Skip to content

polykin.properties.diffusion¤

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.

Tip

This equation can also be applied when the solvent B is itself a mixture of components. In that case, \(M_B\) and \(\phi\) should be taken as the corresponding mole-average properties of the mixture, and \(\eta_B\) should be the viscosity of the solvent mixture.

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 
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
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.

    !!! tip

        This equation can also be applied when the solvent B is itself a mixture
        of components. In that case, $M_B$ and $\phi$ should be taken as the
        corresponding mole-average properties of the mixture, and $\eta_B$
        should be the viscosity of the solvent mixture.

    **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)