Shock propagation in a low-density foam filled with fluid

Abstract

It is found that when a planar shock is imparted to a system of a foam of low mean density filled with fluid (fiber density>ambient fluid density), an undercompressed quasisteady post-shock state is established. In this state, pressure and density are lower than the values predicted by Hugoniot relations for a uniform fluid with the same average fluid-foam density. It is shown that this undercompression phenomenon is due to residual correlations of fluctuations left after the saturation of the initially rapid mixing of fiber material with the background fluid. Generalized Hugoniot relations are derived for quasiplanar shocks in nonuniform systems, with foam as an example. The behavior of fluctuations in such systems is studied. Formulas for the level of fluctuations induced by a shock as it propagates through foam and for the relaxation time of the fluctuations, are derived.