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DL_Wilke_Chang ¤

DL_Wilke_Chang(
    T: float,
    MA: float,
    MB: float,
    rhoA: float,
    viscB: float,
    phi: float = 1.0,
) -> float

Estimate the infinite-dilution coefficient of a solute A in a liquid solvent B, \(D^0_{AB}\), using the Wilke-Chang method.

\[ D^0_{AB} = 5.9\times 10^{-17} \frac{(\phi M_B)^{1/2} T}{\eta_B (M_A/\rho_A)^{0.6}} \]

where the meaning of all symbols is as described below in the parameters section. The numerical factor has been adjusted to convert the equation to SI units.

References

  • RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids 4th edition, 1986, p. 598.
PARAMETER DESCRIPTION
T

Temperature. Unit = K.

TYPE: float

MA

Molar mass of solute A. Unit = kg/mol.

TYPE: float

MB

Molar mass of solvent B. Unit = kg/mol.

TYPE: float

rhoA

Density of solute A at the normal boiling point, \(\rho_A\). Unit = kg/m³.

TYPE: float

viscB

Viscostity of solvent B, \(\eta_B\). Unit = Pa.s.

TYPE: float

phi

Association factor of solvent B, \(\phi\). The following values are recomended: {water: 2.6, methanol: 1.9, ethanol: 1.5, unassociated: 1.0}.

TYPE: float DEFAULT: 1.0

RETURNS DESCRIPTION
float

Diffusion coefficient of A in B at infinite dilution. Unit = m²/s.
See also

Examples:

Estimate the diffusion coefficient of vinyl chloride through liquid water.

>>> from polykin.properties.diffusion import DL_Wilke_Chang
>>> D = DL_Wilke_Chang(
...     T=298.,         # temperature
...     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 boiling point
...     viscB=0.89e-3,  # viscosity of water at solution temperature
...     phi=2.6         # association factor for water (see docstring)
...     )
>>> print(f"{D:.2e} m²/s")
1.34e-09 m²/s
Source code in src/polykin/properties/diffusion/liquid.py 
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def DL_Wilke_Chang(T: float,
                   MA: float,
                   MB: float,
                   rhoA: float,
                   viscB: float,
                   phi: float = 1.0
                   ) -> float:
    r"""Estimate the infinite-dilution coefficient of a solute A in a liquid
    solvent B, $D^0_{AB}$, using the Wilke-Chang method.

    $$
    D^0_{AB} = 5.9\times 10^{-17}
        \frac{(\phi M_B)^{1/2} T}{\eta_B (M_A/\rho_A)^{0.6}}
    $$

    where the meaning of all symbols is as described below in the parameters
    section. The numerical factor has been adjusted to convert the equation to
    SI units.

    **References**

    *   RC Reid, JM Prausniz, and BE Poling. The properties of gases & liquids
        4th edition, 1986, p. 598.

    Parameters
    ----------
    T : float
        Temperature. Unit = K.
    MA : float
        Molar mass of solute A. Unit = kg/mol.
    MB : float
        Molar mass of solvent B. Unit = kg/mol.
    rhoA : float
        Density of solute A at the normal boiling point, $\rho_A$.
        Unit = kg/m³.
    viscB : float
        Viscostity of solvent B, $\eta_B$. Unit = Pa.s.
    phi : float
        Association factor of solvent B, $\phi$. The following values are
        recomended: {water: 2.6, methanol: 1.9, ethanol: 1.5,
        unassociated: 1.0}.

    Returns
    -------
    float
        Diffusion coefficient of A in B at infinite dilution. Unit = m²/s.

    See also
    --------
    * [`DL_Hayduk_Minhas`](DL_Hayduk_Minhas.md): alternative method.

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

    >>> from polykin.properties.diffusion import DL_Wilke_Chang
    >>> D = DL_Wilke_Chang(
    ...     T=298.,         # temperature
    ...     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 boiling point
    ...     viscB=0.89e-3,  # viscosity of water at solution temperature
    ...     phi=2.6         # association factor for water (see docstring)
    ...     )
    >>> print(f"{D:.2e} m²/s")
    1.34e-09 m²/s
    """
    return 7.4e-12*sqrt(phi*MB*1e3)*T/((viscB*1e3)*(1e6*MA/rhoA)**0.6)