Peristaltic Elastic Instability in an Inflated Cylindrical Channel

A long cylindrical cavity through a soft solid forms a soft microfluidic channel, or models a vascular capillary. We observe experimentally that, when such a channel bears a pressurized fluid, it first dilates homogeneously, but then becomes unstable to a peristaltic elastic instability. We combine theory and numerics to fully characterize the instability in a channel with initial radius a through an incompressible bulk neo-Hookean solid with shear modulus mu. We show instability occurs supercritically with wavelength 12.278 ... a when the cavity pressure exceeds 2.052 ... mu. In finite solids, the wavelength for peristalsis lengthens, with peristalsis ultimately being replaced by a long-wavelength bulging instability in thin-walled cylinders. Peristalsis persists in Gent strain-stiffening materials, provided the material can sustain extension by more than a factor of 6. Although naively a pressure driven failure mode of soft channels, the instability also offers a route to fabricate periodically undulating channels, producing, e.g., waveguides with photonic or phononic stop bands.