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Viscosity (polykin.properties.viscosity)¤

This module implements methods to calculate the viscosity of pure gases, gas mixtures, and liquid mixtures.

MULMX2_Perry ¤

MULMX2_Perry(
    x: FloatVectorLike,
    mu: FloatVectorLike,
    hydrocarbons: bool = False,
) -> float

Calculate the viscosity of a liquid mixture from the viscosities of the pure components using the mixing rules recommended in Perry's.

For hydrocarbon mixtures:

\[ \mu_m = \left ( \sum_{i=1}^N x_i \mu_i^{1/3} \right )^3 \]

and for nonhydrocarbon mixtures:

\[ \ln{\mu_m} = \sum_{i=1}^N x_i \ln{\mu_i} \]

References

  • Perry, R. H., D. W. Green, and J. Maloney. Perrys Chemical Engineers Handbook, 7th ed. 1999, p. 2-367.
PARAMETER DESCRIPTION
x

Mole fractions of all components. Unit = mol/mol.

TYPE: FloatVectorLike

mu

Viscosities of all components, \(\mu\). Unit = Any.

TYPE: FloatVectorLike

hydrocarbons

Method selection. True for hydrocarbon mixtures, False for nonhydrocarbon mixtures.

TYPE: bool DEFAULT: False

RETURNS DESCRIPTION
float

Mixture viscosity, \(\mu_m\). Unit = [mu].

Examples:

Estimate the viscosity of a 50 mol% styrene/toluene liquid mixture at 20°C.

>>> from polykin.properties.viscosity import MULMX2_Perry
>>>
>>> x = [0.5, 0.5]
>>> mu = [0.76, 0.59] # cP, from literature
>>>
>>> mu_mix = MULMX2_Perry(x, mu)
>>>
>>> print(f"{mu_mix:.2f} cP")
0.67 cP
Source code in src/polykin/properties/viscosity/liquid.py 
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def MULMX2_Perry(x: FloatVectorLike,
                 mu: FloatVectorLike,
                 hydrocarbons: bool = False,
                 ) -> float:
    r"""Calculate the viscosity of a liquid mixture from the viscosities of the
    pure components using the mixing rules recommended in Perry's.

    For hydrocarbon mixtures:

    $$ \mu_m = \left ( \sum_{i=1}^N x_i \mu_i^{1/3} \right )^3 $$

    and for nonhydrocarbon mixtures:

    $$ \ln{\mu_m} = \sum_{i=1}^N x_i \ln{\mu_i} $$

    **References**

    *   Perry, R. H., D. W. Green, and J. Maloney. Perrys Chemical Engineers
        Handbook, 7th ed. 1999, p. 2-367.

    Parameters
    ----------
    x : FloatVectorLike
        Mole fractions of all components. Unit = mol/mol.
    mu : FloatVectorLike
        Viscosities of all components, $\mu$. Unit = Any.
    hydrocarbons : bool
        Method selection. `True` for hydrocarbon mixtures, `False` for
        nonhydrocarbon mixtures.

    Returns
    -------
    float
        Mixture viscosity, $\mu_m$. Unit = [mu].

    Examples
    --------
    Estimate the viscosity of a 50 mol% styrene/toluene liquid mixture at 20°C.
    >>> from polykin.properties.viscosity import MULMX2_Perry
    >>>
    >>> x = [0.5, 0.5]
    >>> mu = [0.76, 0.59] # cP, from literature
    >>>
    >>> mu_mix = MULMX2_Perry(x, mu)
    >>>
    >>> print(f"{mu_mix:.2f} cP")
    0.67 cP

    """
    x = np.asarray(x)
    mu = np.asarray(mu)

    if hydrocarbons:
        result = dot(x, cbrt(mu))**3
    else:
        result = exp(dot(x, log(mu)))
    return result

MUVMX2_Herning_Zipperer ¤

MUVMX2_Herning_Zipperer(
    y: FloatVectorLike,
    mu: FloatVectorLike,
    M: FloatVectorLike,
) -> float

Calculate the viscosity of a gas mixture from the viscosities of the pure components using the mixing rule of Wilke with the approximation of Herning and Zipperer.

\[ \mu_m = \frac{\displaystyle \sum_{i=1}^N y_i M_i^{1/2} \mu_i} {\displaystyle \sum_{i=1}^N y_i M_i^{1/2}} \]

Note

In this equation, the units of mole fraction \(y_i\) and molar mass \(M_i\) are arbitrary, as they cancel out when considering the ratio of the numerator to the denominator.

References

  • RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, p. 410.
PARAMETER DESCRIPTION
y

Mole fractions of all components. Unit = Any.

TYPE: FloatVectorLike

mu

Viscosities of all components, \(\mu\). Unit = Any.

TYPE: FloatVectorLike

M

Molar masses of all components. Unit = Any.

TYPE: FloatVectorLike

RETURNS DESCRIPTION
float

Mixture viscosity, \(\mu_m\). Unit = [mu].

Examples:

Estimate the viscosity of a 50 mol% ethylene/1-butene gas mixture at 120°C and 1 bar.

>>> from polykin.properties.viscosity import MUVMX2_Herning_Zipperer
>>> y = [0.5, 0.5]
>>> mu = [130e-7, 100e-7] # Pa.s, from literature
>>> M = [28.e-3, 56.e-3]  # kg/mol
>>> mu_mix = MUVMX2_Herning_Zipperer(y, mu, M)
>>> print(f"{mu_mix:.2e} Pa·s")
1.12e-05 Pa·s
Source code in src/polykin/properties/viscosity/vapor.py 
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def MUVMX2_Herning_Zipperer(y: FloatVectorLike,
                            mu: FloatVectorLike,
                            M: FloatVectorLike
                            ) -> float:
    r"""Calculate the viscosity of a gas mixture from the viscosities of the
    pure components using the mixing rule of Wilke with the approximation of
    Herning and Zipperer.

    $$ \mu_m = \frac{\displaystyle \sum_{i=1}^N y_i M_i^{1/2} \mu_i}
                    {\displaystyle \sum_{i=1}^N y_i M_i^{1/2}} $$

    !!! note

        In this equation, the units of mole fraction $y_i$ and molar mass
        $M_i$ are arbitrary, as they cancel out when considering the ratio of
        the numerator to the denominator.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, p. 410.

    Parameters
    ----------
    y : FloatVectorLike
        Mole fractions of all components. Unit = Any.
    mu : FloatVectorLike
        Viscosities of all components, $\mu$. Unit = Any.
    M : FloatVectorLike
        Molar masses of all components. Unit = Any.

    Returns
    -------
    float
        Mixture viscosity, $\mu_m$. Unit = [mu].

    Examples
    --------
    Estimate the viscosity of a 50 mol% ethylene/1-butene gas mixture at 120°C
    and 1 bar.
    >>> from polykin.properties.viscosity import MUVMX2_Herning_Zipperer
    >>> y = [0.5, 0.5]
    >>> mu = [130e-7, 100e-7] # Pa.s, from literature
    >>> M = [28.e-3, 56.e-3]  # kg/mol
    >>> mu_mix = MUVMX2_Herning_Zipperer(y, mu, M)
    >>> print(f"{mu_mix:.2e} Pa·s")
    1.12e-05 Pa·s
    """
    y = np.asarray(y)
    mu = np.asarray(mu)
    M = np.asarray(M)

    a = y*sqrt(M)
    a /= a.sum()
    return dot(a, mu)

MUVMXPC_Dean_Stiel ¤

MUVMXPC_Dean_Stiel(
    v: float,
    y: FloatVectorLike,
    M: FloatVectorLike,
    Tc: FloatVectorLike,
    Pc: FloatVectorLike,
    Zc: FloatVectorLike,
) -> float

Calculate the effect of pressure (or density) on the viscosity of gas mixtures using the method of Dean and Stiel for nonpolar components.

\[ (\mu_m -\mu_m^\circ)\xi = f(\rho_r) \]

where \(\mu_m\) is the dense gas mixture viscosity, \(\mu_m^\circ\) is the low-pressure gas mixture viscosity, \(\xi\) is a group of constants, and \(\rho_r = v_c / v\) is the reduced gas density. This equation is valid in the range \(0 \le \rho_r < 2.5\).

References

  • Dean, D., and Stiel, L. "The viscosity of nonpolar gas mixtures at moderate and high pressures." AIChE Journal 11.3 (1965): 526-532.
PARAMETER DESCRIPTION
v

Gas molar volume. Unit = m³/mol.

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

RETURNS DESCRIPTION
float

Residual viscosity, \((\mu_m - \mu_m^\circ)\). Unit = Pa·s.

Examples:

Estimate the residual viscosity of a 50 mol% ethylene/propylene mixture t 350 K and 100 bar.

>>> from polykin.properties.viscosity import MUVMXPC_Dean_Stiel
>>> v = 1.12e-4  # m³/mol, with Peng-Robinson
>>> y = [0.5, 0.5]
>>> M = [28.05e-3, 42.08e-3] # kg/mol
>>> Tc = [282.4, 364.9]      # K
>>> Pc = [50.4e5, 46.0e5]    # Pa
>>> Zc = [0.280, 0.274]
>>> mu_residual = MUVMXPC_Dean_Stiel(v, y, M, Tc, Pc, Zc)
>>> print(f"{mu_residual:.2e} Pa·s")
2.32e-05 Pa·s
Source code in src/polykin/properties/viscosity/vapor.py 
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def MUVMXPC_Dean_Stiel(v: float,
                       y: FloatVectorLike,
                       M: FloatVectorLike,
                       Tc: FloatVectorLike,
                       Pc: FloatVectorLike,
                       Zc: FloatVectorLike,
                       ) -> float:
    r"""Calculate the effect of pressure (or density) on the viscosity of
    gas mixtures using the method of Dean and Stiel for nonpolar components.

    $$ (\mu_m -\mu_m^\circ)\xi = f(\rho_r) $$

    where $\mu_m$ is the dense gas mixture viscosity, $\mu_m^\circ$ is the
    low-pressure gas mixture viscosity, $\xi$ is a group of constants, and
    $\rho_r = v_c / v$ is the reduced gas density. This
    equation is valid in the range $0 \le \rho_r < 2.5$.

    **References**

    *   Dean, D., and Stiel, L. "The viscosity of nonpolar gas mixtures at
        moderate and high pressures." AIChE Journal 11.3 (1965): 526-532.

    Parameters
    ----------
    v : float
        Gas molar volume. Unit = m³/mol.
    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.

    Returns
    -------
    float
        Residual viscosity, $(\mu_m - \mu_m^\circ)$. Unit = Pa·s.

    Examples
    --------
    Estimate the residual viscosity of a 50 mol% ethylene/propylene mixture
    t 350 K and 100 bar.

    >>> from polykin.properties.viscosity import MUVMXPC_Dean_Stiel
    >>> v = 1.12e-4  # m³/mol, with Peng-Robinson
    >>> y = [0.5, 0.5]
    >>> M = [28.05e-3, 42.08e-3] # kg/mol
    >>> Tc = [282.4, 364.9]      # K
    >>> Pc = [50.4e5, 46.0e5]    # Pa
    >>> Zc = [0.280, 0.274]
    >>> mu_residual = MUVMXPC_Dean_Stiel(v, y, M, Tc, Pc, Zc)
    >>> print(f"{mu_residual:.2e} Pa·s")
    2.32e-05 Pa·s
    """

    y = np.asarray(y)
    M = np.asarray(M)
    Tc = np.asarray(Tc)
    Pc = np.asarray(Pc)
    Zc = np.asarray(Zc)

    # Mixing rules recommended in paper
    M_mix = dot(y, M)
    Tc_mix, Pc_mix, vc_mix, _, _ = pseudocritical_properties(y, Tc, Pc, Zc)

    rhor = vc_mix/v
    # xi = 1e3*Tc_mix**(1/6)/(sqrt(M_mix*1e3)*(Pc_mix/101325)**(2/3))
    xi = 6.87e4*Tc_mix**(1/6)/(sqrt(M_mix)*(Pc_mix)**(2/3))
    a = 10.8e-5*(exp(1.439*rhor) - exp(-1.111*rhor**1.858))

    return a/xi

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 
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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

MUVPC_Jossi ¤

MUVPC_Jossi(
    rhor: float, M: float, Tc: float, Pc: float
) -> float

Calculate the effect of pressure (or density) on gas viscosity using the method of Jossi, Stiel and Thodos for nonpolar gases.

\[ \left[(\mu -\mu^\circ)\xi + 1\right]^{1/4} = 1.0230 + 0.23364\rho_r + 0.58533\rho_r^2 - 0.40758\rho_r^3 + 0.093324\rho_r^4 \]

where \(\mu\) is the dense gas viscosity, \(\mu^\circ\) is the is the low-pressure viscosity, \(\xi\) is a group of constants, and \(\rho_r = v_c / v\) is the reduced gas density. This equation is valid in the range \(0.1 < \rho_r < 3.0\).

References

  • RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, p. 424.
PARAMETER DESCRIPTION
rhor

Reduced gas density, \(\rho_r\).

TYPE: float

M

Molar mass. Unit = kg/mol.

TYPE: float

Tc

Critical temperature. Unit = K.

TYPE: float

Pc

Critical pressure. Unit = Pa.

TYPE: float

RETURNS DESCRIPTION
float

Residual viscosity, \((\mu - \mu^\circ)\). Unit = Pa·s.

Examples:

Estimate the residual viscosity of ethylene at 350 K and 100 bar.

>>> from polykin.properties.viscosity import MUVPC_Jossi
>>> vc = 130. # cm³/mol
>>> v  = 184. # cm³/mol, with Peng-Robinson
>>> rhor = vc/v
>>> mu_residual = MUVPC_Jossi(rhor=rhor, Tc=282.4, Pc=50.4e5, M=28.05e-3)
>>> print(f"{mu_residual:.2e} Pa·s")
6.76e-06 Pa·s
Source code in src/polykin/properties/viscosity/vapor.py 
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def MUVPC_Jossi(rhor: float,
                M: float,
                Tc: float,
                Pc: float
                ) -> float:
    r"""Calculate the effect of pressure (or density) on gas viscosity using
    the method of Jossi, Stiel and Thodos for nonpolar gases.

    $$ \left[(\mu -\mu^\circ)\xi + 1\right]^{1/4} = 1.0230 + 0.23364\rho_r
       + 0.58533\rho_r^2 - 0.40758\rho_r^3 + 0.093324\rho_r^4 $$

    where $\mu$ is the dense gas viscosity, $\mu^\circ$ is the is the
    low-pressure viscosity, $\xi$ is a group of constants, and
    $\rho_r = v_c / v$ is the reduced gas density. This equation is valid in
    the range $0.1 < \rho_r < 3.0$.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, p. 424.

    Parameters
    ----------
    rhor : float
        Reduced gas density, $\rho_r$.
    M : float
        Molar mass. Unit = kg/mol.
    Tc : float
        Critical temperature. Unit = K.
    Pc : float
        Critical pressure. Unit = Pa.

    Returns
    -------
    float
        Residual viscosity, $(\mu - \mu^\circ)$. Unit = Pa·s.

    Examples
    --------
    Estimate the residual viscosity of ethylene at 350 K and 100 bar.
    >>> from polykin.properties.viscosity import MUVPC_Jossi
    >>> vc = 130. # cm³/mol
    >>> v  = 184. # cm³/mol, with Peng-Robinson
    >>> rhor = vc/v
    >>> mu_residual = MUVPC_Jossi(rhor=rhor, Tc=282.4, Pc=50.4e5, M=28.05e-3)
    >>> print(f"{mu_residual:.2e} Pa·s")
    6.76e-06 Pa·s
    """
    a = 1.0230 + 0.23364*rhor + 0.58533*rhor**2 - 0.40758*rhor**3 \
        + 0.093324*rhor**4
    # 1e7*(1/((1e3)**3 * (1/101325)**4))**(1/6)
    xi = 6.872969367e8*(Tc/(M**3 * Pc**4))**(1/6)
    return (a**4 - 1.)/xi

MUV_Lucas ¤

MUV_Lucas(
    T: float,
    P: float,
    M: float,
    Tc: float,
    Pc: float,
    Zc: float,
    dm: float,
) -> float

Calculate the viscosity of a pure gas 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. 421.
PARAMETER DESCRIPTION
T

Temperature. Unit = K.

TYPE: float

P

Pressure. Unit = Pa.

TYPE: float

M

Molar mass. Unit = kg/mol.

TYPE: float

Tc

Critical temperature. Unit = K.

TYPE: float

Pc

Critical pressure. Unit = Pa.

TYPE: float

Zc

Critical compressibility factor.

TYPE: float

dm

Dipole moment. Unit = debye.

TYPE: float

RETURNS DESCRIPTION
float

Gas viscosity, \(\mu\). Unit = Pa·s.

Examples:

Estimate the viscosity of ethylene at 350 K and 10 bar.

>>> from polykin.properties.viscosity import MUV_Lucas
>>> mu = MUV_Lucas(T=350., P=10e5, M=28.05e-3,
...                Tc=282.4, Pc=50.4e5, Zc=0.280, dm=0.)
>>> print(f"{mu:.2e} Pa·s")
1.20e-05 Pa·s
Source code in src/polykin/properties/viscosity/vapor.py 
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def MUV_Lucas(T: float,
              P: float,
              M: float,
              Tc: float,
              Pc: float,
              Zc: float,
              dm: float
              ) -> float:
    r"""Calculate the viscosity of a pure gas 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. 421.

    Parameters
    ----------
    T : float
        Temperature. Unit = K.
    P : float
        Pressure. Unit = Pa.
    M : float
        Molar mass. Unit = kg/mol.
    Tc : float
        Critical temperature. Unit = K.
    Pc : float
        Critical pressure. Unit = Pa.
    Zc : float
        Critical compressibility factor.
    dm : float
        Dipole moment. Unit = debye.

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

    Examples
    --------
    Estimate the viscosity of ethylene at 350 K and 10 bar.

    >>> from polykin.properties.viscosity import MUV_Lucas
    >>> mu = MUV_Lucas(T=350., P=10e5, M=28.05e-3,
    ...                Tc=282.4, Pc=50.4e5, Zc=0.280, dm=0.)
    >>> print(f"{mu:.2e} Pa·s")
    1.20e-05 Pa·s
    """
    Tr = T/Tc
    Pr = P/Pc
    FP0 = _MUV_Lucas_FP0(Tr, Tc, Pc, Zc, dm)
    mu = _MUV_Lucas_mu(Tr, Pr, M, Tc, Pc, FP0)  # type: ignore
    return mu
Gas Liquid
DIPPR equations DIPPR102 DIPPR101, Yaws
Estimation methods MUV_Lucas, MUVMX_Lucas —
Mixing rules MUVMX2_Herning_Zipperer MULMX2_Perry
Pressure correction MUVPC_Jossi, MUVMXPC_Dean_Stiel —

Tutorial