Viscosity as the product of its ideal low-concentration value and a thermodynamic function.

Abstract

The behavior of viscosity, η, as a function of concentration in dense fluids remains an unsolved problem, as is the case with other transport coefficients. Boltzmann's theory and the Chapman-Enskog method predict the value of the viscosity at low concentrations, η_{0}. Here, the hypothesis η=ϕη_{0} is proposed, where ϕ is a function of the thermodynamic state that represents the effects of interactions as concentration increases. We consider that η_{0} is the viscosity in an ideal hypothetical system, where the condition of small interactions applies for the whole density range (ϕ→1 for low concentration). The method proposed to verify this hypothesis involves coupling the system with a solvent represented by a Langevin thermostat, characterized by a damping time t_{d}. Molecular dynamics simulations show that different values of noise intensity modify η and η_{0}, but do not affect ϕ. This result supports the assumption that ϕ is a state function, since the thermodynamic state remains unaltered by the presence of damping and noise. Simulations were conducted for particles that interact via a pseudohard sphere or a Lennard-Jones potential.