A Hyperbolic Model for Phase Transitions Involing Metastability, Symmetry Breaking, Ring Formations and Other Surface Structures

 Haitao Fan

Department of Mathematics
Georgetown University

Abstract:  Liquid/vapor phase transitions occur daily. Many interesting phenomena in liquid/vapor phase changes are related to metastable regions of the fluids. In this talk, a model for fluid flows involving liquid/vapor phase transitions is introduced. This isothermal case of the model, approximating fluids with large molar heat capacities, is studied. Such fluids include many important fluids, such as gasoline. Existence and nonexistence conditions for traveling waves are provided. Wave patterns in the model matches major one-dimensional wave patterns observed in shock tube experiments. A peculiar phenomenon, symmetry breaking and ring formation, observed in experiments is also explained by this model. A mechanism for the generation of ``button" like surface structures at the liquefaction shock fronts is also given.