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

Abstract

The behavior of viscosity, $\eta$, 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, $\eta_0$. Here, the hypothesis $\eta=\phi\, \eta_0$ is proposed, where $\phi$ is a function of the thermodynamic state that represents the effects of interactions as concentration increases. We consider that $\eta_0$ is the viscosity in an ideal hypothetical system, where the condition of small interactions applies for the whole density range ($\phi \to 1$ 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 $\eta$ and $\eta_0$, but do not affect $\phi$. This result supports the assumption that $\phi$ 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 pseudo-hard sphere or a Lennard-Jones potential.