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 ,self) and the Maxwell−Stefan (M−S) diffusivities (Đ 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 ω j of the constituent species in the mixture: D i ,self = ω j where 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: Đ ij = [x i /(x i + x j )]D j ,self + [x j /(x i + x j )]D i ,self, where x i is the mole fraction of species i.