polykin.properties.viscosity

MUVMX_Lucas

MUVMX_Lucas(
    T: float,
    P: float,
    y: FloatVectorLike,
    M: FloatVectorLike,
    Tc: FloatVectorLike,
    Pc: FloatVectorLike,
    Zc: FloatVectorLike,
    dm: FloatVectorLike,
) -> float

Calculate the viscosity of a gas mixture at a given temperature and pressure using the method of Lucas.

References

• RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, p. 431.

PARAMETER	DESCRIPTION
T	Temperature. Unit = K. TYPE: float
P	Pressure. Unit = Pa. TYPE: float
y	Mole fractions of all components. Unit = mol/mol. TYPE: FloatVectorLike
M	Molar masses of all components. Unit = kg/mol. TYPE: FloatVectorLike
Tc	Critical temperatures of all components. Unit = K. TYPE: FloatVectorLike
Pc	Critical pressures of all components. Unit = Pa. TYPE: FloatVectorLike
Zc	Critical compressibility factors of all components. TYPE: FloatVectorLike
dm	Dipole moments of all components. Unit = debye. TYPE: FloatVectorLike

RETURNS	DESCRIPTION
float	Gas mixture viscosity, \(\mu_m\). Unit = Pa·s.

Examples:

Estimate the viscosity of a 60 mol% ethylene/nitrogen gas mixture at 350 K and 10 bar.

>>> from polykin.properties.viscosity import MUVMX_Lucas
>>> y = [0.6, 0.4]
>>> M = [28.e-3, 28.e-3]   # kg/mol
>>> Tc = [282.4, 126.2]    # K
>>> Pc = [50.4e5, 33.9e5]  # Pa
>>> Zc = [0.280, 0.290]
>>> dm = [0., 0.]
>>> mu_mix = MUVMX_Lucas(T=350., P=10e5, y=y, M=M,
...                      Tc=Tc, Pc=Pc, Zc=Zc, dm=dm)
>>> print(f"{mu_mix:.2e} Pa·s")
1.45e-05 Pa·s

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

def MUVMX_Lucas(T: float,
                P: float,
                y: FloatVectorLike,
                M: FloatVectorLike,
                Tc: FloatVectorLike,
                Pc: FloatVectorLike,
                Zc: FloatVectorLike,
                dm: FloatVectorLike
                ) -> float:
    r"""Calculate the viscosity of a gas mixture at a given temperature and
    pressure using the method of Lucas.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, p. 431.

    Parameters
    ----------
    T : float
        Temperature. Unit = K.
    P : float
        Pressure. Unit = Pa.
    y : FloatVectorLike
        Mole fractions of all components. Unit = mol/mol.
    M : FloatVectorLike
        Molar masses of all components. Unit = kg/mol.
    Tc : FloatVectorLike
        Critical temperatures of all components. Unit = K.
    Pc : FloatVectorLike
        Critical pressures of all components. Unit = Pa.
    Zc : FloatVectorLike
        Critical compressibility factors of all components.
    dm : FloatVectorLike
        Dipole moments of all components. Unit = debye.

    Returns
    -------
    float
        Gas mixture viscosity, $\mu_m$. Unit = Pa·s.

    Examples
    --------
    Estimate the viscosity of a 60 mol% ethylene/nitrogen gas mixture at 350 K
    and 10 bar.

    >>> from polykin.properties.viscosity import MUVMX_Lucas
    >>> y = [0.6, 0.4]
    >>> M = [28.e-3, 28.e-3]   # kg/mol
    >>> Tc = [282.4, 126.2]    # K
    >>> Pc = [50.4e5, 33.9e5]  # Pa
    >>> Zc = [0.280, 0.290]
    >>> dm = [0., 0.]
    >>> mu_mix = MUVMX_Lucas(T=350., P=10e5, y=y, M=M,
    ...                      Tc=Tc, Pc=Pc, Zc=Zc, dm=dm)
    >>> print(f"{mu_mix:.2e} Pa·s")
    1.45e-05 Pa·s
    """
    y = np.asarray(y)
    M = np.asarray(M)
    Tc = np.asarray(Tc)
    Pc = np.asarray(Pc)
    Zc = np.asarray(Zc)
    dm = np.asarray(dm)

    Tc_mix = dot(y, Tc)
    M_mix = dot(y, M)
    Pc_mix = R*Tc_mix*dot(y, Zc)/dot(y, R*Tc*Zc/Pc)
    FP0_mix = dot(y, _MUV_Lucas_FP0(T/Tc, Tc, Pc, Zc, dm))
    mu = _MUV_Lucas_mu(
        T/Tc_mix, P/Pc_mix, M_mix, Tc_mix, Pc_mix, FP0_mix)

    return mu