Computational Problems in Multicomponent Materials and Multiphase Fluids

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The main objective of this proposal is to investigate processes fundamental to the behavior of multicomponent fluids andmultiphase materials. We will do this by (1) developing and applying state-of-the-art numerical methods to large scale computation and (2)analytical, numerical and modelling studies of important constituent processes. More specifically, our focus will be on developing, implementing and analyzing successively more realistic models of the diffusional evolution of microstructure in solid/solid phase transitions. Our investigation of multiphase fluids includes a study of ternary fluid flow where only two of the components are immiscible. These projects involve fundamental physical processes whose phenomenology is basic to understanding the behavior of real fluids and the material properties of solids. Both are characterized by the presence of multiple constitutive components, complex pattern formation and/or singularities (i.e. spatial complexity). Although these processes arise in very different physical phenomena (fluids versus solids), both involve free boundary problemswhere the motion of a bounding interface, separating the different components, is driven by a competition between surface energy and either an instability or multi-body interactions. As such, they can be treated using a common set of analytical and computational tools. The highly nonlinear nature of these problems makes fast, accurate and robust numerical methods essential to their study.In this proposal, we bring together mathematical and numericalanalysis, modelling, and large-scale scientific computation to studycertain fundamental problems in fluid dynamics and materialsscience. Our focus will be on developing, implementing and analyzingsuccessively more realistic models of the diffusional evolution of microstructure in solid/solid phase transitions. These transformationsare an important method of processing multicomponent metallic alloys suchsuch as steels. The result of this process is the formation of a multiphasemicrostructure, which is a key variable in setting the macroscopicmechanical properties (i.e. stiffness, strength and toughness) of thealloy. The microstructure is characterized by regions of different metallic components separated from one another by interfaces. The goal of our research is to accurately model and simulate the formation of microstructure in alloys in order to provide metallurgists with a recipe for generating new alloys with desirable material properties. Our investigation of multiphase fluids involves modelling liquid/liquid extraction processes that are widely used in chemical production and waste processing. In these processes, two (or more) fluids are placed in contact and a contaminant in one of the fluids diffuses preferentially into another. The first fluid thus is cleaned and is then extracted. In these processes, two (or more) fluids are placed in contactand a contaminant in one of the fluids diffuses preferentially into another.The first fluid thus is cleaned and is then extracted. If the contaminated fluid is broken up into small droplets, the interfacial area and hence mass transfer is increased. We will use analysis, modeling and large scale scientific computation to study reaction and mixing rates within these systems. The ultimate goal of this work is to provide a theoretical foundation for improving the performance of liquid/liquid extractors.Although the two problems described above arise from very different physical processes (fluids versus solids), they are similar in the sense that the relevant phenomena is strongly influenced by surface tension at the respective interfaces. Consequently, they can be studied using common analytical and computational tools. The highly complex nature of these problems makes fast, accurate and robust numerical methods essential to their study.