Fluid-induced Snapping of Elastic Shells*

We study the fluid-induced snapping of spherical shells in cylindrical channels at low Reynolds numbers. Experiments demonstrate that above a critical flow rate, spherical shells undergo a snapping instability, drastically changing the internal geometry of the channel. By combining experiments, axisymmetric simulations, and theoretical analyses, we vary the geometrical and material parameters of our system to identify the instability threshold, expressed as a critical Cauchy number (i.e., the ratio between viscous and elastic forces). Our findings are summarized in a phase map, expressed in terms of the Cauchy number and a geometrical dimensionless parameter that describes the shell-channel system. This phase map shows a collapse of our experimental and numerical results into a single master curve. It highlights the good agreement between experiments and simulations and provides a design rule for channels with snapping valves.