Source code for openpnm.models.phase.surface_tension._funcs

import numpy as np

from openpnm.models.phase import _phasedocs

__all__ = [
    "water_correlation",
    "liquid_pure_bb",
    "liquid_mixture_wsd",
]



[docs]
@_phasedocs
def water_correlation(
    phase,
    T='pore.temperature',
    salinity='pore.salinity'
):
    r"""
    Calculates surface tension of pure water or seawater at atmospheric
    pressure

    This model uses Eq. (28) given by Sharqawy et al. [1]. Values at
    temperature higher than the normal boiling temperature are calculated at
    the saturation pressure.

    Parameters
    ----------
    %(phase)s
    %(T)s
    %(salinity)s

    Returns
    -------
    value : ndarray
        A numpy ndarray containing surface tension of seawater in [N/m]

    Notes
    -----
    T must be in K, and S in g of salt per kg of phase, or ppt (parts per
    thousand). The correlation is valid for 273 < T < 313 K and
    0 < S < 40 g/kg within 0.2 percent accuracy.

    References
    ----------
    [1] Sharqawy M. H., Lienhard J. H., and Zubair, S. M., Desalination and
    Water Treatment, 2010.

    """
    T = phase[T]
    if salinity in phase.keys():
        S = phase[salinity]
    else:
        S = 0
    sigma_w = 0.2358*((1-(T/647.096))**1.256)*(1-0.625*(1-(T/647.096)))
    a1 = 2.2637334337E-04
    a2 = 9.4579521377E-03
    a3 = 3.3104954843E-02
    TC = T-273.15
    sigma_sw = sigma_w*(1+(a1*TC+a2)*np.log(1+a3*S))
    value = sigma_sw
    return value




[docs]
@_phasedocs
def liquid_pure_bb(
    phase,
    T='pore.temperature',
    Tc='param.critical_temperature',
    Tb='param.boiling_temperature',
    Pc='param.critical_pressure',
):
    r"""
    Computes the surface tension of a pure liquid in its own vapor using the
    correlation in [1]

    Parameters
    ----------
    %(phase)s
    %(T)s
    %(Tc)s
    %(Tb)s
    %(Pc)s

    Returns
    -------
    value : ndarray
        A numpy ndarray containing surface tension values scaled to the
        temperature [N/m]

    References
    ----------
    [1] Brock and Bird

    """
    T = phase[T]
    Tc = phase[Tc]
    Tr = T/Tc
    Tb = phase[Tb]
    Tbr = Tb/Tc
    Pc = phase[Pc]/100000
    Q = 0.1196*(1 + Tbr*np.log(Pc/1.01325)/(1-Tbr))-0.279
    sigma = 1e-3 * Q * (Pc**(2/3)) * (Tc**(1/3)) * ((1-Tr)**(11/9))
    return sigma




[docs]
@_phasedocs
def liquid_mixture_wsd(
    phase,
    sigmas='pore.surface_tension.*',
    rhos='pore.density.*',
    MWs='param.molecular_weight.*',
):
    r"""
    Computes the surface tension of a liqiud mixture with its own vapor using
    the correlation in [1]

    Parameters
    ----------
    %(phase)s
    %(rhos)s
    %(MWs)s
    %(sigmas)s

    Returns
    -------
    sigma : ndarray
        A numpy ndarray containing surface tension values

    References
    ----------
    [1] Winterfeld, Scriven, and Davis

    """
    sigmas = phase.get_comp_vals(sigmas)
    xs = phase['pore.mole_fraction']
    rhos = phase.get_comp_vals(rhos)  # kg/m3
    MWs = phase.get_comp_vals(MWs)  # g/mol
    rhoms = {k: rhos[k]/(MWs[k]/1000) for k in xs.keys()}  # mol/m3
    rhom_mix = np.vstack([rhoms[k]*xs[k] for k in xs.keys()]).sum(axis=0)
    sigma = 0.0
    for i, ki in enumerate(xs.keys()):
        for j, kj in enumerate(xs.keys()):
            num = xs[ki]*xs[kj]*(rhom_mix**2)*(sigmas[ki]*sigmas[kj])**0.5
            denom = rhoms[ki]*rhoms[kj]
            sigma += num/denom
    return sigma