Snapping Shells at low Reynolds Numbers

We investigate the fluid-induced snapping of spherical shells within cylindrical channels at low Reynolds numbers. Experiments reveal that beyond a critical flow rate, spherical shells exhibit a snapping instability, which significantly alters the internal geometry of the channel. Through a combination of experiments, axisymmetric simulations, and theoretical analysis, we systematically vary the geometric and material parameters of the system to determine the instability threshold, expressed as a critical Cauchy number—the ratio of viscous to elastic forces. Our results collapse on a single master curve if represented in terms of the Cauchy number versus a dimensionless geometric factor characterizing the shell-channel configuration, including wall effects. The collapse of experimental and numerical data onto a single master curve highlights the strong agreement between simulations and experiments, while providing a design criterion for channels with snapping valves. This study also paves the way for exploring more complex soft hydraulic systems, where the compliance of soft channels and their valves can be coupled to enhance functionality.