Abstract
A model for the liquid/vapor phase transitions in a shock tube is studied. Mathematical analysis for the one-dimensional isothermal case is carried out. A sufficient condition for the existence of traveling waves is given. These traveling waves represent liquefaction and evaporation shocks. The nonexistence of some of these traveling waves when the shock speed is smaller than some number is proved. Major one-dimensional wave patterns observed in actual experiments with retrograde fluids are also observed in solutions of Riemann problems. A rough estimate of the difference of the calculated pressure in the solution of the Riemann problem and that in experimental data due to the modeling is given.
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