free_path} m") # will produce approx 66.5 nm

from particula.gas.properties import molecule_mean_free_path, get_dynamic_viscosity air_dynamic_viscosity = get_dynamic_viscosity(temperature=298.15) mean_free_path = molecule_mean_free_path( molar_mass=28.97e-3, temperature=298.15, pressure=101325, dynamic_viscosity=air_dynamic_viscosity, ) print(f"mean free path is {mean_free_path} m") # will produce approx 66.5 nm

mean free path is 6.647342358988276e-08 m