Haitao Fan Abstract: The long-range goal for the proposed project is to understand the dynamics of liquid/vapor phase transitions and its mathematical theories. Liquid/vapor phase transitions are important phenomena in science and engineering. Traditional models for the dynamics of phase transition, exhibit gaps when compared with experiments. We propose to investigate the dynamics of liquid/vapor phase transitions through an approach different from traditional models. The model is a system of conservation laws with source terms (the system) based on equations for two-phase reactive flows. Based our preliminary studies, this approach promises to better fit experiment. To accomplish our objective, the following specific sub-objectives will be pursued: 1) Derive qualitative and quantitative asymptotic models for the system. 2) Study issues such as basic wave patterns in the system and its asymptotic models, e.g., traveling waves, admissibility criteria for shocks and phase boundaries, and the Riemann problem. 3) Develop algorithms to carry out numerical simulations on the system and develop test problem to justify such computations. Study issues related to numerical schemes for the system 4) Study the well-posedness of the system or its simplified asymptotic models. The expectations are that, at the conclusion of the proposed period of support, results will have been obtained on qualitative and quantitative behavior of the system, and numerical simulations will have been carried out. Results on qualitative and quantitative behavior of the system will be compared with experiments. Based on these comparisons, the adequateness of the modeling can be assessed, and the modeling can be further improved. It is expected that the results obtained will facilitate understanding of the dynamics of liquid/vapor phase transitions. Tools for numerical simulations of such phenomena will also result from this work. Most materials have four phase s: solid, liquid, vapor and plasma phases. Phase transition, such as the change from water to vapor and vice versa, is fundamental phenomena of materials that occur in daily life and everywhere in our environment. Many manufacturing processes, such as the growth of a single large crystal used in semiconductor manufacturing, involve phase transitions. Liquid/vapor phase transitions happen during the flight of airplane through clouds and during underwater explosions. Liquid/vapor phase changes also occur at high speed moving parts of a vessel, such as the propeller of a submarine, which consumes energy and makes noise detectable by enemies' solar devices. In summary, phase transitions are not only fundamental scientific properties of materials but also vital to industrial competitiveness and national security. The proposed project is to study the evolution of phase changes, in particular the rapid liquid/vapor transitions induced by rapid moving body or waves. The objectives are to establish effective mathematical models for liquid/vapor transitions that agree with experimental data, and to develop numerical simulation tools for such phase transitions.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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John C. Strikwerda
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Georgetown University
United States
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