LONGITUDINAL AND BULK VISCOSITIES OF LENNARD-JONES FLUIDS

Expressions for the longitudinal and bulk viscosities have been derive d using Green Kubo formulae involving the time integral of the longitu dinal and bulk stress autocorrelation functions. The time evolution of stress autocorrelation functions are determined using the Mori formal ism and a memory function which is obtained from the Mori equation of motion. The memory function is of hyperbolic secant form and involves two parameters which are related to the microscopic sum rules of the r espective autocorrelation function. We have derived expressions for th e zeroth-, second-and fourth- order sum rules of the longitudinal and bulk stress autocorrelation functions. These involve static correlatio n functions up to four particles. The final expressions for these have been put in a form suitable for numerical calculations using low- ord er decoupling approximations. The numerical results have been obtained for the sum rules of longitudinal and bulk stress autocorrelation fun ctions. These have been used to calculate the longitudinal and bulk vi scosities and time evolution of the longitudinal stress autocorrelatio n function of the Lennard-Jones fluids over wide ranges of densities a nd temperatures. We have compared our results with the available compu ter simulation data and found reasonable agreement.