Computations of Interface Dynamics in Fluids and Materials

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The investigator studies a variety of problems concerninginterface dynamics in fluids and materials. The problems are 1)control of droplet formation and 2) microstructral evolution inanisotropic and inhomogeneous elastic media. He brings togetherphysical experiments, modeling, mathematical and numericalanalysis, and large-scale scientific computations to studycertain fundamental problems related to interface motion, such asinterfacial pinch-off and evolutions of interfaces inthree-dimensional systems. One of the major goals is to developand apply start-of-the-art computational tools with emphasis onutilizing adaptive methods and parallel computing, and designingrobust numerical methods for integro-differential equationsinvolving multiple physical effects with multiple spatial andtemporal scales. The investigator studies some fundamental problems relatedto multiphase phenomenon in physical systems. In particular, hedevelops mathematical models and performs large-scalecomputations to investigate diffusional evolution ofmicrostructure in solid/solid phase transitions and control ofdroplet formation in a fluid/fluid system. Many structuralmetals, such as steels, aluminum alloys and superalloys, areproducts of solid-state diffusional transformations. Themulti-phase microstructure resulting from such transformations isa key variable in setting the macroscopic mechanical propertiessuch as stiffness, strength and toughness of the alloy. A goal ofthis study is to model and simulate the process of microstructureevolution through mathematics and computations, and eventually toprovide engineers information on how to generate differentmicrostructures with desirable material properties. Theinvestigation of droplets concerns how to control the formationof drops of many sizes (frequently referred to as satellitedrops) in a situation like a dripping faucet or in the breakup ofa jet. The presence of satellite drops is undesirable in manypractical situations such as in ink jet printers and diskatomizers. He studies the use of focused, external acoustic wavesfor the control of satellite drops. If successful, this idea canbe applied to many modern technologies.