Surface tension-driven instability of a soft elastic rod revisited. (1st April 2022) - Yang, Guang; Gao, Cun-Fa; Ru, C.Q.
Abstract: Surface tension-driven morphological instability of a soft (compressible or incompressible) linearly elastic rod is studied based on the Gurtin–Murdoch (GM) theory of surface elasticity. This study is inspirited by instability of shorter wavelength observed in some experiments which are not covered by the existing linear elastic models. Here, unlike the original GM model, the present model addresses the influence of surface tension-induced bulk residual stress on the incremental bulk stress associated with instability. The relation between the dimensionless ratio σ 0 /( μR ) (where σ 0, μ and R are surface tension, shear modulus and radius of the rod) and the unstable mode's wavelength λ is studied based on the present model and the GM model, with comparison to the known results given by the existing linear elastic models. Different than the existing linear elastic models which predict the instability only if σ 0 /( μR ) ≥ 6 with the wavelength λ /(2 R ) > π, the present model and the GM model predict the instability with lower surface tension and much shorter wavelengths (e.g. λ /(2 R )≈1.5), which could offer a plausible explanation for instability observed in some experiments. In addition, the effects of a bulk axial prestress and the Poisson ratio on the surface tension-induced instability of a soft linear elastic rod are examined..