Inferring viscosity from shock wave perturbation decay in laser-driven experiments

Sakharov et al. (1965) proposed an experimental approach to investigate the decaying oscillations of perturbed shock and determine the viscosity of a shocked material. Our study is borne out of interest to apply Sakharov’s method in laser driven experiments to deduce material viscosities at high energy density (HED) pressures. Here, we utilize the radiation hydrodynamics code FLASH to simulate the evolution of single-mode shock perturbation in polystyrene driven by laser ablation. We validate these simulations with a small set of experimental data (Endo et al.,1995) and analytical predictions (Miller et al., 1991 and Ishizaki et al.,1996). We further compare the two-dimensional inviscid simulations with Ishizaki’s model under varying shock pressures (300-900 GPa) and perturbation wavelengths and suggest a correction to the isentropic index to accurately model a non-ideal material like polystyrene. The corrected theoretical model shows excellent agreement with simulations increasing confidence in the predictive capabilities of FLASH. Next, we perform a sequence of viscous simulations with different perturbation wavelengths to quantify the effect of viscosities on the time-dependent shock amplitude and the velocity of shock front oscillations. In principle, the evolution of the shock perturbation amplitude can be measured by resolving the velocity history along a line in the material sample across a few wavelengths using line-VISAR in laser-driven experiments. Our simulation results indicate that VISAR may be capable of measuring such small velocity oscillations to infer viscosities of O (10 Pa-s).