Finite-wavelength surface-tension-driven instabilities in soft solids, including instability in a cylindrical channel through an elastic solid.

Abstract

We deploy linear stability analysis to find the threshold wavelength (λ) and surface tension (γ) of Rayleigh-Plateau type "peristaltic" instabilities in incompressible neo-Hookean solids in a range of cylindrical geometries with radius R_{0}. First we consider a solid cylinder, and recover the well-known, infinite-wavelength instability for γ≥6μR_{0}, where μ is the solid's shear modulus. Second, we consider a volume-conserving (e.g., fluid filled and sealed) cylindrical cavity through an infinite solid, and demonstrate infinite-wavelength instability for γ≥2μR_{0}. Third, we consider a solid cylinder embedded in a different infinite solid, and find a finite-wavelength instability with λ∝R_{0}, at surface tension γ∝μR_{0}, where the constants depend on the two solids' modulus ratio. Finally, we consider an empty cylindrical channel (or filled with expellable fluid) through an infinite solid, and find an instability with finite wavelength, λ≈2R_{0}, for γ≥2.543...μR_{0}. Using finite-strain numerics, we show such a channel jumps at instability to a highly peristaltic state, likely precipitating it's blockage or failure. We argue that finite wavelengths are generic for elastocapillary instabilities, with the simple cylinder's infinite wavelength being the exception rather than the rule.