# Publication: Statistical-mechanical theory of rheology: Lennard-Jones fluids

All || By Area || By YearTitle | Statistical-mechanical theory of rheology: Lennard-Jones fluids |
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Authors/Editors* | Rozita Laghaei, Afshin Eskandari Nasrabad, Byung Chan Eu |

Where published* | The Journal of Chemical Physics |

How published* | Journal |

Year* | 2005 |

Volume | 123 |

Number | |

Pages | 234507 |

Publisher | AIP |

Keywords | |

Link | |

Abstract |
The generalized Boltzmann equation for simple dense ï¬uids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for ï¬uids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple ï¬uid from the stress tensor evolution equation in a suitable ï¬ow conï¬guration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones ï¬uid. For that purpose we have used the density-ï¬uctuation theory for the Newtonian viscosity, the modiï¬ed free volume theory for the self-diffusion coefï¬cient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modiï¬ed free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we ï¬rst have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate * times reduced relaxation time * that is e independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against * * they are found clustered around the reduced e universal non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones ï¬uid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function. |

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