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particula.gas.properties.mean_free_path

mean_free_path

Calculating the mean free path of air.

Long Description

The mean free path is the average distance traveled by a molecule between collisions with other molecules in a medium (air). Typical mean free path values in air are about 65 nm at 298 K and 101325 Pa.

References
  • "Mean Free Path," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Mean_free_path

get_molecule_mean_free_path 

get_molecule_mean_free_path(molar_mass: Union[float, NDArray[float64]] = MOLECULAR_WEIGHT_AIR, temperature: float = 298.15, pressure: float = 101325, dynamic_viscosity: Optional[float] = None) -> Union[float, NDArray[np.float64]]

Calculate the mean free path of a gas molecule in air.

This function calculates λ based on the input conditions. If dynamic_viscosity is not provided, it is computed via get_dynamic_viscosity(temperature).

  • λ = (2 × μ / P) / √(8 × M / (π × R × T))
    • λ is Mean free path [m].
    • μ is Dynamic viscosity [Pa·s].
    • P is Gas pressure [Pa].
    • M is Molar mass [kg/mol].
    • R is Universal gas constant [J/(mol·K)].
    • T is Gas temperature [K].

Parameters:

  • - molar_mass –

    The molar mass of the gas molecule [kg/mol].

  • - temperature –

    The temperature of the gas [K].

  • - pressure –

    The pressure of the gas [Pa].

  • - dynamic_viscosity –

    The dynamic viscosity of the gas [Pa·s]. If None, it will be calculated based on the temperature.

Returns:

  • Union[float, NDArray[float64]] –
    • Mean free path of the gas molecule in meters (m).

Examples:

Example usage
import particula as par
par.gas.get_molecule_mean_free_path()
# Returns mean free path at ~298K and 101325Pa, ~6.5e-8 m
References
  • "Mean Free Path," Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/wiki/Mean_free_path
Source code in particula/gas/properties/mean_free_path.py 
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def get_molecule_mean_free_path(
    molar_mass: Union[float, NDArray[np.float64]] = MOLECULAR_WEIGHT_AIR,  # type: ignore
    temperature: float = 298.15,
    pressure: float = 101325,
    dynamic_viscosity: Optional[float] = None,
) -> Union[float, NDArray[np.float64]]:
    """Calculate the mean free path of a gas molecule in air.

    This function calculates λ based on the input conditions. If
    dynamic_viscosity is not provided, it is computed via
    get_dynamic_viscosity(temperature).

    - λ = (2 × μ / P) / √(8 × M / (π × R × T))
        - λ is Mean free path [m].
        - μ is Dynamic viscosity [Pa·s].
        - P is Gas pressure [Pa].
        - M is Molar mass [kg/mol].
        - R is Universal gas constant [J/(mol·K)].
        - T is Gas temperature [K].

    Arguments:
        - molar_mass : The molar mass of the gas molecule [kg/mol].
        - temperature : The temperature of the gas [K].
        - pressure : The pressure of the gas [Pa].
        - dynamic_viscosity : The dynamic viscosity of the gas [Pa·s].
            If None, it will be calculated based on the temperature.

    Returns:
        - Mean free path of the gas molecule in meters (m).

    Examples:
        ```py title="Example usage"
        import particula as par
        par.gas.get_molecule_mean_free_path()
        # Returns mean free path at ~298K and 101325Pa, ~6.5e-8 m
        ```

    References:
        - "Mean Free Path," Wikipedia, The Free Encyclopedia.
          https://en.wikipedia.org/wiki/Mean_free_path
    """
    # check inputs are positive
    if temperature <= 0:
        logger.error("Temperature must be positive [Kelvin]")
        raise ValueError("Temperature must be positive [Kelvin]")
    if pressure <= 0:
        logger.error("Pressure must be positive [Pascal]")
        raise ValueError("Pressure must be positive [Pascal]")
    if np.any(molar_mass <= 0):
        logger.error("Molar mass must be positive [kg/mol]")
        raise ValueError("Molar mass must be positive [kg/mol]")
    if dynamic_viscosity is None:
        dynamic_viscosity = get_dynamic_viscosity(temperature)
    gas_constant = float(GAS_CONSTANT)

    return (2 * dynamic_viscosity / pressure) / (
        8 * molar_mass / (np.pi * gas_constant * temperature)
    ) ** 0.5