A dynamic analysis of the Rayleigh–Taylor instability in soft solids

Abstract

A soft viscoelastic layer is susceptible to interfacial instability due to self-weight when oriented in a heavy over light configuration. This is the solid Rayleigh–Taylor instability. We perform an elastodynamic stability analysis for the viscoelastic layer in a cylindrical container and compute the dispersion relationship, as it depends upon the dimensionless elastogravity number, elastocapillary number, solid Deborah number, compressibility number, and the aspect ratio. The stability diagram is mapped in the parameter space and we compute the wavenumber and associated growth rate for the dominant mode. The presence of the cylindrical boundary restricts the allowable modes and we show how this affects mode number selection. Our predictions compare favorably to previously reported experimental work in the literature.