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Zero-density Transport models

Chapman-Enskog Model

Chapman-Enskog model for transport properties at the zero-density limit based on the kinetic gas theory.

\[\begin{aligned} \eta_{\varrho \rightarrow 0} &= \frac{5}{16} \sqrt{\frac{M k_{\rm B} T}{\pi N_{\rm A}}} \frac{1}{\sigma^2 \Omega^{(2,2)}} \\ \lambda_{\varrho \rightarrow 0} &= \frac{75}{64} k_{\rm B} \sqrt{\frac{R T}{M \pi}} \frac{1}{\sigma^2 \Omega^{(2,2)}}\\ D_{\varrho \rightarrow 0} \varrho^{\rm m} &= \frac{3}{8} \sqrt{\frac{M k_{\rm B} T}{\pi N_{\rm A}}} \frac{1}{\sigma^2 \Omega^{(1,1)}} \end{aligned}\]

EntropyScaling.ChapmanEnskog — Type
ChapmanEnskog <: ChapmanEnskogModel
ChapmanEnskog(components; userlocations=String[], collision_integral=KimMonroe())

Chapman-Enskog transport properties for the zero-density limit.

Parameters

  • σ::SingleParam{T}: Lennard-Jones size parameter ([σ] = Å)
  • ε::SingleParam{T}: Lennard-Jones energy parameter ([ε] = K)
  • Mw::SingleParam{T}: molar mass ([Mw] = g mol⁻¹)
  • collision::C: collision integral method (KimMonroe() (default) or Neufeld(), see Ω)

Currently, parameters from Poling et al. [8] and Yang et al. [3] are in the database. Mixture properties are calculated according to the models from Wilke [9] (viscosity), Mason and Saxena [10] (thermal conductivity), and Miller and Carman [11] (self-diffusion).

Example

using EntropyScaling

# Construction with custom parameters
model_methane = ChapmanEnskog("methane"; userlocations=(;sigma=3.758, epsilon=148.6, Mw=16.043)

η = viscosity(model_methane, NaN, 300.)
D = self_diffusion_coefficient(model_methane, NaN, 300.)

# Construction from database
model_mix = ChapmanEnskog(["butane","methanol"])

η_mix = viscosity(model_mix, NaN, 300., [.5,.5])
D_mix = self_diffusion_coefficient(model_mix, NaN, 300., [.5,.5])
source
EntropyScaling.Ω — Function
Ω(poperty::AbstractTransportProperty, model::ChapmanEnskogModel, T)

Calculates the collision integral for a given model and property (Ω₁₁ for diffusion coefficients and Ω₂₂ for viscosity/thermal conductivity) at the specified temperature T.

Two methods are implemented:

  • KimMonroe() [12]
  • Neufeld() [13]
source

Polynomial Dilute Gas Model

EntropyScaling.PolynomialDiluteGas — Type
PolynomialDiluteGas <: AbstractDiluteGasModel

PolynomialDiluteGas(components; userlocations=String[], prop=Viscosity())

Polynomial model for dilute gas transport properties (only temperature-dependent).

Currently, only parameters for the viscosity from Martinek et al. [5] are available in the database.

Fields

  • m::NTuple{5,SingleParam{T}}: polynomial coefficients mᵢ
  • Mw::SingleParam{T}: molar mass ([Mw] = g mol⁻¹)

Constructor

  • PolynomialDiluteGas(components; userlocations=String[], prop=Viscosity()): database constructor

Example

using EntropyScaling 

model = PolynomialDiluteGas(["butane","methanol"])
η_mix = viscosity(model, NaN, 300., [.5,.5])
source