Viscoelastic behaviour of fluids with steeply repulsive potentials

We analyse the shear stress, Cs(t) and pressure or ʹbulkʹ, Cb(t) time-correlation functions for steeply repulsive inverse power fluids (SRP) in which the particles interact via a pair potential with the analytic form, phi(r) = epsilon(sigma/r) n , in a new approach to the understanding of their viscoelastic properties. We show analytically, and confirm by molecular dynamics simulations, that close to the hard-sphere limit both these timecorrelation functions have the analytic form, Cs(t)/Cs(0) and Cb(t)/Cb(0) = 1-T *(nt*)2+ O((nt*)4), where T* = kBT/epsilon, is the reduced temperature, kB is Boltzmannʹs constant and t* = (epsilon/m sigma2)1/2 t is the reduced time. This leads to an alternative and much simpler derivation of formulae for the shear and bulk viscosities which for the limiting case of hard spheres are numerically very close to the traditional Enskog relations. These simple relations for the finite and continuous SRP interaction are in satisfactory agreement with the essentially exact molecular dynamics simulation results for ca. n > 18.