Collaborative Research: Symmetry-Breaking Bifurcations in an Oscillating Fluid Layer

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PROPOSAL NO.: CTS-0604376/0620872PRINCIPAL INVESTIGATORS: MARK R. PAUL/EDGAR KNOBLOCHINSTITUTION: VPI/ UNIVERSITY OF CAL- BERKELEYSGER: Collaborative Research: Symmetry-Breaking Bifurcations in an Oscillating Fluid Layer This grant will support exploratory research to investigate symmetry-breaking bifurcations in fluid dynamics. The investigation focuses on the numerical exploration of a new class of pattern-forming equations governing the interplay between spontaneous and forced symmetry breaking in a fluid system of direct experimental interest - complex wave dynamics on the surface of a vertically oscillating fluid layer in a gravitational field, also known as the Faraday system. Faraday waves are common in low gravity environments where residual acceleration or g-jitter, due to crew maneuvering and machinery, has a significant impact on both material processing systems and on-board experiments. Also, sensors have been proposed to measure the properties of protein monolayers through measurable effects upon the Faraday wave damping. The coupled amplitude-streaming flow equations are more complex than amplitude equations and more complex than Navier-Stokes hydrodynamics since the boundary conditions are given in terms of the wave amplitudes. However, they are substantially simpler to solve than the governing viscous free-surface problem because all terms are formally of order one and the boundary conditions are applied at the undisturbed surface. A numerical exploration of the coupled amplitude-streaming flow equations for realistic experimental geometries will provide a unique opportunity to probe the fundamental physics governing the Faraday problem. The approach is risky in that there is no guarantee that the coupled amplitude-streaming flow equations capture all of the physics necessary to describe the intriguing experimental results. In particular, there is much uncertainty concerning the role of meniscus dynamics at the lateral walls and, in fact, many experiments do not report the necessary experimental parameter values that would permit detailed modeling. The outcomes of this work are applicable to a variety of technologies, e.g. design and operation of future microgravity vehicles and experiments, the development of large-scale uniform patterning technologies, and molecular sensors. Additionally, the findings of this research will be used to help support the development of a new graduate course at Virginia Tech on the theoretical modeling of spatiotemporal dynamics.