def Duckler(x, mul, mug, rhol, rhog):
    r'''Calculates a suggested definition for liquid-gas two-phase flow 
    viscosity in internal pipe flow according to the form in [1]_ and shown
    in [2]_, [3]_, and [4]_.
        
    .. math::
        \mu_m = \frac{\frac{x\mu_g}{\rho_g} + \frac{(1-x)\mu_l}{\rho_l} }
        {\frac{x}{\rho_g} + \frac{(1-x)}{\rho_l}   }
        
    Parameters
    ----------
    x : float
        Quality of the gas-liquid flow, [-]
    mul : float
        Viscosity of liquid, [Pa*s]
    mug : float
        Viscosity of gas, [Pa*s]
    rhol : float
        Density of the liquid, [kg/m^3]
    rhog : float
        Density of the gas, [kg/m^3]

    Returns
    -------
    mu_lg : float
        Liquid-gas viscosity (**a suggested definition, potentially useful
        for empirical work only!**) [Pa*s]

    Notes
    -----
    This model converges to the liquid or gas viscosity as the quality
    approaches either limits.
    
    This has also been expressed in the following form:
        
    .. math::
        \mu_m = \rho_m \left[x\left(\frac{\mu_g}{\rho_g}\right) 
        + (1 - x)\left(\frac{\mu_l}{\rho_l}\right)\right]
        
    According to the homogeneous definition of two-phase density.
        
    Examples
    --------
    >>> Duckler(x=0.4, mul=1E-3, mug=1E-5, rhol=850, rhog=1.2)
    1.2092040385066917e-05

    References
    ----------
    .. [1] Fourar, M., and S. Bories. "Experimental Study of Air-Water 
       Two-Phase Flow through a Fracture (Narrow Channel)." International 
       Journal of Multiphase Flow 21, no. 4 (August 1, 1995): 621-37. 
       doi:10.1016/0301-9322(95)00005-I.
    .. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for 
       Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33,
       no. 1 (October 1, 2008): 106-13. 
    .. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and
       Predictive Methods for Pressure Drop in Adiabatic, Condensing and
       Boiling Mini/Micro-Channel Flows." International Journal of Heat and
       Mass Transfer 77 (October 2014): 74-97.
       doi:10.1016/j.ijheatmasstransfer.2014.04.035.
    .. [4] Aung, NZ, and T. Yuwono. "Evaluation of Mixture Viscosity Models in 
       the Prediction of Two-Phase Flow Pressure Drops." ASEAN Journal on 
       Science and Technology for Development 29, no. 2 (2012). 
    '''
    return (x*mug/rhog + (1. - x)*mul/rhol)/(x/rhog + (1. - x)/rhol)