Nonlinear behavior leading to real rarefaction shocks and related phenomena

Abstract

Early calculations by Bethe, Zel'dovich, and others have suggested the possibility of rarefaction shocks in fluids and solids. Recent experiments have demonstrated the existence of rarefaction shocks in rubber (Kolsky and Rader), quartz (Barker and Hollenbach), iron (Erkman, Ivanov, and Novikov), fluids at near‐critical states (Borisov et al.), and in evaporating mixtures (Chaves, Thompson et al.). Analogous discontinuities are found in second sound in superfluid helium. The assertion that all rarefaction shocks violate the second law is untrue, both in theory and practice! Physical experiments in fluids leading to a single‐phase rarefaction shock, or to a complete rarefaction‐evaporation shock have, until now not been realized. Key ingredients for real rarefaction shocks include a negative nonlinearity parameter Γ, usually some degree of metastability, Chapman‐Jouguet conditions, and in the case of fluids, a large molar heat capacity (many molecular degrees of freedom). Examples and related phenomena are discussed.