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Wilson_gamma ¤

Wilson_gamma(
    x: FloatVector, Lambda: FloatSquareMatrix
) -> FloatVector

Calculate the activity coefficients of a multicomponent mixture according to the Wilson model.

\[ \ln{\gamma_i} = -\ln{\left(\displaystyle\sum_{j}{x_{j}\Lambda_{ij}}\right)} + 1 - \sum_{k}{\frac{x_{k}\Lambda_{ki}} {\displaystyle\sum_{j}{x_{j}\Lambda_{kj}}}} \]

where \(x_i\) are the mole fractions and \(\Lambda_{ij}\) are the interaction parameters.

References

  • G.M. Wilson, J. Am. Chem. Soc., 1964, 86, 127.
PARAMETER DESCRIPTION
x

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

TYPE: FloatVector(N)

Lambda

Interaction parameters, \(\Lambda_{ij}\). It is expected (but not checked) that \(\Lambda_{ii}=1\).

TYPE: FloatSquareMatrix(N, N)

RETURNS DESCRIPTION
FloatVector(N)

Activity coefficients of all components.
See also
Source code in src/polykin/thermo/acm/wilson.py 
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def Wilson_gamma(x: FloatVector,
                 Lambda: FloatSquareMatrix
                 ) -> FloatVector:
    r"""Calculate the activity coefficients of a multicomponent mixture
    according to the Wilson model.

    $$ \ln{\gamma_i} = 
    -\ln{\left(\displaystyle\sum_{j}{x_{j}\Lambda_{ij}}\right)} + 1 -
    \sum_{k}{\frac{x_{k}\Lambda_{ki}}
    {\displaystyle\sum_{j}{x_{j}\Lambda_{kj}}}} $$

    where $x_i$ are the mole fractions and $\Lambda_{ij}$ are the interaction
    parameters.

    **References**

    *   G.M. Wilson, J. Am. Chem. Soc., 1964, 86, 127.

    Parameters
    ----------
    x : FloatVector (N)
        Mole fractions of all components. Unit = mol/mol.
    Lambda : FloatSquareMatrix (N,N)
        Interaction parameters, $\Lambda_{ij}$. It is expected (but not
        checked) that $\Lambda_{ii}=1$.

    Returns
    -------
    FloatVector (N)
        Activity coefficients of all components.

    See also
    --------
    * [`Wilson`](Wilson.md): related class.

    """
    A = dot(Lambda, x)
    return exp(1. - dot(x/A, Lambda))/A