def axial_dispersion_coeff_sc(Dm, epsilon, Re, Sc):
    """
    Estimate the axial dispersion coefficient under supercritical conditions
    using the correlation of Funazukuri et al.

    .. math:: D_{ax} = \\frac{D_m}{\\varepsilon} 1.317 (\\varepsilon Re Sc)^{1.392}

    Valid for:

    .. math:: \\varepsilon Re Sc > 0.3, 3.9 < Sc < 665

    Parameters
    ----------
    Dm : float
        Molecular diffusion coefficient [m^2/s]
    epsilon : float
        Bed porosity [-]
    Re : float
        Reynolds number [-]
    Sc : float
        Schmidt number [-]

    Returns
    -------
    Dax : float
        Axial dispersion coefficient [m^2/s]
    
    Raises
    ------
    ValueError
        If epsilon*Re*Sc is not > 0.3 or Sc in not in range 3.9 - 665

    Example
    -------
    >>> axial_dispersion_coeff_sc(4.7e-9, 0.4, 1100.0, 135.0)
    0.06835

    References
    ----------
    T. Funazukuri, C. Kong, and S. Kagei. Effective axial dispersion
    coefficients in packed beds under supercritical conditions.
    J. Supercrit. Fluid, 1998, 13 (1–3), 169–175.
    """
    if (epsilon*Re*Sc > 0.3) and (3.9 < Sc < 665):
        Dax = Dm/epsilon * 1.317 * (epsilon * Re * Sc)**1.392
    else:
        raise ValueError(
            f'Correlation not applicable in the given conditions. \n'
            f'epsilon*Re*Sc must be > 0.3. It is {epsilon*Re*Sc:.2f}. \n'
            f'Sc must be in range 3.9 - 665. It is {Sc:.2f}. \n'
        )
    return Dax