The Shock Wave as a Nonequilibrium Transport Process

Abstract

Shock-wave propagation involves mass, momentum, and energy transport in a medium. The state of a medium is determined by the exchange processes with surroundings through the interphase boundaries and the transport processes occurring within it. The transport processes in a medium are characterized by their rates, intensity, and the initial state of the medium. There a problem arises: how does one determine the state of the medium under given loading conditions? Following Maxwell, the medium state can be determined only with respect to the applied loading conditions. Under a short-time loading a medium demonstrates its solid properties and, when subject to a long-time force, the same medium behaves more as a liquid. There have been many attempts to describe plastic properties of deformed solids by methods similar to those used for hydrodynamic flow. Classical hydrodynamics, however, is valid only for fluids near thermodynamic equilibrium. From the point of view of nonequilibrium statistical mechanics, the deviation of the state of the system from thermodynamic equilibrium is closely connected with the correlation concept. A solid body subject to a very low velocity impact moves without deformation owing to the rigid correlation among the particles of the medium. All particles are linked together and their typical correlation length corresponds to the size of the body. In this case, we have mechanical transport only at the macroscopic scale. If we have a fluid in thennodynamic equilibrium, and if the applied loading isn’t highrate and intense, its behavior is that of an ideal fluid without relaxation. All particles are moving chaotically without any correlation. The typical correlation length is zero. More intense loading produces nonequilibrium transport characterized by finite space-time correlation scales. In all intermediate cases, we have a finite correlation length within which collective motion of particles of the medium occurs. This means that the medium does not behave as a simple fluid when subjected to load. Rather than being a structure less continuum, it is a medium having a complicated internal structure.