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polykin.properties.viscosity¤

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