functionbinaryDiffCoeff_ij_Chapman_Enskog
General binary diffusion coefficient calculation via Chapman–Enskog theory (unit = m2/s)
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
| [Poling2020] |
Poling, Bruce E.; Prausnitz, John M.; O'Connell, John P. (2020): Properties of Gases and Liquids, Fifth Edition. Fifth edition. New York, N.Y.: McGraw-Hill Education; McGraw Hill (McGraw-Hill's AccessEngineering).
|
| [Bird2007] |
Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2007): Transport phenomena. Rev. 2nd ed. New York: J. Wiley
|