Fluid-induced snap-through instability of spherical shells

Abstract

We study the snapping instability of a spherical elastic shell induced by a viscous flow, the umbrella flipping problem when life is at low Reynolds numbers. We combine precision desktop-scale experiments, fluid-structure simulations, shell theory, fluid mechanics, and scaling analysis to determine the instability threshold as a function of the geometrical and material parameters of the system. Building on these findings, we devise a snapping-based valve that passively and abruptly alters the hydraulic resistance of a channel, offering robust flow control without active components. Beyond the application, our study presents what we believe to be a prototypical example of fluid-induced elastic instability in viscous flow, providing a foundation for future explorations in soft hydraulics and flow-responsive structures.

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