Shear-rate nonanalyticity in simple liquids (Q1098693)

A non-equilibrium thermodynamic theory of shear relaxation in a small subvolume of a simple liquid introduces the volume, temperature, particle number, traceless elastic shearing strain \(\sigma^{\dag}_{ij}\), and the volume fraction \(\zeta\), of locally-dilated spherical regions as internal state variables. From the Gibbs equation and integrability condition for the Helmholtz function, one can calculate the terms in the thermodynamic pressure and internal energy which are of order \((\zeta - \zeta_ 0)\sigma^ 2\), with \(\zeta_ 0\) the equilibrium \(\zeta\) and \(\sigma\) the non-zero off-diagonal component of \(\sigma^{\dag}_{ij}\). Into these terms are substituted steady-state asymptotic solutions at high shear-rate, C, of the thermodynamic phenomenological rate equations. The steady-state solution exhibits bifurcation, and some of the possible steady states, with \(\zeta -\zeta_ 0<0\), predicts the \(O(C^{3/2})\) nonanalyticity seen in molecular dynamics simulations by \textit{H. J. M. Hanley} and \textit{D. J. Evans} [J. Chem. Phys. 76, 3226 ff (1982)]. The predicted signs and orders-of-magnitude also agree with computer studies. One can also predict the \(C^{1/2}\)-dependence in the non-Newtonian viscosity.