Wilke Method for Low-pressure Gas Mixture Viscosity#

The ViscosityWilke mixture gas dynamic viscosity model can be imported from idaes.models.properties.modular_properties.transport_properties, while additional rules and utility functions can be imported from idaes.models.properties.modular_properties.transport_properties.viscosity_wilke.

Formulation#

This description of the Wilke method to calculate gas mixture viscosity is derived from that in The Properties of Gases and Liquids, Section 9-5. Viscosity is given by the formula

\[\mu_m = \sum_{i=1}^n \frac{y_i \mu_i}{\sum_{j=1}^n y_j \phi_{ij}}\]

in which \(\mu_m\) is the mixture dynamic viscosity, \(\mu_i\) is the pure component viscosity of component \(i\), \(y_i\) is the gas mole fraction of component \(i\), and \(\phi_{ij}\) is a mixing function defined below.

Callbacks for Mixing Function#

These callbacks provide expressions for the mixing function \(\phi_{ij}\).

idaes.models.properties.modular_properties.transport_properties.viscosity_wilke.wilke_phi_ij_callback(b, i, j, pname, mw_dict)[source]#

Equation 9.5.14 from Properties of Gases and Liquids.

\[\phi_{ij} = \frac{[1 + (\mu_i/\mu_j)^{1/2}(M_j/M_i)^{1/4}]^2}{[8(1+M_i/M_j)]^{1/2}}\]

in which \(M_i\) is the molecular weight of component \(i\).

idaes.models.properties.modular_properties.transport_properties.viscosity_wilke.herring_zimmer_phi_ij_callback(b, i, j, pname, mw_dict)[source]#

Equation 9.5.17 from Properties of Gases and Liquids.

\[\phi_{ij} = \left(\frac{M_j}{M_i}\right)^{1/2}\]

in which \(M_i\) is the molecular weight of component \(i\).

List of Parameters#

Parameter Name	Description	Units
`mw`	Molecular weight \(M_i\)	Mass/Amount
`visc_d_phase_comp`	Pure component viscosity \(\mu_i\)	Pressure*Time
`viscosity_phi_ij_callback`	Callback to use for \(\phi_{ij}\)	n/a

Example#

The code snippet below demonstrates how to specify use of the ViscosityWilke model for pure component vapor viscosity as part of the modular property framework.

from idaes.models.properties.modular_properties.pure import ChapmanEnskogLennardJones
from idaes.models.properties.modular_properties.transport_properties import ViscosityWilke
from idaes.models.properties.modular_properties.transport_properties.viscosity_wilke import wilke_phi_ij_callback, herring_zimmer_phi_ij_callback

configuration = {
  "components":{
    "H2O": {
      "type": Component,
      "valid_phase_types": [PhaseType.vaporPhase],
      ...
      "visc_d_phase_comp": {"Vap": ChapmanEnskogLennardJones}
      ...
    }
    "H2": {
      "type": Component,
      "valid_phase_types": [PhaseType.vaporPhase],
      ...
      "visc_d_phase_comp": {"Vap": ChapmanEnskogLennardJones}
      ...
    }
  }
  "phases":{
    "Vap": {
      "type": VaporPhase,
      ...
      "visc_d_phase": ViscosityWilke,
      "transport_property_options": {
        "viscosity_phi_ij_callback": wilke_phi_ij_callback,
      }
    },
    ...
  }
  ...
}

References#

Poling, Bruce, E. et al. The Properties of Gases and Liquids. 5th ed. New York: NcGraw-Hill, 2001.

Wilke Method for Low-pressure Gas Mixture Viscosity

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