Thermal relaxation in a dense liquid under shock compression

Abstract

We have studied by means of molecular dynamics the propagation of a planar shock wave in a dense, three-dimensional column of a simple modified Lennard-Jones liquid. The column is $49.37{\ensuremath{\sigma}}^{2}$ in cross section, and $238.5\ensuremath{\sigma}$ in length, where $\ensuremath{\sigma}$ is the length parameter in the potential. The column contains approximately 10 000 atoms. It is initially in equilibrium at a density of $0.85{\ensuremath{\sigma}}^{\ensuremath{-}3}$ and temperature of $\frac{1.16\ensuremath{\epsilon}}{k}$, where $\ensuremath{\epsilon}$ is the energy parameter in the potential. Shock compression is effected by causing the column to move in the longitudinal direction with a velocity of --- ${U}_{p}$ and to collide with its mirror image across a mirror located at the origin. From the motion of the atoms in response to this kind of excitation, we calculate the shock velocity and the shock-front structure in the liquid, as well as the profiles of mass density, stress distribution, and energy density behind the shock front. Our shock-front structure agrees well with that obtained from the Navier-Stokes equations, but we also find important differences between our shock profiles and those postulated or computed from the continuum theory. In particular, we find that in 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}11}$ s, the longest time of our calculations, the stress components did not relax to a hydrostatic condition, and the corresponding kinetic temperature profile showed a relaxation process similar to what we found earlier in a crystalline solid. We examine the atomistic mechanisms of the various relaxation processes, and discuss their implications on the shock compression of dense systems of solids and liquids as opposed to rarefield systems of gases.