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-i,D-self) and the Maxwell-Stefan (M-S) diffusivities (-D-ij) were determined from the MD simulations for various mixture compositions. The self-diffusivity was determined to be a linear function of the mass fractions omega(j) of the constituent species in the mixture: D-i,D-self = Sigma(j=n) (j=1) omega jD(i)(self)(x)(j -> 1) where D-ilself(xj -> 1) 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: -D-ij = [x(i)/(x(i) + x(j))]D-j,D-self + [x(j)/(x(i) + x(j))]D-i,D-self,D- where x(i) is the mole fraction of species i.