Shock-wave viscosity measurement

The problem of measuring the viscosity of fluids under shock-loading conditions is discussed. The authors examine in detail the method of Sakharov et al. (1965) and Zaidel' (1967) for measuring shear viscosity from the decay of perturbations on a corrugated shock front. The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satsified. The corrugated shock front induces mixing of the shocked sample. This mixing is particularly vigorous in viscous materials and may be responsible for the rapid rate of some shock-induced chemical reactions. The experimental results for water at 15 GPa are discussed, and several possibilities are considered to explain why the viscosity obtained by these experiments is so different from those obtained by other methods. Two possible reasons are favored: (1) the analytic method may be inappropriate because it ignores possible complications at the onset of the shock perturbations, and (2) the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot. The latter interpretation reconciles the experimental results with estimates and measurements obtained by other means and is consistent with pressure-volume-temperature Hugoniot data and the phase diagram of ${\mathrm{H}}_2$O.