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The Enskog theory for the self-diffusion coefficient for fluids with continuous potentials, such as the Lennard-Jones, is developed. Starting from the Green–Kubo formula (rather than the conventional kinetic equation) and introducing the similar assumptions upon which the Boltzmann equation is based, we derived a general expression for the memory kernel and the self-diffusion coefficient. The numerical analysis is implemented for the Lennard-Jones fluid. The time-dependent memory kernel is calculated and compared with the latest molecular dynamics simulations. Excellent agreement is obtained at the low density. The self-diffusion coefficient is evaluated for various temperatures and densities. The ratio of the Enskog self-diffusion coefficient to the simulation value is plotted against density. Significant difference of this density dependence from that for the hard-sphere fluid is observed. In particular, the well-known maximum observed (in the diffusion versus density plot) for the hard sphere fluid is found to be completely absent in the Lennard-Jones fluid. Our results reduce to the conventional Chapman–Enskog expression in the low density limit and can be applicable to the systems with singular potentials such as the hard sphere

The Enskog theory for transport coefficients of simple fluids with continuous potentials