Rayleigh–Taylor instability in a confined elastic soft cylinder

Abstract

Rayleigh–Taylor instability can be often observed in various hydrodynamic systems. The reduction of the gravity potential of the system drives the instability of the interface between two fluids with different densities. Recently, similar gravity-induced surface instabilities have also been observed in soft solids. The following theoretical analyses of Rayleigh–Taylor instabilities in soft solids were either based on the plane-strain condition or the assumption of infinitely large lateral dimensions. There has been no study on the effects of lateral constraint on Rayleigh–Taylor instability of soft solids. In this article, we investigate Rayleigh–Taylor instability in an elastic soft gel confined by a rigid cylindrical container. Based on linear stability analysis, we find that both critical load and instability pattern on the surface of the gel can be greatly affected by the aspect ratio of the cylindrical gel. Through nonlinear finite element simulations, we further find that the Rayleigh–Taylor instability in a confined elastic soft cylinder is subcritical. Our theoretical predictions agree well with our experimental results.