Passive flow selection via elastic buckling in narrow channels

We study the fluid-structure interaction of a clamped beam in a rectangular channel at low Reynolds numbers. Experiments show that, beyond a critical flow rate, the beam undergoes a buckling instability, ultimately bending until it encounters the wall. Via a combination of such experiments with simulations and scaling analyses, we identify the instability threshold as a function of the material, geometric, and fluid parameters. The buckling Cauchy number (i.e. the ratio between viscous and elastic forces) depends on the confinement ratio of the beam within the channel. Several scaling regimes are identified depending on the confinement of the beam in both directions and rationalized via theoretical considerations. We summarize our findings in a phase map expressed in terms of Cauchy number and confinement ratio and provide insights into the design of passive flow selectors in narrow microfluidic channels.