SHEAR-FLOW IN THE INFINITE-SHEAR-RATE LIMIT

Computer simulations have revealed the existence of a disorder-order phase transition in simple shearing liquids [J. J. Erpenbeck, Phys. Rev. Lett. 52, 1333 (1984)]. Above a certain shear rate, the motion of the particles becomes ordered. This high-shear-rate structure, the so-called string phase, is studied numerically in order to investigate the possibility of such a transition taking place in real systems. At first we determined the optimal arrangements of spherical particles in the string phase. In the high-density infinite-shear-rate limit, where the random thermal motion of particles is negligible, minimum energy structures can be found as functions of density and interaction. We identify these structures and relate them to equilibrium ones. Utilizing the symmetry of the limit structure, we perform nonequilibrium molecular dynamics simulations at high but finite shear rates in order to study the coexistence conditions of liquid and string Phases as a function of periodic boundary symmetry and system size. The stability of the string phase depends significantly on these aspects of the simulations. The larger the system, the less stable the pure string phase is compared to the coexisting liquid-string formation. This calls into question the existence of this phase transition in real shearing fluids. We also study the liquid-string transition in terms of the so-called phase space compressibility factor (Lambda), since it was found recently [D. J. Evans and A. Baranyai, Phys. Rev. Lett. 67, 2597 (1991)] that this simple phase variable exhibits a local extremum property even far from equilibrium. In the thermodynamic limit, (Lambda) correctly estimates the shear rate at which the liquid phase becomes unstable in computer simulations.