Mathematical Analysis of Some Fundamental Problems in Solid-Liquid Interaction

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Over the past decades, the study of the motion of solids in a viscous liquid has become one of the main focuses of applied research. This project will address some fundamental aspects of solid-liquid interaction directed toward the accomplishment of the following objectives. The first one concerns the vibration-induced motion of a rigid body in a viscous liquid. A particularly significant case is when the vibration is induced by a time-periodically displaced mass inside the body. The second one is devoted to the motion of a deformable solid in a viscous liquid. This study will include propulsion of bodies by time-periodic shape-changes, as well as the determination, and possible bifurcation, of equilibrium configurations of elastic bodies subject to a constant force.The interaction of a viscous liquid with a solid body (either rigid or deformable) constitutes a complex and intriguing topic of theoretical and applied research. In fact, not only is it of fundamental theoretical interest, but it also represents the focus of many engineering, biological and medical studies at different scales. Important applications include damage of structures due to the impinging of the liquid, like in dams or ships, animal locomotion, like the flying of birds and the swimming of fish, manufacturing of short-fiber composites, where the addition of short fiber-like particles to a polymer matrix will enhance the mechanical properties of the material, separation of macromolecules by electrophoresis, and DNA sequencing. Another, but no less important, application of solid-liquid interaction occurs in blood flow, in the study of the interaction of blood with arterial walls, and of the motion of blood cells within the plasma.