polykin.properties.diffusion

DV_Wilke_Lee

DV_Wilke_Lee(
    T: float,
    P: float,
    MA: float,
    MB: float,
    rhoA: float,
    rhoB: float | None,
    TA: float,
    TB: float | None,
) -> float

Estimate the mutual diffusion coefficient of a binary gas mixture, \(D_{AB}\), using the Wilke-Lee method.

Note

If air is one of the components of the mixture, arguments TB and rhoB should both be set to None.

References

• RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, p. 587.

PARAMETER	DESCRIPTION
T	Temperature. Unit = K. TYPE: float
P	Pressure. Unit = Pa. TYPE: float
MA	Molar mass of component A. Unit = kg/mol. TYPE: float
MA	Molar mass of component B. Unit = kg/mol. TYPE: float
rhoA	Density of component A at the normal boiling point. Unit = kg/m³. TYPE: float
rhoB	Density of component B at the normal boiling point. If None, air is assumeed to be the component B. Unit = kg/m³. TYPE: float | None
TA	Normal boiling temperature of component A. Unit = K. TYPE: float
TB	Normal boiling temperature of component B. If None, air is assumeed to be the component B. Unit = K. TYPE: float | None

RETURNS	DESCRIPTION
float	Binary diffusion coefficient. Unit = m²/s.

Examples:

Estimate the diffusion coefficient of vinyl chloride through water vapor.

>>> from polykin.properties.diffusion import DV_Wilke_Lee
>>> D = DV_Wilke_Lee(
...     T=298.,       # temperature
...     P=1e5,        # pressure
...     MA=62.5e-3,   # molar mass of vinyl chloride
...     MB=18.0e-3,   # molar mass of water
...     rhoA=910.,    # density of vinyl chloride at the normal boiling point
...     rhoB=959.,    # density of water at the normal boiling point
...     TA=260.,      # normal boiling point of vinyl chloride
...     TB=373.,      # normal boiling point of water
...     )
>>> print(f"{D:.2e} m²/s")
1.10e-05 m²/s

Estimate the diffusion coefficient of vinyl chloride through air.

>>> from polykin.properties.diffusion import DV_Wilke_Lee
>>> D = DV_Wilke_Lee(
...     T=298.,       # temperature
...     P=1e5,        # pressure
...     MA=62.5e-3,   # molar mass of vinyl chloride
...     MB=18.0e-3,   # molar mass of water
...     rhoA=910.,    # density of vinyl chloride at the normal boiling point
...     rhoB=None,    # air
...     TA=260.,      # normal boiling point of vinyl chloride
...     TB=None,      # air
...     )
>>> print(f"{D:.2e} m²/s")
1.37e-05 m²/s

Source code in src/polykin/properties/diffusion/vapor.py

def DV_Wilke_Lee(T: float,
                 P: float,
                 MA: float,
                 MB: float,
                 rhoA: float,
                 rhoB: float | None,
                 TA: float,
                 TB: float | None
                 ) -> float:
    r"""Estimate the mutual diffusion coefficient of a binary gas mixture,
    $D_{AB}$, using the Wilke-Lee method.

    !!! note
        If air is one of the components of the mixture, arguments `TB` and
        `rhoB` should both be set to `None`.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, p. 587.

    Parameters
    ----------
    T : float
        Temperature. Unit = K.
    P : float
        Pressure. Unit = Pa.
    MA : float
        Molar mass of component A. Unit = kg/mol.
    MA : float
        Molar mass of component B. Unit = kg/mol.
    rhoA : float
        Density of component A at the normal boiling point. Unit = kg/m³.
    rhoB : float | None
        Density of component B at the normal boiling point. If `None`,
        air is assumeed to be the component B. Unit = kg/m³.
    TA : float
        Normal boiling temperature of component A. Unit = K.
    TB : float | None
        Normal boiling temperature of component B. If `None`, air is assumeed
        to be the component B. Unit = K.

    Returns
    -------
    float
        Binary diffusion coefficient. Unit = m²/s.

    Examples
    --------
    Estimate the diffusion coefficient of vinyl chloride through water vapor.

    >>> from polykin.properties.diffusion import DV_Wilke_Lee
    >>> D = DV_Wilke_Lee(
    ...     T=298.,       # temperature
    ...     P=1e5,        # pressure
    ...     MA=62.5e-3,   # molar mass of vinyl chloride
    ...     MB=18.0e-3,   # molar mass of water
    ...     rhoA=910.,    # density of vinyl chloride at the normal boiling point
    ...     rhoB=959.,    # density of water at the normal boiling point
    ...     TA=260.,      # normal boiling point of vinyl chloride
    ...     TB=373.,      # normal boiling point of water
    ...     )
    >>> print(f"{D:.2e} m²/s")
    1.10e-05 m²/s

    Estimate the diffusion coefficient of vinyl chloride through air.

    >>> from polykin.properties.diffusion import DV_Wilke_Lee
    >>> D = DV_Wilke_Lee(
    ...     T=298.,       # temperature
    ...     P=1e5,        # pressure
    ...     MA=62.5e-3,   # molar mass of vinyl chloride
    ...     MB=18.0e-3,   # molar mass of water
    ...     rhoA=910.,    # density of vinyl chloride at the normal boiling point
    ...     rhoB=None,    # air
    ...     TA=260.,      # normal boiling point of vinyl chloride
    ...     TB=None,      # air
    ...     )
    >>> print(f"{D:.2e} m²/s")
    1.37e-05 m²/s
    """

    MAB = 1e3*2/(1/MA + 1/MB)

    # ϵ_AB and σ_AB
    eA = 1.15*TA
    sA = 1.18*(1e6*MA/rhoA)**(1/3)
    if rhoB is None and TB is None:
        # values for air
        sB = 3.62
        eB = 97.
    elif rhoB is not None and TB is not None:
        sB = 1.18*(1e6*MB/rhoB)**(1/3)
        eB = 1.15*TB
    else:
        raise ValueError(
            "Invalid input. `rhoB` and `TB` must both be None or floats.")

    eAB = sqrt(eA*eB)
    sAB = (sA + sB)/2

    # Ω_D
    Ts = T/eAB
    A = 1.06036
    B = 0.15610
    C = 0.19300
    D = 0.47635
    E = 1.03587
    F = 1.52996
    G = 1.76474
    H = 3.89411
    omegaD = A/Ts**B + C/exp(D*Ts) + E/exp(F*Ts) + G/exp(H*Ts)

    return 1e-2*(3.03 - 0.98/sqrt(MAB))*T**1.5 / (P*sqrt(MAB)*sAB**2*omegaD)