.TILMedia.Internals.GasDiffusionCoefficients.binaryDiffCoeff_ij_Chapman_Enskog

Information

Calculation of binary gas diffusion coefficients according to [Poling2020] and [Bird2007]: \\[ D_{i,j} = 0.0018583 \frac{\sqrt{T^3 \left(\frac{1}{M_i}+\frac{1}{M_j} \right)}}{p \sigma_{i,j}^2 \Omega_{D,i,j}} \\] Here \\(D_{i,j}\\) is the binary diffusion coefficient (\\(\mathrm{cm^2/s}\\)) of species \\(i\\) and \\(j\\), \\(p\\) is the total pressure (bar), \\(T\\) is the temperature (K) and \\(M_i\\), \\(M_j\\) are the molecular weights. The charateristic length \\(\sigma_{i,j}\\) (\\( \mathrm{10^{-10} m}\\)) is calculated with \\[ \sigma_{i,j}= \frac{\sigma_{i}+\sigma_{j}}{2} \\] The characteristic Lennard-Jones lengths \\(\sigma_{i}\\) and \\(\sigma_{j}\\) are tabulated (e.g. in [Poling2020]). The dimensionless diffusion collision integral \\(\Omega_{D,i,j}\\) is a function of \\(T^\* =k T /\varepsilon_{ij}\\). Here \\(k \\) is the Boltzman constant and T the temperature of the gases. \\(\varepsilon_{ij}\\) is calculated with the tabulated characteristic Lennard-Jones energies \\(\varepsilon_i\\) and \\(\varepsilon_j\\) (e.g. in [Poling2020] or [Bird2007]): \\[ \varepsilon_{i,j}= \left(\varepsilon_i \varepsilon_j \right)^{\frac{1}{2}} \\] The solution of the function \\(\Omega_{D,i,j}= f \left(k T /\varepsilon_{ij} \right)\\) can be found in form of a table or as a function, e.g. (in [Poling2020] or [Bird2007])): \\[ \Omega_{D,i,j}= f \left(k T /\varepsilon_{ij} \right)= \frac{1.06036}{{{T^*}^{0.15610}}} + \frac{0.19300}{\exp{\left( 0.47635 T^\* \right)}}+ \frac{1.03587}{\exp{\left( 1.52996 T^\* \right)}}+ \frac{1.76474}{\exp{\left( 3.89411 T^\* \right)}} \\] The way of calculating \\(\Omega_{D,i,j}\\) via \\(\sigma_{i,j}= \frac{\sigma_{i}+\sigma_{j}}{2}\\) and \\(\varepsilon_{i,j}= \left(\varepsilon_i \varepsilon_j \right)^{\frac{1}{2}}\\) is valid for unpolar gases [Bird2007].

References

Interface

function binaryDiffCoeff_ij_Chapman_Enskog
  input Modelica.Units.SI.AbsolutePressure p "Pressure";
  input Modelica.Units.SI.Temperature T "Temperature";
  input Integer i "First component ID";
  input Integer j "Second component ID";
  input TILMedia.GasTypes.BaseGas gasType "Gas type";
  output Modelica.Units.SI.DiffusionCoefficient D_ij "Binary diffusion coefficient";
  import k_b = Modelica.Constants.k;
end binaryDiffCoeff_ij_Chapman_Enskog;