Abstract
In the history of the kinetic theory of fluids, 1969–1970 was a crucial year. In that year Alder and Wainwright [2] published a paper in which they demonstrated the breakdown of the ‘Molecular Chaos’ assumption. The Molecular Chaos assumption, originally introduced by Boltzmann as the ‘Stoßzahlansatz’, states that the collisions experienced by a molecule in a fluid are uncorrelated. One consequence of this assumption is that the velocity autocorrelation function (VACF) of a tagged particle in fluid should decay exponentially. What Alder and Wainwright found is that the VACF of a particle in a moderately dense fluid of hard spheres or hard disks does not decay exponentially but algebraically. These algebraic long-time tails are the consequence of coupling between particle diffusion and shear modes in the fluid.
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Frenkel, D., van der Hoef, M. (1990). A Test of Mode-Coupling Theory. In: Mareschal, M. (eds) Microscopic Simulations of Complex Flows. NATO ASI Series, vol 236. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1339-7_20
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