Traveling and standing waves in liquid-vapor phase transitions and related problems

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This proposal studies phase transition waves in liquid aerosols, including one-dimensional traveling waves and three-dimensional spherically symmetric standing waves. These waves can be subsonic, supersonic or transonic; the PI aims to characterize all possible wave patterns, completing a partial list obtained by Fan, Lin and Wechselberger. The proposal also studies some related problems: phase transition and chemical reaction waves in porous media, stability of KPP-type waves in large bounded domains, multi-front wave patterns described by a concatenation of simple traveling waves, and numerical methods for computing traveling waves.The main goal of this proposal is to study the liquid-vapor phase transition in liquid aerosols, suspensions of fine liquid droplets in a gas, such as the gasoline-air mixture in the fuel injection nozzle of a combustion engine cylinder. The PI will investigate evaporation waves in conical nozzles as models of evaporation of fuel in injection nozzles of gasoline engines. Understanding the parameter regime for the existence and stability of such waves is important, and can help achieve a well-mixed fuel and air ratio before ignition, which in turn will help improve the fuel efficiency of the engine and reduce emission of carbon monoxide and hydrocarbons into the environment. In addition, the PI will study some related problems on phase transition that have applications to fuel cell batteries and oil recovery processes.