Viscosity as the product of its ideal low-concentration value and 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 thermodynamic function representing 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 ($phi o 1$ 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 thermodynamic 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.