The darken relation for multicomponent diffusion in liquid mixtures of linear alkanes: an investigation using molecular dynamics (MD) simulations

Molecular dynamics (MD) simulations have been performed for binary, ternary, and quaternary liquid mixtures of linear alkanes containing 1-16 carbons. Both the self-diffusivities (D<SUB>i,self</SUB>) and the Maxwell-Stefan (M-S) diffusivities (Ð <SUB>ij</SUB>) were determined from the MD simulations for various mixture compositions. The self-diffusivity was determined to be a linear function of the mass fractions ω<SUB>j</SUB> of the constituent species in the mixture: D<SUB>i,self</SUB> = Σ <SUP>j-n</SUP><SUB>j=1</SUB> Σ<SUB>j</SUB> D<SUP>xj→1</SUP> <SUB>i,self</SUB>where D<SUP>xj→1</SUP><SUB>i,self</SUB> is the self-diffusivity of infinitely dilute species i in species j. The Maxwell-Stefan diffusivity of the binary i-j pair in a multicomponent mixture was determined to be predicted reasonably well by the generalization of the Darken relation: Ð <SUB>ij</SUB> = [x<SUB>i</SUB>/(x<SUB>i</SUB> + x<SUB>j</SUB>)]D<SUB>j,self</SUB> + [x<SUB>j</SUB>/(x<SUB>i</SUB> + x<SUB>j</SUB>)]D<SUB>i,self</SUB>, where x<SUB>i</SUB> is the mole fraction of species i