ITR: Free-Boundary Problems in Precipitative Growth

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0219411GoldsteinThis project addresses mathematical and computational challenges posed by growth phenomena involving novel and difficult free-boundary problems in fluid flow, precipitation/crystallization and evaporation. These appear in contexts as diverse as hydrothermal vents in the ocean floor, terrestrial caves, and electrochemical pattern formation, where one finds growth of complex structures by precipitation. These range from hollow soda-straw stalactites to fantastic curved helictites and undulating sheet-like draperies in limestone caves, to iron-sulfide chimneys tens of meters high on the ocean floor. Despite years of empirical study, these fascinating growth morphologies are largely unexplained in any quantitative manner. We will develop computational methods to study precipitative growth phenomena, based primarily on boundary-integral and differential geometric methods in the study of surface evolution. The enormous geological time scales on which many of these structures form has created a paucity of experimental results, and few if any laboratory analogs have been created. We will also develop and explore experimentally model systems that can display such pattern formation on accessible time scales. One such system, discovered in our laboratory, involves tubular growth by electrodeposition, in which macroscopic tubular deposits grow in tens of minutes around bubbles of hydrogen gas evolving off a cathode. Theoretical approaches will include the study of the underlying electrokinetics at large Peclet number and depletion layer modifications due to Lorentz forces, all as a means of understanding the geometrical laws of surface growth that can produce the rich and fascinating morphologies seen in nature, and the computational techniques to study such laws.