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

Abstract

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 (Ð _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 = Σ ^j-n_j=1 Σ_j D^xj→1 _i,selfwhere D^xj→1_i,self 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 _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.